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

Abstract

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.

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

“…Since the method proposed in this paper cannot handle multi-attribute decision making in complex q-rung linguistic fuzzy environments or complex q-rung fuzzy N-soft environments, in future work, we will extend Frank aggregation operators under complex q-rung linguistic orthopair fuzzy environments, complex q-rung fuzzy N-soft environments and T‐spherical fuzzy environments, or develop Frank aggregation operators to 3, 4-quasirung fuzzy sets (Seikh and Mandal, 2022 ). In addition, we shall further generalize these defined operators to deal with Biogas plant implementation problem (Karmakar et al 2021 ), plastic ban problem (Seikh et al 2021a ), market share problem (Seikh et al 2021b ), social network analysis (Liu et al 2022a ), social trust propagation mechanism (Liu et al 2022b ) and incomplete probabilistic linguistic preference relations (Wang et al 2021 ; Liu et al 2020a , 2020b , 2020c ), or extend the aggregation operators to other domains, such as pattern recognition, cluster analysis and investment decisions.…”

Analysis of Factors Affecting Human Reliability in the Mining Process Design Using Fuzzy Delphi and DEMATEL Methods

“…More research should be conducted to determine the relationship between variables. Therefore, it is proposed that further studies should be done, focusing more on MCDM and new tools and approaches such as intuitionistic fuzzy set [96], type-2 fuzzy variable [97], and Rough interval [98], considering the challenges and control strategies for reaching a consensus via a group decision-making process [99,100]. In conclusion, the findings of this study can improve the status of health and environmental indicators and help achieve sustainable development goals in surface mines by identifying and prioritizing factors influencing DE and recommending practical solutions to eliminate and control such errors.…”

A Mathematical Modeling Approach of Target Damage Strategy on the Intersection Confrontation

“…Then, any optimal strategies ε * of the projectile in the game must abandon the pure strategy. That is, if it is known that one optimal strategy ε * of the projectile satisfies ε * > 0, it must be the case that E(λ k , ε * ) = v. If it is determined that the sum of the optimal strategies of the projectile and the aircraft target is greater than zero, there is an inequality group, which can be expressed by Formulas ( 15) and ( 16) [39][40][41].…”