Multiple-criteria decision analysis

216:: These problems consist of a finite number of alternatives, explicitly known in the beginning of the solution process. Each alternative is represented by its performance in multiple criteria. The problem may be defined as finding the best alternative for a decision-maker (DM), or finding a set of good alternatives. One may also be interested in "sorting" or "classifying" alternatives. Sorting refers to placing alternatives in a set of preference-ordered classes (such as assigning credit-ratings to countries), and classifying refers to assigning alternatives to non-ordered sets (such as diagnosing patients based on their symptoms). Some of the MCDM methods in this category have been studied in a comparative manner in the book by Triantaphyllou on this subject, 2000. 165:

solutions. A solution is called nondominated if it is not possible to improve it in any criterion without sacrificing it in another. Therefore, it makes sense for the decision-maker to choose a solution from the nondominated set. Otherwise, they could do better in terms of some or all of the criteria, and not do worse in any of them. Generally, however, the set of nondominated solutions is too large to be presented to the decision-maker for the final choice. Hence we need tools that help the decision-maker focus on the preferred solutions (or alternatives). Normally one has to "tradeoff" certain criteria for others.

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concept of "outranking relations", analytical hierarchy process, and some rule-based decision methods try to solve multiple criteria evaluation problems utilizing prior articulation of preferences. Similarly, there are methods developed to solve multiple-criteria design problems using prior articulation of preferences by constructing a value function. Perhaps the most well-known of these methods is goal programming. Once the value function is constructed, the resulting single objective mathematical program is solved to obtain a preferred solution.

53: 157:"Solving" can be interpreted in different ways. It could correspond to choosing the "best" alternative from a set of available alternatives (where "best" can be interpreted as "the most preferred alternative" of a decision-maker). Another interpretation of "solving" could be choosing a small set of good alternatives, or grouping alternatives into different preference sets. An extreme interpretation could be to find all "efficient" or " 1174: 1555: 1201: 815: 122:. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected by the consequences. 825: 115:, managers are interested in getting high returns while simultaneously reducing risks; however, the stocks that have the potential of bringing high returns typically carry high risk of losing money. In a service industry, customer satisfaction and the cost of providing service are fundamental conflicting criteria. 222:: In these problems, the alternatives are not explicitly known. An alternative (solution) can be found by solving a mathematical model. The number of alternatives is either finite or infinite (countable or not countable), but typically exponentially large (in the number of variables ranging over finite domains.) 550: 1865:

The AHP first decomposes the decision problem into a hierarchy of subproblems. Then the decision-maker evaluates the relative importance of its various elements by pairwise comparisons. The AHP converts these evaluations to numerical values (weights or priorities), which are used to calculate a score

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EMO algorithms start with an initial population, and update it by using processes designed to mimic natural survival-of-the-fittest principles and genetic variation operators to improve the average population from one generation to the next. The goal is to converge to a population of solutions which

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The achievement scalarizing function can be used to project any point (feasible or infeasible) on the efficient frontier. Any point (supported or not) can be reached. The second term in the objective function is required to avoid generating inefficient solutions. Figure 3 demonstrates how a feasible

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In Figure 1, the extreme points "e" and "b" maximize the first and second objectives, respectively. The red boundary between those two extreme points represents the efficient set. It can be seen from the figure that, for any feasible solution outside the efficient set, it is possible to improve both

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Some methods require preference information from the DM throughout the solution process. These are referred to as interactive methods or methods that require "progressive articulation of preferences". These methods have been well-developed for both the multiple criteria evaluation (see for example,

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Garnett, H. M., Roos, G., & Pike, S. (2008, September). Reliable, Repeatable Assessment for Determining Value and Enhancing Efficiency and Effectiveness in Higher Education. OECD, Directorate for Education, Programme on Institutional Management in Higher Education [IMHE) Conference, Outcomes of

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The decision space corresponds to the set of possible decisions that are available to us. The criteria values will be consequences of the decisions we make. Hence, we can define a corresponding problem in the decision space. For example, in designing a product, we decide on the design parameters

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Let us assume that we evaluate solutions in a specific problem situation using several criteria. Let us further assume that more is better in each criterion. Then, among all possible solutions, we are ideally interested in those solutions that perform well in all considered criteria. However, it

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MCDM has been an active area of research since the 1970s. There are several MCDM-related organizations including the International Society on Multi-criteria Decision Making, Euro Working Group on MCDA, and INFORMS Section on MCDM. For a history see: Köksalan, Wallenius and Zionts (2011). MCDM draws

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Weakly nondominated points include all nondominated points and some special dominated points. The importance of these special dominated points comes from the fact that they commonly appear in practice and special care is necessary to distinguish them from nondominated points. If, for example, we

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Multiple-criteria design problems typically require the solution of a series of mathematical programming models in order to reveal implicitly defined solutions. For these problems, a representation or approximation of "efficient solutions" may also be of interest. This category is referred to as

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Several papers reviewed the application of MCDM techniques in various disciplines such as fuzzy MCDM, classic MCDM, sustainable and renewable energy, VIKOR technique, transportation systems, service quality, TOPSIS method, energy management problems, e-learning, tourism and hospitality, SWARA and

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or value functions are elicited and used to identify the most preferred alternative or to rank order the alternatives. Elaborate interview techniques, which exist for eliciting linear additive utility functions and multiplicative nonlinear utility functions, may be used (Keeney and Raiffa, 1976).

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The MCDM problem can be represented in the criterion space or the decision space. Alternatively, if different criteria are combined by a weighted linear function, it is also possible to represent the problem in the weight space. Below are the demonstrations of the criterion and weight spaces as

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The difficulty of the problem originates from the presence of more than one criterion. There is no longer a unique optimal solution to an MCDM problem that can be obtained without incorporating preference information. The concept of an optimal solution is often replaced by the set of nondominated

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Achievement scalarizing functions also combine multiple criteria into a single criterion by weighting them in a very special way. They create rectangular contours going away from a reference point towards the available efficient solutions. This special structure empower achievement scalarizing

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Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and

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If we combine the multiple criteria into a single criterion by multiplying each criterion with a positive weight and summing up the weighted criteria, then the solution to the resulting single criterion problem is a special efficient solution. These special efficient solutions appear at corner

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There are methods that require the DM's preference information at the start of the process, transforming the problem into essentially a single criterion problem. These methods are said to operate by "prior articulation of preferences". Methods based on estimating a value function or using the

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or price is usually one of the main criteria, and some measure of quality is typically another criterion, easily in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider – it is unusual that the cheapest car is the most

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When the mathematical programming models contain integer variables, the design problems become harder to solve. Multiobjective Combinatorial Optimization (MOCO) constitutes a special category of such problems posing substantial computational difficulty (see Ehrgott and Gandibleux, 2002, for a

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We present the criterion space graphically in Figure 2. It is easier to detect the nondominated points (corresponding to efficient solutions in the decision space) in the criterion space. The north-east region of the feasible space constitutes the set of nondominated points (for maximization

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objectives by some points on the efficient set. Conversely, for any point on the efficient set, it is not possible to improve both objectives by moving to any other feasible solution. At these solutions, one has to sacrifice from one of the objectives in order to improve the other objective.

1169:{\displaystyle {\begin{aligned}\max f_{1}(\mathbf {x} )&=-x_{1}+2x_{2}\\\max f_{2}(\mathbf {x} )&=2x_{1}-x_{2}\\{\text{subject to}}\\x_{1}&\leq 4\\x_{2}&\leq 4\\x_{1}+x_{2}&\leq 7\\-x_{1}+x_{2}&\leq 3\\x_{1}-x_{2}&\leq 3\\x_{1},x_{2}&\geq 0\end{aligned}}} 3555:

Mardani, Abbas; Zavadskas, Edmundas Kazimieras; Khalifah, Zainab; Zakuan, Norhayati; Jusoh, Ahmad; Nor, Khalil Md; Khoshnoudi, Masoumeh (1 May 2017). "A review of multi-criteria decision-making applications to solve energy management problems: Two decades from 1995 to 2015".

