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

Ankan Bhaumik, Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore-721102, West Bengal, India, Sankar Kumar Roy, Gerhard Wilhelm Weber, Faculty of Engineering Management, Poznan University of Technology, ul. Jacka Rychlewskiego 2, 61-138 Poznan, Poland; METU, 06800 Ankara, Turkey
2019 Journal of Dynamics & Games  
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
more » ... oncerning 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. 2020 Mathematics Subject Classification. Primary: 91A86, 91A10; Secondary: 91A80, 90B50.
doi:10.3934/jdg.2020031 fatcat:a4rhrib5yfg6vnlom5b423yggy