Algorithms for interval-valued fuzzy soft sets in stochastic multi-criteria decision making based on regret theory and prospect theory with combined weight
01 May 2017-Vol. 54, pp 415-430
TL;DR: Two interval-valued fuzzy soft approaches based on prospect theory and regret theory are proposed and two algorithms to solve stochastic multi-criteria decision making problem are proposed that take regret aversion and prospect preference of decision makers into consideration in the decision process.
Abstract: Graphical abstractDisplay Omitted HighlightsWe initiate a new axiomatic definition of interval-valued fuzzy distance measure.We propose the method of computing objective weights.We propose two algorithms to solve stochastic multi-criteria decision making problem.The effectiveness and feasibility of two algorithms are demonstrated by two numerical examples.Two interval-valued fuzzy soft approaches based on prospect theory and regret theory are proposed. This paper presents two novel interval-valued fuzzy soft set approaches. First, we initiate a new axiomatic definition of interval-valued fuzzy distance measure, which is expressed by interval-valued fuzzy number (IVFN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via normal distribution. Combining objective weights with subjective weights, we present the combined weights, which can reflect both the subjective considerations of the decision maker and the objective information. Later, we propose two algorithms to solve stochastic multi-criteria decision making problem, which take regret aversion and prospect preference of decision makers into consideration in the decision process. Finally, the effectiveness and feasibility of two approaches are demonstrated by two numerical examples.
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TL;DR: A new score function of q‐rung orthopair fuzzy number (q‐ROFN) is presented for solving the failure problems when comparing two q‐ ROFNs and has a great power in distinguishing the optimal alternative.
Abstract: q‐Rung orthopair fuzzy set (q‐ROFS) is a powerful tool that attracts the attention of many scholars in dealing with uncertainty and vagueness. The aim of paper is to present a new score function of q‐rung orthopair fuzzy number (q‐ROFN) for solving the failure problems when comparing two q‐ROFNs. Then a new exponential operational law about q‐ROFNs is defined, in which the bases are positive real numbers and the exponents are q‐ROFNs. Meanwhile, some properties of the operational law are investigated. Later, we apply them to derive the q‐rung orthopair fuzzy weighted exponential aggregation operator. Additionally, an approach for multicriteria decision‐making problems under the q‐rung orthopair fuzzy data is explored by applying proposed aggregation operator. Finally, an example is investigated to illustrate the feasibility and validity of the proposed approach. The salient features of the proposed method, compared to the existing q‐rung orthopair fuzzy decision‐making methods, are (1) it can obtain the optimal alternative without counterintuitive phenomena; (2) it has a great power in distinguishing the optimal alternative.
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TL;DR: These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator.
Abstract: The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.
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TL;DR: A new score function for interval-valued fuzzy number is proposed for tackling the comparison problem, the formulae of information measures are introduced and their transformation relations are pioneered, and the objective weights of various parameters are determined via new entropy method.
150 citations
Cites background or methods or result from "Algorithms for interval-valued fuzz..."
...Definition 5.6 (Feng et al., 2010)....
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...Moreover, our weight determining method has keep in accordance with the references (Peng et al., 2017; Peng & Yang, 2017) when using the corresponding decision making method for achieving the final decision results....
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...Definition 2.2 (Xu and Da, 2002)....
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...…then the deviation function of F A( , ) is defined as follows: ∑ ∑ ⎜ ⎟= ⎛ ⎝ + − − ⎞ ⎠= = − + d F A mn F ε x F ε x s F A(( , )) 1 ( )( ) ( )( ) 1 2 (( , )) . i m j n j i j i p 1 1 2 (3) Based on above score function and deviation function, Peng and Yang (2017) derive the following comparative law....
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...Definition 3.1 (Liu, 1992)....
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TL;DR: An overview on neutrosophic set is presented with the aim of offering a clear perspective on the different concepts, tools and trends related to their extensions and indicates that some developing economics (such as China, India, Turkey) are quite active in neutrosophile set research.
Abstract: Neutrosophic set, initiated by Smarandache, is a novel tool to deal with vagueness considering the truth-membership T, indeterminacy-membership I and falsity-membership F satisfying the condition $$0\le T+I+F\le 3$$. It can be used to characterize the uncertain information more sufficiently and accurately than intuitionistic fuzzy set. Neutrosophic set has attracted great attention of many scholars that have been extended to new types and these extensions have been used in many areas such as aggregation operators, decision making, image processing, information measures, graph and algebraic structures. Because of such a growth, we present an overview on neutrosophic set with the aim of offering a clear perspective on the different concepts, tools and trends related to their extensions. A total of 137 neutrosophic set publication records from Web of Science are analyzed. Many interesting results with regard to the annual trends, the top players in terms of country level as well as institutional level, the publishing journals, the highly cited papers, and the research landscape are yielded and explained in-depth. The results indicate that some developing economics (such as China, India, Turkey) are quite active in neutrosophic set research. Moreover, the co-authorship analysis of the country and institution, the co-citation analysis of the journal, reference and author, and the co-occurrence analysis of the keywords are presented by VOSviewer software.
150 citations
Posted Content•
TL;DR: In this paper, a new axiomatic definition of single-valued neutrosophic similarity measure, which is expressed by singlevalued neutroophic number (SVNN) was introduced, and the objective weights of various parameters were determined via grey system theory.
Abstract: This paper presents three novel single-valued neutrosophic soft set (SVNSS) methods. First, we initiate a new axiomatic definition of single-valued neutrosophic similarity measure, which is expressed by single-valued neutrosophic number (SVNN) that will reduce the information loss and remain more original information. Then, the objective weights of various parameters are determined via grey system theory.
148 citations
References
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01 Aug 1996
TL;DR: A separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
Abstract: A fuzzy set is a class of objects with a continuum of grades of membership. Such a set is characterized by a membership (characteristic) function which assigns to each object a grade of membership ranging between zero and one. The notions of inclusion, union, intersection, complement, relation, convexity, etc., are extended to such sets, and various properties of these notions in the context of fuzzy sets are established. In particular, a separation theorem for convex fuzzy sets is proved without requiring that the fuzzy sets be disjoint.
52,705 citations
TL;DR: In this paper, the authors present a critique of expected utility theory as a descriptive model of decision making under risk, and develop an alternative model, called prospect theory, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights.
Abstract: This paper presents a critique of expected utility theory as a descriptive model of decision making under risk, and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low prob- abilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling. EXPECTED UTILITY THEORY has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (24), and widely applied as a descriptive model of economic behavior, e.g. (15, 4). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (47, 36), and that most people actually do, most of the time. The present paper describes several classes of choice problems in which preferences systematically violate the axioms of expected utility theory. In the light of these observations we argue that utility theory, as it is commonly interpreted and applied, is not an adequate descriptive model and we propose an alternative account of choice under risk. 2. CRITIQUE
35,067 citations
TL;DR: Cumulative prospect theory as discussed by the authors applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses, and two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting function.
Abstract: We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability. Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer, 1989; Fishburn, 1988; Machina, 1987). Some time ago we presented a model of choice, called prospect theory, which explained the major violations of expected utility theory in choices between risky prospects with a small number of outcomes (Kahneman and Tversky, 1979; Tversky and Kahneman, 1986). The key elements of this theory are 1) a value function that is concave for gains, convex for losses, and steeper for losses than for gains,
13,433 citations
TL;DR: Much of what constitutes the core of scientific knowledge may be regarded as a reservoir of concepts and techniques which can be drawn upon to construct mathematical models of various types of systems and thereby yield quantitative information concerning their behavior.
12,530 citations
01 Jan 1975
8,942 citations