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Whether it is an evaluation problem or a design problem, preference information of DMs is required in order to differentiate between solutions. The solution methods for MCDM problems are commonly classified based on the timing of preference information obtained from the DM.

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is unlikely to have a single solution that performs well in all considered criteria. Typically, some solutions perform well in some criteria and some perform well in others. Finding a way of trading off between criteria is one of the main endeavors in the MCDM literature.

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for each alternative (Saaty, 1980). A consistency index measures the extent to which the decision-maker has been consistent in her responses. AHP is one of the more controversial techniques listed here, with some researchers in the MCDA community believing it to be flawed.

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An Interactive Approach for Multi-Criterion Optimization, with an Application to the Operation of an Academic Department, A. M. Geoffrion, J. S. Dyer and A. Feinberg, Management Science, Vol. 19, No. 4, Application Series, Part 1 (Dec., 1972), pp. 357–368 Published by:

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If an MCDM problem represents a decision situation well, then the most preferred solution of a DM has to be an efficient solution in the decision space, and its image is a nondominated point in the criterion space. Following definitions are also important.

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is a polyhedron defined by linear inequalities and equalities. If all the objective functions are linear in terms of the decision variables, this variation leads to multiple objective linear programming (MOLP), an important subclass of MCDM problems.

1745:: Phases of computation alternate with phases of decision-making (Benayoun et al., 1971; Geoffrion, Dyer and Feinberg, 1972; Zionts and Wallenius, 1976; Korhonen and Wallenius, 1988). No explicit knowledge of the DM's value function is assumed. 586:

There are several definitions that are central in MCDM. Two closely related definitions are those of nondominance (defined based on the criterion space representation) and efficiency (defined based on the decision variable representation).

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maximize a single objective, we may end up with a weakly nondominated point that is dominated. The dominated points of the weakly nondominated set are located either on vertical or horizontal planes (hyperplanes) in the criterion space.

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Zavadskas, Edmundas Kazimieras; Mardani, Abbas; Turskis, Zenonas; Jusoh, Ahmad; Nor, Khalil MD (1 May 2016). "Development of TOPSIS Method to Solve Complicated Decision-Making Problems — An Overview on Developments from 2000 to 2015".

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There are several ways to generate nondominated solutions. We will discuss two of these. The first approach can generate a special class of nondominated solutions whereas the second approach can generate any nondominated solution.

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Zare, Mojtaba; Pahl, Christina; Rahnama, Hamed; Nilashi, Mehrbakhsh; Mardani, Abbas; Ibrahim, Othman; Ahmadi, Hossein (1 August 2016). "Multi-criteria decision making approach in E-learning: A systematic review and classification".

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Millar, L. A., McCallum, J., & Burston, L. M. (2010). Use of the conjoint value hierarchy approach to measure the value of the national continence management strategy. Australian and New Zealand Continence Journal, The, 16(3),

799:: (in criterion space) represents the worst (the minimum for maximization problems and the maximum for minimization problems) of each objective function among the points in the nondominated set and is typically a dominated point. 1472:

points of the set of available solutions. Efficient solutions that are not at corner points have special characteristics and this method is not capable of finding such points. Mathematically, we can represent this situation as

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Different schools of thought have developed for solving MCDM problems (both of the design and evaluation type). For a bibliometric study showing their development over time, see Bragge, Korhonen, H. Wallenius and J. Wallenius .

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The purpose is to set apriori target values for goals, and to minimize weighted deviations from these goals. Both importance weights as well as lexicographic pre-emptive weights have been used (Charnes and Cooper, 1961).

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represent the nondominated set (Schaffer, 1984; Srinivas and Deb, 1994). More recently, there are efforts to incorporate preference information into the solution process of EMO algorithms (see Deb and Köksalan, 2010).

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The ideal point and the nadir point are useful to the DM to get the "feel" of the range of solutions (although it is not straightforward to find the nadir point for design problems having more than two criteria).

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MCDM is concerned with structuring and solving decision and planning problems involving multiple criteria. The purpose is to support decision-makers facing such problems. Typically, there does not exist a unique

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Sałabun, W., Piegat, A. (2016). Comparative analysis of MCDM methods for the assessment of mortality in patients with acute coronary syndrome. Artificial Intelligence Review. First Online: 3 September 2016.

793:: (in criterion space) represents the best (the maximum for maximization problems and the minimum for minimization problems) of each objective function and typically corresponds to an infeasible solution. 360:

The quotation marks are used to indicate that the maximization of a vector is not a well-defined mathematical operation. This corresponds to the argument that we will have to find a way to resolve the

4058: 1738:: The purpose of vector maximization is to approximate the nondominated set; originally developed for Multiple Objective Linear Programming problems (Evans and Steuer, 1973; Yu and Zeleny, 1975). 239:"posterior articulation of preferences", implying that the DM's involvement starts posterior to the explicit revelation of "interesting" solutions (see for example Karasakal and Köksalan, 2009). 1715:

using an achievement scalarizing function. The dashed and solid contours correspond to the objective function contours with and without the second term of the objective function, respectively.

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Kylili, Angeliki; Christoforou, Elias; Fokaides, Paris A.; Polycarpou, Polycarpos (2016). "Multicriteria analysis for the selection of the most appropriate energy crops: The case of Cyprus".

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Sałabun, W. (2015). The Characteristic Objects Method: A New Distance-based Approach to Multicriteria Decision-making Problems. Journal of Multi-Criteria Decision Analysis, 22(1-2), 37-50.

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By varying the weights, weighted sums can be used for generating efficient extreme point solutions for design problems, and supported (convex nondominated) points for evaluation problems.

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Mardani, Abbas; Jusoh, Ahmad; Zavadskas, Edmundas Kazimieras (15 May 2015). "Fuzzy multiple criteria decision-making techniques and applications – Two decades review from 1994 to 2014".

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Köksalan, M.M. and Sagala, P.N.S., M. M.; Sagala, P. N. S. (1995). "Interactive Approaches for Discrete Alternative Multiple Criteria Decision Making with Monotone Utility Functions".

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There are different classifications of MCDM problems and methods. A major distinction between MCDM problems is based on whether the solutions are explicitly or implicitly defined.

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Ehrgott, Matthias; Gandibleux, Xavier (2003). "Multiobjective Combinatorial Optimization – Theory, Methodology, and Applications". In Ehrgott, Matthias; Gandibleux, Xavier (eds.).

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Another approach is to elicit value functions indirectly by asking the decision-maker a series of pairwise ranking questions involving choosing between hypothetical alternatives (

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Fuzzy sets were introduced by Zadeh (1965) as an extension of the classical notion of sets. This idea is used in many MCDM algorithms to model and solve fuzzy problems.

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Geoffrion, A.; Dyer, J.; Feinberg, A. (1972). "An Interactive Approach for Multicriterion Optimization with an Application to the Operation of an Academic Department".

545:{\displaystyle {\begin{aligned}\max q&=f(x)=f(x_{1},\ldots ,x_{n})\\{\text{subject to}}\\q\in Q&=\{f(x):x\in X,\,X\subseteq \mathbb {R} ^{n}\}\end{aligned}}} 118:

In their daily lives, people usually weigh multiple criteria implicitly and may be comfortable with the consequences of such decisions that are made based on only

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Mardani, Abbas; Nilashi, Mehrbakhsh; Zakuan, Norhayati; Loganathan, Nanthakumar; Soheilirad, Somayeh; Saman, Muhamad Zameri Mat; Ibrahim, Othman (1 August 2017).

