Multi-classification decision-making method for interval-valued intuitionistic fuzzy three-way decisions and its applica
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ORIGINAL ARTICLE
Multi‑classification decision‑making method for interval‑valued intuitionistic fuzzy three‑way decisions and its application in the group decision‑making Dajun Ye1,2 · Decui Liang3 · Tao Li3 · Shujing Liang1 Received: 1 March 2020 / Accepted: 1 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract With the introduction of the interval-valued intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy numbers are used instead of precise numbers to provide fuzzy characterization of feature attribute values and misclassification loss function values, which is more in line with the realistic fuzzy decision-making environment. Also, the constructive covering algorithm is introduced into the three-way decisions model, which effectively solves the shortcomings of the traditional decision-theoretic rough sets model in dealing with multi-classification problems, such as too many artificial parameters, complicated computation, redundant decisions, decisional conflicts and excessively large boundary domains. At the same time, in order to avoid the one-sidedness of individual decisions, the group decision-making method is introduced into the preliminarily constructed multi-classification model in this paper to build a multi-classification group decision-making model for interval-valued intuitionistic fuzzy three-way decisions based on the constructive covering algorithm. This model determines the initial weights of feature attributes by the precise weighting method, and determines the expert weights by the grey relational precise weighting method, which effectively achieves the consistency of group decision-making. The decision-making process and rules are also deduced, which expand the model of three-way decisions as well as its practical application value and scope. Keywords Three-way decisions · Multi-classification · Constructive covering algorithm · Interval-valued intuitionistic fuzzy sets · Group decision-making
1 Introduction The rough sets theory gives the definition of upper and lower approximation by setting through the two algebraic inclusion relations of equivalence classes and target concept classes and further defines the positive, negative and boundary domains [23]. The decision-theoretic rough sets (DTRSs) introduced the Bayesian theory into rough sets, * Decui Liang [email protected] 1
School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China
2
Sichuan College of Architectural Technology, Deyang 618000, China
3
School of Management and Economics, University of Electronic Science and Technology of China, Chengdu 610054, China
which described the risk of decision making with a cost function and derived the decision rules based on the minimum expected risk. It divided a unified set into three regions that did not intersect each other, and proposed a three-way decisions (3WD) model by developed a corresponding decision-making strategy (decision rule) for each region [31, 35]. It provided a new idea and met
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