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m-Polar Generalization of Fuzzy T-Ordering Relations: An Approach to Group Decision Making. Symmetry (Basel) 2020. [DOI: 10.3390/sym13010051] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
Recently, T-orderings, defined based on a t-norm T and infimum operator (for infinite case) or minimum operator (for finite case), have been applied as a generalization of the notion of crisp orderings to fuzzy setting. When this concept is extending to m-polar fuzzy data, it is questioned whether the generalized definition can be expanded for any aggregation function, not necessarily the minimum operator, or not. To answer this question, the present study focuses on constructing m-polar T-orderings based on aggregation functions A, in particular, m-polar T-preorderings (which are reflexive and transitive m-polar fuzzy relations w.r.t T and A) and m-polar T-equivalences (which are symmetric m-polar T-preorderings). Moreover, the construction results for generating crisp preference relations based on m-polar T-orderings are obtained. Two algorithms for solving ranking problem in decision-making are proposed and validated by an illustrative example.
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Some Construction Methods of Aggregation Operators in Decision-Making Problems: An Overview. Symmetry (Basel) 2020. [DOI: 10.3390/sym12050694] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Aggregating data is the main line of any discipline dealing with fusion of information from the knowledge-based systems to decision-making. The purpose of aggregation methods is to convert a list of objects, all belonging to a given set, into a single representative object of the same set usually by an n-ary function, so-called aggregation operator. As the useful aggregation functions for modeling real-life problems are limited, the basic problem is to construct a proper aggregation operator, usually a symmetric one, for each situation. During the last decades, a number of construction methods for aggregation functions have been developed to build new classes based on the existing well-known operators. There are three main construction methods in common use: transformation, composition, and convex combination. This paper compares these methods with respect to the type of aggregating problems that can be handled by each of them.
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Alcantud JCR, Khameneh AZ, Kilicman A. Aggregation of infinite chains of intuitionistic fuzzy sets and their application to choices with temporal intuitionistic fuzzy information. Inf Sci (N Y) 2020. [DOI: 10.1016/j.ins.2019.12.008] [Citation(s) in RCA: 58] [Impact Index Per Article: 14.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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