Mathematical-Programming Approach to Matrix Games With Payoffs Represented by Atanassov's Interval-Valued Intuitionistic Fuzzy Sets

2010 ◽  
Vol 18 (6) ◽  
pp. 1112-1128 ◽  
Author(s):  
Deng-Feng Li
Keyword(s):  
Mathematical Programming ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Programming Approach ◽  
Matrix Games ◽  
Intuitionistic Fuzzy ◽  
Mathematical Programming Approach ◽  
Interval Valued

scholarly journals Solutions of Matrix Games Involving Linguistic Interval-Valued Intuitionistic Fuzzy Sets

2021 ◽  
Author(s):  
Deeba Naqvi ◽  
Rajkumar Verma ◽  
Abha Aggarwal ◽  
Geeta Sachdev
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Intuitionistic Fuzzy Sets ◽  
Linguistic Terms ◽  
Matrix Games ◽  
Suggested Approach ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Life Decision

Abstract In real-life decision-making challenges, experts quite frequently have a preference for expressing their perspective in natural linguistic terms rather than definite numerical format. These linguistic representation has been utilized to resolve plenty of decision-making problems. This paper displays the thorough study of matrix games where in the payoffs are characterized through linguistic interval-valued intuitionistic fuzzy sets (LIVIFSs). Solution of these matrix games are attained by resolving a duo of linear or nonlinear programming problems, originated through non-linear bi-objective programming problems. Finally, a numerical example is used to demonstrate the applicability of the suggested approach.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

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