On the solutions of lattice-valued matrix game with fuzziness

Yang Xu, Jun Liu, Jun Ma

Research output: Contribution to conferencePaperpeer-review

2 Citations (Scopus)

Abstract

Game theory is a very important branch of applied mathematics. There have been a lot of excellent results within eighty years of its history. Many research areas have been developed, but most of them are limited to the real domain. A great amount of non-real practical game problems, especially the lattice-valued game, remains unexplored. This paper focus on the lattice-valued matrix game. Firstly, we propose the concept of lattice-valued matrix game with pure strategy and discuss the sufficient and necessary conditions for the existence of the solution of the lattice-valued matrix game with pure strategy. Then considering the real situation that the strategy set of the players are often fuzzy set and the matrix are often described by fuzzy sets, we investigate the lattice-valued matrix game with fuzziness. Especially, we investigate the determination of solution of a lattice-valued matrix game with pure strategy and fuzzy value matrix, with fuzzy strategy and classical game matrix, as well as with fuzzy strategy and the function value game matrix. In the following, we assume that L={, ∧ ∨} is a lattice, "≤" is the partial order in L.

Original languageEnglish
Pages2301-2304
Number of pages4
Publication statusPublished - 2001
EventJoint 9th IFSA World Congress and 20th NAFIPS International Conference - Vancouver, BC, Canada
Duration: 25 Jul 200128 Jul 2001

Conference

ConferenceJoint 9th IFSA World Congress and 20th NAFIPS International Conference
CountryCanada
CityVancouver, BC
Period25/07/0128/07/01

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