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Karasakal, E. K. and Köksalan, M., E.; Koksalan, M. (2009). "Generating a Representative Subset of the Efficient Frontier in Multiple Criteria Decision Making".

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Amoyal, Justin (2018). "Decision analysis : Biennial survey demonstrates continuous advancement of vital tools for decision-makers, managers and analysts".

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Mahmoudi, Amin; Deng, Xiaopeng; Javed, Saad Ahmed; Zhang, Na (January 2021). "Sustainable Supplier Selection in Megaprojects: Grey Ordinal Priority Approach".

146:. Stanley Zionts helped popularizing the acronym with his 1979 article "MCDM – If not a Roman Numeral, then What?", intended for an entrepreneurial audience. 4065: 2685:

Bragge, J.; Korhonen, P.; Wallenius, H.; Wallenius, J. (2010). "Bibliometric Analysis of Multiple Criteria Decision Making/Multiattribute Utility Theory".

3478:"Application of multiple-criteria decision-making techniques and approaches to evaluating of service quality: a systematic review of the literature" 1781:

has a wide application in real-world situations. In this regard, some MCDM methods were designed to handle ordinal data as input data. For example,

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Hansen, Paul; Ombler, Franz (2008). "A new method for scoring additive multi-attribute value models using pairwise rankings of alternatives".

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Benayoun, R.; deMontgolfier, J.; Tergny, J.; Larichev, O. (1971). "Linear Programming with Multiple Objective Functions: Step-method (STEM)".

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between criteria (typically based on the preferences of a decision maker) when a solution that performs well in all criteria does not exist.

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Roughly speaking, a solution is nondominated so long as it is not inferior to any other available solution in all the considered criteria.

130:, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy. 4682: 4454: 1992: 2471: 2222:

Weistroffer, HR, and Li, Y (2016). "Multiple criteria decision analysis software". Ch 29 in: Greco, S, Ehrgott, M and Figueira, J, eds,

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family of outranking methods that originated in France during the mid-1960s. The method was first proposed by Bernard Roy (Roy, 1968).

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Javed, S. A. (2020). "Grey Absolute Decision Analysis (GADA) Method for Multiple Criteria Group Decision-Making Under Uncertainty".

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The following two-variable MOLP problem in the decision variable space will help demonstrate some of the key concepts graphically.

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functions to reach any efficient solution. This is a powerful property that makes these functions very useful for MCDM problems.

3371:"Sustainable and Renewable Energy: An Overview of the Application of Multiple Criteria Decision Making Techniques and Approaches" 1886: 3437:"Multiple criteria decision-making techniques in transportation systems: a systematic review of the state of the art literature" 3277: 3148: 2702: 2669: 2465: 2098: 4051: 3644:"A systematic review and meta-Analysis of SWARA and WASPAS methods: Theory and applications with recent fuzzy developments" 38: 3110:

Deb, K.; Köksalan, M. (2010). "Guest Editorial Special Issue on Preference-Based Multiobjective Evolutionary Algorithms".

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is defined explicitly (by a set of alternatives), the resulting problem is called a multiple-criteria evaluation problem.

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Multi-Criteria Inventory Classification Using a New Method of Evaluation Based on Distance from Average Solution (EDAS)

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Mardani, Abbas; Jusoh, Ahmad; Nor, Khalil MD; Khalifah, Zainab; Zakwan, Norhayati; Valipour, Alireza (1 January 2015).

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solution for such problems and it is necessary to use decision-makers' preferences to differentiate between solutions.

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Mardani, Abbas; Jusoh, Ahmad; Zavadskas, Edmundas Kazimieras; Cavallaro, Fausto; Khalifah, Zainab (19 October 2015).

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is defined implicitly (by a set of constraints), the resulting problem is called a multiple-criteria design problem.

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Mardani, Abbas; Zavadskas, Edmundas Kazimieras; Govindan, Kannan; Amat Senin, Aslan; Jusoh, Ahmad (4 January 2016).

3330:"Multiple criteria decision-making techniques and their applications – a review of the literature from 2000 to 2014" 4817: 4765: 4101: 3476:

Mardani, Abbas; Jusoh, Ahmad; Zavadskas, Edmundas Kazimieras; Khalifah, Zainab; Nor, Khalil MD (3 September 2015).

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Zionts, S.; Wallenius, J. (1976). "An Interactive Programming Method for Solving the Multiple Criteria Problem".

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In this example a company should prefer product B's risk and payoffs under realistic risk preference coefficients

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Franco, L.A.; Montibeller, G. (2010). "Problem structuring for multicriteria decision analysis interventions".

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Serafim, Opricovic; Gwo-Hshiung, Tzeng (2007). "Extended VIKOR Method in Comparison with Outranking Methods".

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Rezaei, Jafar (2016). "Best-worst multi-criteria decision-making method: Some properties and a linear model".

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Mardani, Abbas; Zavadskas, Edmundas Kazimieras; Khalifah, Zainab; Jusoh, Ahmad; Nor, Khalil MD (2 July 2016).

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Srinivas, N.; Deb, K. (1994). "Multiobjective Optimization Using Nondominated Sorting in Genetic Algorithms".

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Geoffrion, Dyer and Feinberg, 1972, and Köksalan and Sagala, 1995 ) and design problems (see Steuer, 1986).

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Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John Wiley & Sons.

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proposed Grey System Theory (GST) and its first multiple-attribute decision-making model, called Deng's

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Mathematically, a multiple-criteria design problem can be represented in the decision space as follows:

4904: 4438: 1892: 1858: 1853:'s Absolute GRA model, Grey Target Decision Making (GTDM) and Grey Absolute Decision Analysis (GADA). 4738: 4551: 4545: 4282: 3994:"An assessment of sustainable housing affordability using a multiple criteria decision making method" 2019: 2010: 1927: 1782: 87:(both in daily life and in settings such as business, government and medicine). It is also known as 4704: 4520: 4265: 4135: 3861:

Edwards, W.; Baron, F.H. (1994). "Improved simple methods for multiattribute utility measurement".

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Evans, J.; Steuer, R. (1973). "A Revised Simplex Method for Linear Multiple Objective Programs".

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Due to its simplicity, the above problem can be represented in criterion space by replacing the

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Figure 3. Projecting points onto the nondominated set with an Achievement Scalarizing Function

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Mathematically, the MCDM problem corresponding to the above arguments can be represented as

4655: 4568: 4444: 4222: 3765: 2755:"The Set of All Non-Dominated Solutions in Linear Cases and a Multicriteria Simplex Method" 2279: 193: 4035: 3061:

Some Experiments in Machine Learning Using Vector Evaluated Genetic Algorithms, PhD thesis

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Multiple-criteria design problems (multiple objective mathematical programming problems)

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The following MCDM methods are available, many of which are implemented by specialized

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Uses and limitations of the AHP method : a non-mathematical and rational analysis

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Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems

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Technique for the Order of Prioritisation by Similarity to Ideal Solution (TOPSIS)

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Multiple Criteria Optimization: State of the Art Annotated Bibliographic Surveys

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Wiley Encyclopedia of Operations Research and Management Science

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The French school focuses on decision aiding, in particular the

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Figure 2. Demonstration of the solutions in the criterion space

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Potentially All Pairwise RanKings of all possible Alternatives

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Mathematically, we can represent the corresponding problem as

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Disaggregation – Aggregation Approaches (UTA*, UTAII, UTADIS)

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Multiple Criteria Decision Analysis: An Integrated Approach

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Revue d'Informatique et de Recherche Opérationelle (RIRO)

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Evaluation Based on Distance from Average Solution (EDAS)

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Multiple Criteria Decision Making Theory and Application

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Conflicting criteria are typical in evaluating options:

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is weakly nondominated if there does not exist another

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Grey Data Analysis - Methods, Models and Applications

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Korhonen, P.; Wallenius, J. (1988). "A Pareto Race".

