STUDIES OF FUZZY DECISION PROCESSES AND THEIR APPLICATIONS

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The aim of this research is analysis of the mathematical structure of dynamic fuzzy systems and its application to decision making. The main results are as follows.(i) Limit theorems of sequences of fuzzy states in dynamic fuzzy systems are studied when fuzzy relations are monotone/transitive.(ii) The space of the solutions of fuzzy relational equations is characterized.(iii) The recurrence and the cyclic behavior of the dynamic fuzzy systems are analyzed.(iv) The optimal stopping problems in dynamic fuzzy systems are studied by introducing fuzzy reward, and the optimal rewards are characterized by unique solutions of fuzzy relational equation. The fuzzy rewards are estimated by a fuzzy expectation induced from fuzzy goals, and an optimal stopping times is also given.(v) In the two-person zero-sum stopping games in dynamic fuzzy systems with fuzzy rewards, a minimax theorem is proved and optimal stopping points and the value of the game are also given.(vi) The duality of the dynamic fuzzy systems is discussed for a stopping problem, and the solutions are characterized by the recurrence set.(vii) fuzzy decision processes, under the criteria of time-average rewards, are discussed from a viewpoint of a dynamic fuzzy system and fuzzy dynamic programming. The time-average reward is characterized, by introducing a relative value function, as a unique solution of the associated equation.These results are published by the international journals, Fuzzy Sets and Systems, Information Sciences, Computers and Mathematics with Applications, Mathematical and Computer Modelling, Journal of Math. Analy. Appl. and so on. We have also presented some results at international conferences a d workshops, KES '98, EUFIT '98, IIZUKA '98, IFSA '99 and so on.In this research, we have analyzed the mathematical structure of dynamic fuzzy systems and we have obtained its application to decision making.