Methodology for Interval-Valued Matrix Games with 2-Tuple Fuzzy Linguistic Information
- 17 Downloads
In this paper, we consider a non-cooperative 2-player zero-sum interval-valued 2-tuple fuzzy linguistic (IVTFL) matrix game and develop a methodology to evaluate its saddle point and optimal interval-valued linguistic value of the game. In this direction, we have constructed an auxiliary pair of interval-valued linguistic linear programming (IVLLP) problem that is further transformed into conventional interval linear programming (ILP) problem to obtain optimal strategy sets of both players as the region that is not only completely feasible but also totally optimal. The proposed method is illustrated via a hypothetical example to show its applicability in the real world. To validate the suggested solution scheme, the transformed ILP problems are solved using best-worst case (BWC) approach, enhanced-interval linear programming (EILP) method and linguistic linear programming (LLP) technique of solving interval linguistic matrix game problems and lastly the obtained results are compared.
Keywords2-tuple fuzzy linguistic model Interval-valued 2-tuple fuzzy linguistic model Interval linear programming Interval-valued linguistic linear programming Matrix game problem
This work was financially supported by Delhi Technological University Ref. No. DTU/IRD/619/2019/2107 and Ref. No. DTU/Maths/387/2019-20/2108.
- 2.Singh, A., Gupta, A., Mehra, A.: Matrix games with 2-tuple linguistic information. Ann. Oper. Res. (2018). https://doi.org/10.1007/s10479-018-2810-6
- 4.Singh, A., Gupta, A., Mehra, A.: An AHP-PROMETHEE II method for 2-tuple linguistic multicriteria group decision making. In: 2015 4th International Conference on Reliability, Infocom Technologies and Optimization (ICRITO) (Trends and Future Directions), pp. 1–6. IEEE (2015). https://doi.org/10.1109/ICRITO.2015.7359374
- 10.Sengupta, A., Pal, T.K.: A-index for ordering interval numbers. In: Indian Science Congress, pp. 3–8 (1997)Google Scholar
- 22.Kurano, M., Yasuda, M., Nakagami, J.I., Yoshida, Y.: An interval matrix game and its extensions to fuzzy and stochastic games (2002). http://www.math.s.chiba-u.ac.jp/~yasuda/accept/SIG2.pdf. Accessed 5 June 2018