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Evolutionary multiobjective optimization school (EMO)

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Organizational Behavior and Human Decision Processes

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Köksalan, M., Wallenius, J., and Zionts, S. (2011).

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Nonstructural Fuzzy Decision Support System (NSFDSS)

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is weakly efficient if there does not exist another

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Multi-Criteria Decision Making: A Comparative Study

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System Redesigning to Creating Shared Value (SYRCS)

3934: 1729:Multiple objective mathematical programming school 1168: 807:Illustrations of the decision and criterion spaces 544: 246: 3005: 2759:Journal of Mathematical Analysis and Applications 2591: 2218: 2216: 2186: 2039:Stratified Multi Criteria Decision Making (SMCDM) 255: 4891: 3246: 2152:Rew, L. (1988). "Intuition in Decision-making". 2036:Simple Multi-Attribute Rating Technique (SMART) 897: 833: 602:is nondominated if there does not exist another 391: 368: 4073: 3745:Higher Education–Quality, Relevance and Impact. 3109: 3074: 2717: 2043:Stochastic Multicriteria Acceptability Analysis 574:A well-developed special case is obtained when 161:" alternatives (which we will define shortly). 79:that explicitly evaluates multiple conflicting 2453: 2213: 1683:, are projected onto the nondominated points, 818:Figure 1. Demonstration of the decision space 323:criterion functions (objective functions) and 4143: 4059: 4036:A Brief History prepared by Steuer and Zionts 3894:Information Systems and E-Business Management 3112:IEEE Transactions on Evolutionary Computation 2624: 650:is efficient if there does not exist another 3860: 3482:Journal of Business Economics and Management 3011: 2920:: CS1 maint: multiple names: authors list ( 2752: 2577:: CS1 maint: multiple names: authors list ( 2535: 2521:: CS1 maint: multiple names: authors list ( 2439:: CS1 maint: multiple names: authors list ( 2234: 2232: 535: 486: 4683:Hazard analysis and critical control points 4019: 3992:Mulliner E, Smallbone K, Maliene V (2013). 3964: 3176:(1). Research Information Ltd. (UK): 1–11. 3014:Journal of Multi-Criteria Decision Analysis 2272:International Journal of Sustainable Energy 1993:Multi-Attribute Global Inference of Quality 571:is the decision variable vector of size n. 4150: 4136: 4066: 4052: 2651: 2134:Superiority and inferiority ranking method 2049:Superiority and inferiority ranking method 3982: 3837: 3493: 3452: 3419: 3386: 3345: 2957: 2770: 2229: 525: 516: 169:upon knowledge in many fields including: 126:methods, many implemented by specialized 4656:Structured or semi-structured interviews 3971:Journal of Retail & Leisure Property 3937:European Journal of Operational Research 3558:Renewable and Sustainable Energy Reviews 3334:Economic Research-Ekonomska Istraživanja 3143:. Singapore: Springer. pp. 67–104. 3064:(phd). Nashville: Vanderbilt University. 2447: 2007:Markovian Multi Criteria Decision Making 1718: 1553: 1199: 813: 51: 3764:Keshavarz Ghorabaee, M. et al. (2015) " 3057: 2151: 1887:Aggregated Indices Randomization Method 14: 4892: 3699: 3672: 3265: 3205:International Journal of Fuzzy Systems 3039:Roy, B. (1968). "La méthode ELECTRE". 2398:: CS1 maint: archived copy as title ( 2238: 4131: 4047: 3854: 3787:Business Strategy and the Environment 3237: 3202: 2934: 2124:Multicriteria classification problems 2099:Architecture tradeoff analysis method 1918:Characteristic Objects METhod (COMET) 214:Multiple-criteria evaluation problems 3610: 2997:Keeney, R. & Raiffa, H. (1976). 1707:, respectively, along the direction 97:multiple attribute preference theory 39:Micro Channel Developers Association 4900:Multiple-criteria decision analysis 4157: 3623:from the original on 29 August 2017 3252:Belton, V, and Stewart, TJ (2002). 3163: 3136: 3038: 2354:from the original on 7 October 2017 2324:from the original on 3 October 2017 2004:Multi-attribute value theory (MAVT) 144:multiple-criteria decision analysis 111:comfortable and the safest one. In 69:multiple-criteria decision analysis 24: 4786:Bayesian statistics and Bayes nets 3958: 3259: 2474:from the original on 24 June 2010. 2166:10.1111/j.1547-5069.1988.tb00056.x 1948:Dominance-based rough set approach 134:Foundations, concepts, definitions 25: 4931: 4715:Failure mode and effects analysis 4020:Maliene, V.; et al. (2002). 3272:. Eloy Hontoria. Cham: Springer. 2129:Rank reversals in decision-making 1790:Multi-attribute utility theorists 1455:Generating nondominated solutions 252:well as some formal definitions. 140:multiple-criteria decision-making 101:multi-objective decision analysis 89:multiple attribute utility theory 61:Multiple-criteria decision-making 4818:Multi-criteria decision analysis 4766:Reliability centered maintenance 4102:Computer supported brainstorming 3303:Expert Systems with Applications 1859:Analytic hierarchy process (AHP) 1548:Achievement scalarizing function 914: 850: 4029:FIG XXII International Congress 3928: 3881: 3813: 3778: 3775:", Informatica, 26(3), 435-451. 3758: 3748: 3738: 3729: 3720: 3693: 3666: 3635: 3604: 3576: 3548: 3510: 3469: 3428: 3395: 3362: 3321: 3294: 3231: 3196: 3157: 3130: 3103: 3068: 3051: 3032: 2990: 2928: 2895: 2868: 2841: 2814: 2779: 2746: 2711: 2678: 2645: 2618: 2585: 2544: 2529: 2488: 2478: 2419:. Singapore: World Scientific. 