Solving matrix games involving the level (Klower, Kupper) interval valued trapezoidal fuzzy payoffs: Signed distance ranking approach

In this paper, a two-player constant-sum interval-valued 2-tuple linguistic matrix game is construed. The value of a linguistic matrix game is proven as a non-decreasing function of the linguistic values in the payoffs, and, hence, a pair of auxiliary linguistic linear programming (LLP) problems is formulated to obtain the linguistic lower bound and the linguistic upper bound of the interval-valued linguistic value of such class of games. The duality theorem of LLP is also adopted to establish the equality of values of the interval linguistic matrix game for players I and II. A flowchart to summarize the proposed algorithm is also given. The methodology is then illustrated via a hypothetical example to demonstrate the applicability of the proposed theory in the real world. The designed algorithm demonstrates acceptable results in the two-player constant-sum game problems with interval-valued 2-tuple linguistic payoffs.

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

IEEE Transactions on Fuzzy Systems ◽

10.1109/tfuzz.2010.2065812 ◽

2010 ◽

Vol 18 (6) ◽

pp. 1112-1128 ◽

Cited By ~ 88

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

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Ranking and Similarity Measures of Interval-Valued Pentagonal Fuzzy Numbers

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.d9498.118419 ◽

2019 ◽

Vol 8 (4) ◽

pp. 9314-9320

Keyword(s):

Fuzzy Numbers ◽

Similarity Measures ◽

Flow Chart ◽

Geometric Distance ◽

Signed Distance ◽

Mathematical Formulas ◽

Interval Valued

We define generalized interval-valued pentagonal fuzzy numbers. Based on the height of the lower and upper pentagonal fuzzy numbers we propose to categorize interval-valued pentagonal fuzzy numbers into three different categories. Using signed distance concept de-fuzzification of interval-valued pentagonal fuzzy numbers is proposed and mathematical formulas are derived using   cut representations. We also introduce two similarity measures for interval-valued pentagonal fuzzy numbers based on geometric distance, area and height of pentagonal fuzzy numbers and geometric distance, perimeter and height of pentagonal fuzzy numbers respectively. Algorithms for finding de-fuzzification value and similarity measures are proposed with flow-chart illustration.

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