Solution of matrix games with rough interval pay‐offs and its application in the telecom market share problem

Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual‐layer information. In real‐life problems, there are many situations where players of a matrix game cannot assess th...

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Veröffentlicht in:International journal of intelligent systems Jg. 36; H. 10; S. 6066 - 6100
Hauptverfasser: Seikh, Mijanur R., Dutta, Shibaji, Li, Deng‐Feng
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York John Wiley & Sons, Inc 01.10.2021
Schlagworte:
Environment models
expected value
Fuzzy sets
Games
Intelligent systems
Intervals
Linear programming
linear programming problem
Market shares
Mathematical programming
matrix game
Parameter uncertainty
rough interval
Simplex method
Telecommunications
ISSN:0884-8173, 1098-111X
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Zusammenfassung:Rough interval (RI) is an appropriate generalization of the crisp interval and is very much useful to express uncertain parameters or partially unknown variables when they contain dual‐layer information. In real‐life problems, there are many situations where players of a matrix game cannot assess their pay‐offs by using fuzzy sets/intuitionistic fuzzy sets or ordinary intervals. RIs are used as an excellent tool to handle such situations. This paper explores matrix games with RI pay‐offs and investigates two different solution methodologies to solve such a game. In the first approach, a pair of auxiliary linear programming problems with RI coefficients for the players has been constructed. Then each of the two auxiliary programming problems is converted into two linear programming problems with interval coefficients (LPPICs) using lower and upper approximation intervals of the RI. Finally from each LPPIC, two classical linear programming problems (LPPs) are constructed. In the second approach, the expected value technique for RI is used for transforming auxiliary mathematical programming models under the RI environment to crisp LPP. A case study on the telecom market share problem is considered to show the applicability of the proposed approaches and results are compared and analyzed with an existing method.
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ISSN:0884-8173
1098-111X
DOI:10.1002/int.22542