2197:10.1002/9780470400531.eorms0683 2020:Ordinal Priority Approach (OPA) 1873: 247:Representations and definitions 93:multiple attribute value theory 18:Multicriteria decision analysis 4734:Cause and consequence analysis 4608:Occupational safety and health 4516:Identity and access management 3826:Operations Management Research 2366: 2336: 2306: 2263: 2154:Journal of Nursing Scholarship 2145: 1999:Multi-attribute utility theory 1924:Conjoint Value Hierarchy (CVA) 918: 910: 854: 846: 498: 492: 454: 422: 413: 407: 256:Criterion space representation 138:MCDM or MCDA are acronyms for 13: 1: 3617:www.transformations.knf.vu.lt 3495:10.3846/16111699.2015.1095233 3454:10.3846/16484142.2015.1121517 3347:10.1080/1331677X.2015.1075139 2959:10.1016/S0019-9958(65)90241-X 2753:Yu, P.L.; Zeleny, M. (1975). 2344:"Welcome to EWG-MCDA website" 2139: 1963:Evidential reasoning approach 369:Decision space representation 204: 4694:Structured What If Technique 4677:Hazard and operability study 4533:Business continuity planning 2772:10.1016/0022-247X(75)90189-4 2695:10.1007/978-3-642-04045-0_22 2662:10.1007/978-3-642-48782-8_32 2292:10.1080/14786451.2014.898640 1921:Choosing By Advantages (CBA) 1803:; Hansen and Ombler, 2008). 46:Multi-objective optimization 7: 4671:Preliminary hazard analysis 4490:Operational risk management 4013:10.1016/j.omega.2012.05.002 3714:10.1016/j.omega.2015.12.001 3687:10.1016/j.omega.2014.11.009 2454:Triantaphyllou, E. (2000). 2092: 1672:, and an infeasible point, 10: 4936: 4755:Human reliability analysis 4439:Enterprise risk management 3949:10.1016/j.ejor.2006.01.020 3906:10.1007/s10257-021-00525-4 3839:10.1007/s12063-021-00178-z 3660:10.1016/j.asoc.2017.03.045 3598:10.1016/j.asoc.2016.04.020 3570:10.1016/j.rser.2016.12.053 3315:10.1016/j.eswa.2015.01.003 3217:10.1007/s40815-020-00827-8 3211:(4). Springer: 1073–1090. 3182:10.1007/s40815-020-00827-8 3170:The Journal of Grey System 1893:Analytic hierarchy process 1773:Ordinal data based methods 43: 36: 29: 4915:Mathematical optimization 4827: 4744:Layer protection analysis 4739:Cause-and-effect analysis 4621: 4546:Financial risk management 4428: 4393: 4283:Vulnerability (computing) 4172: 4165: 4082: 3534:10.1142/S0219622016300019 3266:Munier, Nolberto (2021). 3124:10.1109/TEVC.2010.2070371 3089:10.1162/evco.1994.2.3.221 2952:(3). San Diego: 338–353. 2011:New Approach to Appraisal 1928:Data envelopment analysis 1783:Ordinal Priority Approach 75:) is a sub-discipline of 4705:Business impact analysis 4521:Vulnerability management 4467:Personal risk management 4266:Global catastrophic risk 3771:2 September 2016 at the 3242:. New York: McGraw-Hill. 3077:Evolutionary Computation 2877:Naval Research Logistics 2788:Mathematical Programming 2720:Mathematical Programming 2119:Decisional balance sheet 2109:Decision-making software 1981:Inner product of vectors 1975:Grey relational analysis 1899:Analytic network process 1880:decision-making software 1847:Grey relational analysis 1467:(Gass & Saaty, 1955) 563:is the feasible set and 128:decision-making software 4586:Precautionary principle 4538:Disaster risk reduction 4117:Nominal group technique 2945:Information and Control 2602:10.1007/0-306-48107-3_8 2540:. New York: John Wiley. 2249:10.1287/orms.2018.05.13 2114:Decision-making paradox 1796:Multi-attribute utility 1751:Goal programming school 1743:Interactive programming 4781:Monte Carlo simulation 4771:Sneak circuit analysis 4166:Risk type & source 3875:10.1006/obhd.1994.1087 3648:Applied Soft Computing 3586:Applied Soft Computing 3058:Shaffer, J.D. (1984). 2565:10.1287/opre.1080.0581 2509:10.1287/mnsc.41.7.1158 2080:Weighted product model 1785:and Qualiflex method. 1559: 1205: 1170: 819: 546: 57: 4806:Cost/benefit analysis 4450:Regulatory compliance 4076:creativity techniques 2862:10.1287/mnsc.22.6.652 2835:10.1287/mnsc.19.4.357 2829:(4–Part–1): 357–368. 2536:Steuer, R.E. (1986). 2226:, Springer: New York. 1719:Solving MCDM problems 1557: 1203: 1171: 817: 547: 329:is the feasible set, 55: 32:Meta-cold dark matter 4569:Strategic management 4445:Corporate governance 4223:Anthropogenic hazard 3965:Maliene, V. (2011). 3238:Saaty, T.L. (1980). 3164:Liu, Sifeng (2013). 3137:Liu, Sifeng (2017). 2639:10.1287/opre.2.3.316 2348:www.cs.put.poznan.pl 1944:(Rough set approach) 1904:Balance Beam process 826: 384: 194:Software engineering 113:portfolio management 4729:Event tree analysis 4724:Fault tree analysis 4710:Root cause analysis 4689:Toxicity assessment 4631:Exposure assessment 4601:Disaster management 4528:Incident management 4511:Security management 4204:Psychosocial hazard 4187:Reputational damage 3611:Diedonis, Antanas. 3381:(10): 13947–13984. 2627:Operations Research 2553:Operations Research 2318:www.mcdmsociety.org 2284:2016IJSE...35...47K 1763:Fuzzy-set theorists 1736:Vector maximization 199:Information systems 189:Computer technology 77:operations research 4910:Management systems 4811:Risk–benefit ratio 4613:Swiss cheese model 4574:Risk communication 4482:Disease management 4356:Exchange rate risk 4351:Interest rate risk 4087:6-3-5 Brainwriting 3984:10.1057/rlp.2011.7 3388:10.3390/su71013947 3001:. 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New York: Wiley. 