Multi-objective linguistic-neutrosophic matrix game and its applications to tourism management

Date

2021-04-01

Author

Bhaumik, Ankan
Roy, Sankar Kumar
Weber, Gerhard Wilhelm

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Game theory plays an important role in numerous decision-oriented real-life problems. Nowadays, many such problems are basically characterized by various uncertainties. Uncertainties come to happen due to decision makers' collection of data, intuition, assumption, judgement, behaviour, evaluation and lastly, due to the problem itself. Fuzzy concept with membership degree made an initialization towards the treatment of uncertainty, but it was not enough. Intuitionistic fuzzy concept was evolved concerning with both membership and non-membership degrees but failed to express reality more accurately. Then, neutrosophy logic was developed with a new degree in uncertainty, say, indeterminacy degree besides membership and non-membership degrees. Multi-objective optimization is an area of multiple-criteria decision making related with mathematical optimization problems involving more than one objective function to be optimized at the same time. Game theory (matrix game) problems with imprecise, vague information, like neutrosophic, can be formed with multiple objective functions. We develop and analyse a matrix game with multiple objectives, and solve the problem under a single-valued neutrosophic environment in linguistic approach. The main achievement of our study is that we here introduce a problem-oriented example to justify our designed methodologies with a successful real-life implications using linguistic neutrosophic data rather than crisp data as used in previous researches.

Subject Keywords

Multi-objective optimization, uncertainty, neutrosophic set, linguistic neutrosophic number, matrix game

URI

https://hdl.handle.net/11511/90739

Journal

JOURNAL OF DYNAMICS AND GAMES

DOI

https://doi.org/10.3934/jdg.2020031

Collections

Graduate School of Applied Mathematics, Article

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Citation Formats

A. Bhaumik, S. K. Roy, and G. W. Weber, “Multi-objective linguistic-neutrosophic matrix game and its applications to tourism management,” JOURNAL OF DYNAMICS AND GAMES, pp. 101–118, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/90739.