An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis
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ORIGINAL ARTICLE
An approach to interval-valued intuitionistic stochastic multi-criteria decision-making using set pair analysis Yong-xi Cao1 • Huan Zhou1 • Jian-qiang Wang1
Received: 16 December 2015 / Accepted: 22 August 2016 Springer-Verlag Berlin Heidelberg 2016
Abstract This paper proposes an approach to intervalvalued intuitionistic stochastic multi-criteria decisionmaking (MCDM) problems using set pair analysis. This approach is applicable to MCDM problems in which the criterion weights are incomplete or the weights are certain, and evaluation values of alternatives take the form of interval-valued intuitionistic stochastic variables. To begin with, we briefly introduce the concepts of interval-valued intuitionistic fuzzy set, interval-valued intuitionistic stochastic variable, and set pair analysis. Then, we define a new similarity measure between interval-valued intuitionistic fuzzy numbers, after which we establish a mathematical programming model based on the technique for order preference by similarity to an ideal solution method and the maximizing deviation method in order to determine criterion weights. We then use connection degree to represent interval-valued intuitionistic fuzzy information and transform the interval-valued intuitionistic stochastic decision-making matrixes into corresponding connection degree matrixes. Finally, we rank the alternatives according to the value of set pair potential after calculating the connection degree of each alternative. After defining the method, we apply it to a practical decision-making problem and provide a comparison analysis with existing methods to illustrate the feasibility and validity of the proposed approach.
& Jian-qiang Wang [email protected] 1
School of Business, Central South University, Changsha 410083, China
Keywords Interval-valued intuitionistic stochastic multi-criteria decision-making Interval-valued intuitionistic fuzzy set Interval-valued intuitionistic stochastic variable Similarity measure Set pair analysis
1 Introduction Multi-criteria decision-making (MCDM) refers to evaluating, ranking, or selecting alternatives on the basis of several conflicting criteria or preferences. Due to the complexity of life, the real world contains many MCDM problems in which the preference information and criterion weights are inaccurate, uncertain, or incomplete. To address these circumstances, Zadeh introduced the concept of fuzzy set (FS) [1], wherein an element’s membership degree with regard to a set is represented by a real number between zero and one. FS was identified as an excellent theory with which to describe inexact, uncertain, and imprecise information, and has been extended to many application domains such as e-commerce, link prediction, machine learning, fuzzy classification, intrusion detection [2–8]. Considering that the single membership function is insufficient to express the information completely, building upon FS, Atanassov introduced intuitionistic fuzzy set (IFS) [9], which takes the membership degree and nonmember
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