2850:Management Science 2823:Management Science 2800:10.1007/bf01584098 2732:10.1007/BF01580111 2497:Management Science 2086:Weighted sum model 1914:Brown–Gibson model 1834:Grey system theory 1560: 1550:(Wierzbicki, 1980) 1206: 1166: 1164: 820: 542: 540: 58: 4905:Decision analysis 4887: 4886: 4700:Scenario analysis 4641:Scenario planning 4596:Crisis management 4477:Stress management 4424: 4423: 4317:Reputational risk 4125: 4124: 3421:10.3390/su8010037 3279:978-3-030-60392-2 3256:, Kluwer: Boston. 3150:978-981-10-1841-1 2704:978-3-642-04044-3 2671:978-3-540-09963-5 2467:978-0-7923-6607-2 2380:on 11 August 2011 2069:Value engineering 1908:Best worst method 961: 464: 319:is the vector of 179:Decision analysis 16:(Redirected from 4927: 4879:Opportunity cost 4828:Related concepts 4761:Bow tie analysis 4646:Contingency plan 4472:Health insurance 4460:Internal control 4301:Operational risk 4216:Natural disaster 4170: 4169: 4152: 4145: 4138: 4129: 4128: 4092:Affinity diagram 4068: 4061: 4054: 4045: 4044: 4032: 4026: 4016: 3998: 3988: 3986: 3953: 3952: 3932: 3926: 3925: 3885: 3879: 3878: 3858: 3852: 3851: 3841: 3832:(1–2): 208–232. 3817: 3811: 3810: 3799:10.1002/bse.2623 3782: 3776: 3762: 3756: 3752: 3746: 3742: 3736: 3733: 3727: 3724: 3718: 3717: 3697: 3691: 3690: 3670: 3664: 3663: 3639: 3633: 3632: 3630: 3628: 3608: 3602: 3601: 3580: 3574: 3573: 3552: 3546: 3545: 3514: 3508: 3507: 3497: 3488:(5): 1034–1068. 3473: 3467: 3466: 3456: 3432: 3426: 3425: 3423: 3399: 3393: 3392: 3390: 3366: 3360: 3359: 3349: 3325: 3319: 3318: 3309:(8): 4126–4148. 3298: 3292: 3291: 3263: 3257: 3250: 3244: 3243: 3235: 3229: 3228: 3200: 3194: 3193: 3161: 3155: 3154: 3134: 3128: 3127: 3107: 3101: 3100: 3072: 3066: 3065: 3055: 3049: 3048: 3036: 3030: 3029: 3026:10.1002/mcda.428 3009: 3003: 3002: 2994: 2988: 2987: 2961: 2932: 2926: 2925: 2919: 2911: 2902:Charnes, A. and 2899: 2893: 2892: 2872: 2866: 2865: 2845: 2839: 2838: 2818: 2812: 2811: 2783: 2777: 2776: 2774: 2750: 2744: 2743: 2715: 2709: 2708: 2682: 2676: 2675: 2649: 2643: 2642: 2622: 2616: 2615: 2589: 2583: 2582: 2576: 2568: 2548: 2542: 2541: 2533: 2527: 2526: 2520: 2512: 2503:(7): 1158–1171. 2492: 2486: 2482: 2476: 2475: 2451: 2445: 2444: 2438: 2430: 2410: 2404: 2403: 2397: 2389: 2387: 2385: 2376:. 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652–663. 2840: 2813: 2778: 2765:(2): 430–468. 2745: 2710: 2703: 2677: 2670: 2644: 2633:(3): 316–319. 2617: 2610: 2584: 2543: 2528: 2487: 2477: 2466: 2446: 2425: 2405: 2365: 2335: 2305: 2262: 2228: 2212: 2205: 2179: 2160:(3): 150–154. 2143: 2141: 2138: 2137: 2136: 2131: 2126: 2121: 2116: 2111: 2106: 2101: 2094: 2091: 2090: 2089: 2083: 2077: 2072: 2066: 2063:Value analysis 2060: 2055: 2052: 2046: 2040: 2037: 2034: 2028: 2022: 2017: 2014: 2008: 2005: 2002: 1996: 1990: 1984: 1978: 1972: 1966: 1960: 1957: 1951: 1945: 1939: 1936: 1930: 1925: 1922: 1919: 1916: 1911: 1905: 1902: 1896: 1890: 1875: 1872: 1841:In the 1980s, 1801:PAPRIKA method 1720: 1717: 1709: 1700: 1696: 1688: 1677: 1666: 1658: 1657: 1656: 1655: 1654: 1653: 1637: 1636: 1635: 1634: 1628: 1627: 1626: 1625: 1617: 1608: 1599: 1589: 1552: 1551: 1541: 1540: 1539: 1538: 1537: 1536: 1520: 1519: 1518: 1517: 1511: 1510: 1509: 1508: 1492: 1480: 1469: 1468: 1456: 1453: 1448: 1447: 1446: 1445: 1444: 1443: 1438: 1431: 1419: 1418: 1417: 1416: 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509: 506: 503: 500: 497: 494: 491: 488: 485: 482: 480: 478: 475: 472: 469: 468: 460: 459: 456: 451: 447: 443: 440: 437: 432: 428: 424: 421: 418: 415: 412: 409: 406: 403: 400: 398: 396: 393: 390: 389: 370: 367: 311: 310: 309: 308: 307: 306: 290: 289: 288: 287: 281: 280: 279: 278: 272: 257: 254: 248: 245: 224: 223: 217: 206: 203: 202: 201: 196: 191: 186: 181: 176: 135: 132: 26: 9: 6: 4: 3: 2: 4932: 4921: 4918: 4916: 4913: 4911: 4908: 4906: 4903: 4901: 4898: 4897: 4895: 4880: 4877: 4873: 4870: 4869: 4868: 4865: 4863: 4860: 4858: 4855: 4853: 4852:Risk appetite 4850: 4848: 4845: 4841: 4840:ISO/IEC 31010 4838: 4837: 4836: 4833: 4832: 4830: 4826: 4819: 4816: 4812: 4809: 4808: 4807: 4804: 4802: 4799: 4797: 4794: 4792: 4789: 4787: 4784: 4782: 4779: 4777: 4774: 4772: 4769: 4767: 4764: 4762: 4759: 4756: 4753: 4751: 4750:Decision tree 4748: 4745: 4742: 4740: 4737: 4735: 4732: 4730: 4727: 4725: 4722: 4720: 4716: 4713: 4711: 4708: 4706: 4703: 4701: 4698: 4695: 4692: 4690: 4687: 4684: 4681: 4678: 4675: 4672: 4669: 4667: 4664: 4662: 4661:Delphi method 4659: 4657: 4654: 4652: 4651:Brainstorming 4649: 4647: 4644: 4642: 4639: 4637: 4634: 4632: 4629: 4628: 4626: 4624: 4620: 4614: 4611: 4609: 4606: 4602: 4599: 4598: 4597: 4594: 4592: 4589: 4587: 4584: 4580: 4577: 4576: 4575: 4572: 4570: 4567: 4563: 4560: 4558: 4555: 4553: 4550: 4549: 4548: 4547: 4543: 4539: 4536: 4534: 4531: 4529: 4526: 4522: 4519: 4517: 4514: 4513: 4512: 4509: 4507: 4504: 4502: 4499: 4497: 4494: 4493: 4492: 4491: 4487: 4483: 4480: 4478: 4475: 4473: 4470: 4469: 4468: 4465: 4461: 4458: 4456: 4453: 4451: 4448: 4446: 4443: 4442: 4441: 4440: 4436: 4435: 4433: 4431: 4427: 4417: 4416:Vulnerability 4414: 4412: 4409: 4407: 4404: 4402: 4399: 4398: 4396: 4392: 4386: 4385:Residual risk 4383: 4381: 4380: 4376: 4372: 4371:Systemic risk 4369: 4367: 4364: 4362: 4359: 4357: 4354: 4352: 4349: 4347: 4344: 4342: 4339: 4338: 4337: 4336: 4332: 4328: 4325: 4323: 4320: 4318: 4315: 4313: 4310: 4308: 4305: 4304: 4303: 4302: 4298: 4294: 4291: 4289: 4286: 4284: 4281: 4280: 4279: 4278:Security risk 4276: 4274: 4273:Safety hazard 4271: 4267: 4264: 4262: 4259: 4258: 4257: 4256:External risk 4253: 4250: 4246: 4243: 4241: 4238: 4237: 4236: 4233: 4229: 4226: 4225: 4224: 4221: 4217: 4214: 4213: 4212: 4209: 4205: 4202: 4200: 4197: 4196: 4195: 4194:Personal risk 4192: 4188: 4185: 4184: 4183: 4182: 4178: 4177: 4175: 4171: 4168: 4164: 4160: 4153: 4148: 4146: 4141: 4139: 4134: 4133: 4130: 4118: 4115: 4113: 4110: 4108: 4107:Disney method 4105: 4103: 4100: 4098: 4097:Brainstorming 4095: 4093: 4090: 4088: 4085: 4084: 4081: 4077: 4069: 4064: 4062: 4057: 4055: 4050: 4049: 4046: 4039: 4037: 4034: 4030: 4023: 4018: 4014: 4010: 4007:(2): 270–79. 