Fuzzy optimality relation for perceptive MDPs - the average case

In this paper, the fuzzy perceptive model for average reward Markov decision processes is defined and a method of computing the corresponding fuzzy perceptive values is proposed. Under the minorization condition for fuzzy perceptive transition matrices, it is characterized by the optimal average expected reward, called the average perceptive value, using a fuzzy optimality relation. Also, we give a simple numerical example.

[1]  Masanori Hosaka,et al.  CONTROLLED MARKOV SET-CHAINS WITH DISCOUNTING , 1998 .

[2]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[3]  Régis Sabbadin,et al.  A Possibilistic Model for Qualitative Sequential Decision Problems under Uncertainty in Partially Observable Environments , 1999, UAI.

[4]  Masami Yasuda,et al.  ORDERING OF CONVEX FUZZY SETS - A BRIEF SURVEY AND NEW RESULTS , 2000 .

[5]  Lotfi A. Zadeh Toward a perception-based theory of probabilistic reasoning with imprecise probabilities , 2003 .

[6]  Masami Kurano Fuzzy Perceptive Values for MDPs with Discounting , 2005 .

[7]  Etienne Kerre,et al.  A fuzzy ordering on multi-dimensional fuzzy sets induced from convex cones , 2002, Fuzzy Sets Syst..

[8]  E. Nummelin General irreducible Markov chains and non-negative operators: List of symbols and notation , 1984 .

[9]  Cyrus Derman,et al.  Finite State Markovian Decision Processes , 1970 .

[10]  Ronald A. Howard,et al.  Dynamic Programming and Markov Processes , 1960 .

[11]  G. Dantzig,et al.  On the continuity of the minimum set of a continuous function , 1967 .

[12]  Jérôme Lang,et al.  Towards qualitative approaches to multi-stage decision making , 1998, Int. J. Approx. Reason..

[13]  P. Schweitzer Perturbation theory and finite Markov chains , 1968 .

[14]  Rutherford Aris,et al.  Discrete Dynamic Programming , 1965, The Mathematical Gazette.

[15]  Yuji Yoshida,et al.  A fuzzy treatment of uncertain Markov decision processes : Average case (Mathematical Decision Making under uncertainty and ambiguity) , 2000 .

[16]  Eilon Solan Continuity of the Value of Competitive Markov Decision Processes , 2003 .

[17]  安田 正実,et al.  A Fuzzy Stopping Problem with the Concept of Perception (不確実性の下での意思決定の数理 研究集会報告集) , 2003 .

[18]  Masami Yasuda,et al.  A Fuzzy Stopping Problem with the Concept of Perception (Mathematics of Decision-making under uncertainty) , 2003 .

[19]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[20]  Masami Yasuda,et al.  Fuzzy Perceptive Values for MDPs with Discounting (Mathematical Theory and Applications of Uncertainty Sciences and Decision Making) , 2005 .

[21]  L. Zadeh Toward a Perception-Based Theory of Probabilistic Reasoning , 2000, Rough Sets and Current Trends in Computing.

[22]  Masami Yasuda,et al.  A Fuzzy Stopping Problem with the Concept , 2004, Fuzzy Optim. Decis. Mak..