4006: 4002: 3995: 3990: 3985: 3980: 3977:(5): 443–50. 3976: 3972: 3968: 3963: 3962: 3950: 3946: 3942: 3938: 3931: 3923: 3919: 3915: 3911: 3907: 3903: 3899: 3895: 3891: 3884: 3876: 3872: 3868: 3864: 3857: 3849: 3845: 3840: 3835: 3831: 3827: 3823: 3816: 3808: 3804: 3800: 3796: 3792: 3788: 3781: 3774: 3770: 3767: 3761: 3751: 3741: 3732: 3723: 3715: 3711: 3707: 3703: 3696: 3688: 3684: 3680: 3676: 3669: 3661: 3657: 3653: 3649: 3645: 3638: 3622: 3618: 3614: 3607: 3599: 3595: 3591: 3587: 3579: 3571: 3567: 3563: 3559: 3551: 3543: 3539: 3535: 3531: 3527: 3523: 3522: 3513: 3505: 3501: 3496: 3491: 3487: 3483: 3479: 3472: 3464: 3460: 3455: 3450: 3446: 3442: 3438: 3431: 3422: 3417: 3413: 3409: 3405: 3398: 3389: 3384: 3380: 3376: 3372: 3365: 3357: 3353: 3348: 3343: 3339: 3335: 3331: 3324: 3316: 3312: 3308: 3304: 3297: 3289: 3285: 3281: 3275: 3271: 3270: 3262: 3255: 3249: 3241: 3234: 3226: 3222: 3218: 3214: 3210: 3206: 3199: 3191: 3187: 3183: 3179: 3175: 3171: 3167: 3160: 3152: 3146: 3142: 3141: 3133: 3125: 3121: 3117: 3113: 3106: 3098: 3094: 3090: 3086: 3082: 3078: 3071: 3063: 3062: 3054: 3046: 3042: 3035: 3027: 3023: 3019: 3015: 3008: 3000: 2993: 2985: 2981: 2977: 2973: 2969: 2965: 2960: 2955: 2951: 2947: 2946: 2941: 2938:(June 1965). 2937: 2931: 2923: 2917: 2909: 2905: 2898: 2890: 2886: 2882: 2878: 2871: 2863: 2859: 2855: 2851: 2844: 2836: 2832: 2828: 2824: 2817: 2809: 2805: 2801: 2797: 2793: 2789: 2782: 2773: 2768: 2764: 2760: 2756: 2749: 2741: 2737: 2733: 2729: 2725: 2721: 2714: 2706: 2700: 2696: 2692: 2688: 2681: 2673: 2667: 2663: 2659: 2655: 2648: 2640: 2636: 2632: 2628: 2621: 2613: 2611:9780306481079 2607: 2603: 2599: 2595: 2588: 2580: 2574: 2566: 2562: 2558: 2554: 2547: 2539: 2532: 2524: 2518: 2510: 2506: 2502: 2498: 2491: 2481: 2473: 2469: 2463: 2459: 2458: 2450: 2442: 2436: 2428: 2426:9789814335591 2422: 2418: 2417: 2409: 2401: 2395: 2379: 2375: 2369: 2353: 2349: 2345: 2339: 2323: 2319: 2315: 2309: 2301: 2297: 2293: 2289: 2285: 2281: 2277: 2273: 2266: 2258: 2254: 2250: 2246: 2242: 2235: 2233: 2225: 2219: 2217: 2208: 2206:9780470400531 2202: 2198: 2194: 2190: 2183: 2175: 2171: 2167: 2163: 2159: 2155: 2148: 2144: 2135: 2132: 2130: 2127: 2125: 2122: 2120: 2117: 2115: 2112: 2110: 2107: 2105: 2102: 2100: 2097: 2096: 2087: 2084: 2081: 2078: 2076: 2073: 2070: 2067: 2064: 2061: 2059: 2056: 2053: 2050: 2047: 2044: 2041: 2038: 2035: 2032: 2029: 2026: 2023: 2021: 2018: 2015: 2012: 2009: 2006: 2003: 2000: 1997: 1994: 1991: 1988: 1985: 1982: 1979: 1976: 1973: 1970: 1967: 1964: 1961: 1958: 1955: 1952: 1949: 1946: 1943: 1940: 1937: 1934: 1931: 1929: 1926: 1923: 1920: 1917: 1915: 1912: 1909: 1906: 1903: 1900: 1897: 1894: 1891: 1888: 1885: 1884: 1883: 1881: 1871: 1867: 1863: 1862: 1861: 1860: 1854: 1852: 1848: 1844: 1839: 1838: 1837: 1836:based methods 1835: 1829: 1825: 1824: 1823: 1818: 1816: 1811: 1810: 1809: 1808:French school 1804: 1802: 1797: 1793: 1792: 1791: 1786: 1784: 1780: 1776: 1775: 1774: 1769: 1766: 1765: 1764: 1759: 1755: 1754: 1753: 1752: 1746: 1744: 1739: 1737: 1732: 1731: 1730: 1725: 1716: 1712: 1703: 1699: 1691: 1687: 1680: 1676: 1669: 1665: 1651: 1647: 1643: 1642: 1641: 1640: 1639: 1638: 1632: 1631: 1630: 1629: 1620: 1616: 1611: 1607: 1602: 1597: 1592: 1583: 1580: 1576: 1571: 1570: 1569: 1568: 1567: 1564: 1556: 1549: 1546: 1545: 1544: 1534: 1530: 1526: 1525: 1524: 1523: 1522: 1521: 1515: 1514: 1513: 1512: 1503: 1499: 1495: 1487: 1483: 1477: 1476: 1475: 1474: 1473: 1466: 1465:Weighted sums 1463: 1462: 1461: 1452: 1437: 1430: 1425: 1424: 1423: 1422: 1421: 1420: 1408: 1401: 1397: 1396: 1395: 1394: 1393: 1392: 1380: 1373: 1368: 1367: 1366: 1365: 1364: 1363: 1351: 1344: 1340: 1339: 1338: 1337: 1336: 1335: 1323: 1316: 1312: 1311: 1310: 1309: 1308: 1307: 1295: 1288: 1283: 1282: 1281: 1280: 1279: 1278: 1266: 1259: 1255: 1254: 1253: 1252: 1251: 1250: 1244: 1243: 1242: 1241: 1227: 1226: 1225: 1224: 1210: 1209: 1208: 1207: 1202: 1198: 1181: 1159: 1156: 1154: 1147: 1143: 1139: 1134: 1130: 1122: 1119: 1117: 1110: 1106: 1102: 1097: 1093: 1085: 1082: 1080: 1073: 1069: 1065: 1060: 1056: 1052: 1045: 1042: 1040: 1033: 1029: 1025: 1020: 1016: 1008: 1005: 1003: 996: 992: 984: 981: 979: 972: 968: 949: 945: 941: 936: 932: 928: 925: 923: 905: 901: 888: 884: 880: 877: 872: 868: 864: 861: 859: 841: 837: 822: 821: 816: 812: 804: 800: 798: 794: 792: 788: 784: 779: 775: 771: 767: 760: 756: 750: 746: 742: 741:Definition 4. 738: 735: 731: 725: 721: 715: 711: 707: 706:Definition 3. 703: 699: 695: 691: 687: 683: 676: 672: 668: 664: 658: 654: 648: 644: 640: 639:Definition 2. 636: 633: 630: 626: 620: 616: 610: 606: 600: 596: 592: 591:Definition 1. 588: 584: 579: 572: 568: 560: 530: 520: 517: 513: 510: 507: 504: 501: 495: 489: 483: 481: 476: 473: 470: 449: 445: 441: 438: 435: 430: 426: 419: 416: 410: 404: 401: 399: 394: 380: 379: 378: 375: 366: 364: 358: 355: 349: 346: 340: 337: 333: 327: 322: 317: 304: 300: 296: 295: 294: 293: 292: 291: 285: 284: 283: 282: 275: 269: 268: 267: 266: 265: 262: 253: 244: 240: 236: 232: 228: 221: 218: 215: 212: 211: 210: 200: 197: 195: 192: 190: 187: 185: 182: 180: 177: 175: 172: 171: 170: 166: 162: 160: 155: 153: 147: 145: 141: 131: 129: 123: 121: 116: 114: 109: 104: 102: 98: 94: 90: 86: 82: 78: 74: 70: 66: 62: 54: 50: 47: 40: 33: 19: 4544: 4496:Supply chain 4488: 4466: 4437: 4377: 4333: 4322:Country risk 4299: 4277: 4261:Extreme risk 4211:Natural risk 4193: 4179: 4028: 4004: 4000: 3974: 3970: 3940: 3936: 3930: 3897: 3893: 3883: 3866: 3862: 3856: 3829: 3825: 3815: 3790: 3786: 3780: 3760: 3750: 3740: 3731: 3722: 3705: 3701: 3695: 3678: 3674: 3668: 3651: 3647: 3637: 3625:. Retrieved 3616: 3606: 3589: 3585: 3578: 3561: 3557: 3550: 3525: 3519: 3512: 3485: 3481: 3471: 3444: 3440: 3430: 3411: 3407: 3397: 3378: 3374: 3364: 3337: 3333: 3323: 3306: 3302: 3296: 3268: 3261: 3253: 3248: 3239: 3233: 3208: 3204: 3198: 3173: 3169: 3159: 3139: 3132: 3115: 3111: 3105: 3080: 3076: 3070: 3060: 3053: 3044: 3040: 3034: 3017: 3013: 3007: 2998: 2992: 2949: 2943: 2940:"Fuzzy sets" 2930: 2907: 2904:Cooper, W.W. 2897: 2880: 2876: 2870: 2853: 2849: 2843: 2826: 2822: 2816: 2791: 2787: 2781: 2762: 2758: 2748: 2723: 2719: 2713: 2686: 2680: 2653: 2647: 2630: 2626: 2620: 2593: 2587: 2573:cite journal 2556: 2552: 2546: 2537: 2531: 2517:cite journal 2500: 2496: 2490: 2480: 2456: 2449: 2415: 2408: 2382:. Retrieved 2378:the original 2368: 2356:. Retrieved 2347: 2338: 2326:. Retrieved 2317: 2308: 2278:(1): 47–58. 2275: 2271: 2265: 2240: 2223: 2188: 2182: 2157: 2153: 2147: 2075:VIKOR method 2051:(SIR method) 2033:(Outranking) 1956:(Outranking) 1877: 1874:MCDM methods 1868: 1864: 1857: 1856: 1855: 1840: 1832: 1831: 1830: 1826: 1821: 1820: 1819: 1812: 1807: 1806: 1805: 1794: 1789: 1788: 1787: 1779:Ordinal data 1777: 1772: 1771: 1770: 1767: 1762: 1761: 1760: 1756: 1749: 1748: 1747: 1742: 1740: 1735: 1733: 1728: 1727: 1726: 1722: 1710: 1701: 1697: 1689: 1685: 1678: 1674: 1667: 1663: 1659: 1649: 1645: 1618: 1614: 1609: 1605: 1600: 1595: 1590: 1581: 1578: 1574: 1565: 1561: 1547: 1542: 1532: 1528: 1501: 1497: 1493: 1485: 1481: 1470: 1464: 1458: 1449: 1435: 1428: 1406: 1399: 1378: 1371: 1349: 1342: 1321: 1314: 1293: 1286: 1264: 1257: 1197:as follows: 1182: 1178: 810: 801: 796: 795: 790: 789: 785: 777: 773: 769: 765: 758: 754: 748: 744: 740: 739: 733: 729: 723: 719: 713: 709: 705: 704: 700: 693: 689: 685: 681: 674: 670: 666: 662: 656: 652: 646: 642: 638: 637: 634: 628: 624: 618: 614: 608: 604: 598: 594: 590: 589: 585: 577: 573: 566: 558: 554: 376: 372: 359: 353: 350: 344: 341: 335: 331: 325: 320: 315: 312: 302: 298: 273: 263: 259: 250: 241: 237: 233: 229: 225: 219: 213: 208: 167: 163: 159:nondominated 156: 148: 143: 139: 137: 124: 117: 105: 100: 96: 92: 88: 72: 68: 64: 60: 59: 49: 4862:Rare events 4801:Risk Matrix 4411:Uncertainty 4394:Risk source 4366:Profit risk 4361:Market risk 4341:Credit risk 4199:Health risk 3869:: 306–325. 3708:: 126–130. 3654:: 265–292. 3592:: 108–128. 3564:: 216–256. 2936:Zadeh, L.A. 2794:: 366–375. 2559:: 187–199. 2241:OR/MS Today 1843:Deng Julong 1451:problems). 797:Nadir point 791:Ideal point 174:Mathematics 4894:Categories 4857:Hazard map 4796:Risk index 4327:Legal risk 4312:Model risk 4252:Macro risk 3288:1237399430 2976:0139.24606 2140:References 1851:Liu Sifeng 1633:subject to 1516:subject to 1245:subject to 960:subject to 762:such that 727:such that 660:such that 612:such that 463:subject to 286:subject to 205:A typology 44:See also: 4835:ISO 31000 4717:(FMEA) / 4666:Checklist 4591:Insurance 4562:Risk pool 4173:Risk type 3922:236544531 3914:1617-9846 3848:232240914 3807:224917346 3681:: 49–57. 3627:29 August 3542:0219-6220 3504:1611-1699 3463:1648-4142 3441:Transport 3414:(1): 37. 3356:1331-677X 3225:219090787 3190:219090787 2984:Q25938993 2968:0019-9958 2916:cite book 2726:: 54–72. 2435:cite book 2300:108512639 2031:PROMETHEE 2027:(PAPRIKA) 1989:(MACBETH) 1942:Rough set 1588:Min {max 1190:with the 1157:≥ 1120:≤ 1103:− 1083:≤ 1053:− 1043:≤ 1006:≤ 982:≤ 942:− 865:− 521:⊆ 508:∈ 474:∈ 439:… 363:trade-off 243:review). 184:Economics 120:intuition 4872:Security 4791:FN curve 4406:Conflict 4293:Accident 4112:Mind map 4031:: 19–26. 3769:Archived 3621:Archived 3097:13997318 3047:: 57–75. 2980:Wikidata 2906:(1961). 2808:29348836 2740:32037123 2472:Archived 2394:cite web 2384:7 August 2358:26 April 2352:Archived 2328:26 April 2322:Archived 2093:See also 1579:g, q, w, 81:criteria 4920:Utility 4696:(SWIFT) 4685:(HACCP) 4679:(HAZOP) 4506:Quality 4501:Project 4240:IT risk 2485:INFORMS 2280:Bibcode 2174:3169833 1995:(MAGIQ) 1954:ELECTRE 1815:ELECTRE 1661:point, 772:) > 152:optimal 4820:(MCDA) 4746:(LOPA) 4401:Hazard 4288:Threat 4074:Group 3920: 3912: 3846: 3805: 3540: 3502: 3461: 3354: 3286: 3276: 3223: 3188: 3147: 3095: 2982: 2974: 2966: 2806: 2738: 2701: 2668: 2608: 2464: 2423: 2298: 2257:642562 2255: 2203: 2172: 2045:(SMAA) 2013:(NATA) 2001:(MAUT) 1950:(DRSA) 1889:(AIRM) 555:where 313:where 271:"max" 99:, and 4757:(HRA) 4719:FMECA 4673:(PHA) 4557:Hedge 4025:(PDF) 4001:Omega 3997:(PDF) 3918:S2CID 3844:S2CID 3803:S2CID 3702:Omega 3675:Omega 3221:S2CID 3186:S2CID 3093:S2CID 2804:S2CID 2736:S2CID 2296:S2CID 2253:S2CID 2088:(WSM) 2082:(WPM) 1983:(IPV) 1977:(GRA) 1935:(DEX) 1910:(BWM) 1901:(ANP) 1895:(AHP) 1504:> 732:> 67:) or 4847:COSO 3910:ISSN 3629:2017 3538:ISSN 3500:ISSN 3459:ISSN 3352:ISSN 3284:OCLC 3274:ISBN 3145:ISBN 2964:ISSN 2922:link 2699:ISBN 2666:ISBN 2606:ISBN 2579:link 2523:link 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Multiple-criteria decision analysis

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