Markov-type fuzzy decision processes with a discounted reward on a closed interval |
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| Institution: | 1. Faculty of Education, Chiba University, Chiba 263, Japan;2. Faculty of Science, Chiba University, Chiba 263, Japan;3. Faculty of Economics, Kitakyushu University, Kitakyushu 802, Japan;1. Department of Biomedical Laboratory Science, Jungwon University, 85 Munmu-ro, Goesan-eup, Goesan-gun, Chungbuk, 28024 South Korea;2. College of Pharmacy, Natural Product Research Institute, Seoul National University, 1 Gwanak-ro, Gwanak-gu, Seoul, 08826 South Korea;3. Stem Cells and Metabolism Research Program, Faculty of Medicine / Helsinki Institute of Life Science, University of Helsinki, Finland;4. Institute of Human Genomic Study, Korea Unversity Ansan Hospital, 516 Gojan-1-dong, Danwon-gu, Gyeonggi-do, Ansan 425-707, South Korea;5. Department of Neurology, Seoul National University Bundang Hospital, Seoul National University College of Medicine 82, Gumi-ro 173 Beon-gil, Bundang-gu, Seongnam-si 13620, Gyeonggi-do, South Korea;6. Department of Pulmonary, Sleep and Critical Care Medicine, College of Medicine, Korea University Ansan Hospital, 516 Gojan-1-dong, Danwon-gu, Gyeonggi-do, Ansan 425-707, South Korea;1. Center for Excellence in Regional Atmospheric Environment, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, 361021, China;2. Key Lab of Urban Environmental Processes and Pollution Control, Ningbo Urban Environment Observation and Research Station-NUEORS, Chinese Academy of Sciences, Ningbo, 315830, China;3. Key Lab of Urban Environment and Health, Institute of Urban Environment, Chinese Academy of Sciences, Xiamen, 361021, China;4. University of Chinese Academy of Sciences, Beijing, China;5. Environment Monitoring Center of Ningbo, Ningbo, 315012, China |
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| Abstract: | We formulate a new multi-stage decision process with Markov-type fuzzy transition, which is termed Markov-type fuzzy decision process. In the general framework of the decision process, both of state and action are assumed to be fuzzy itself. The transition of states is defined using the fuzzy relation with Markov property and the discounted total reward is described as a fuzzy number on a closed bounded interval. To discuss the optimization problem, a partial order of convex fuzzy numbers is introduced. In this paper the discounted total reward associated with an admissible stationary policy is characterized by a unique fixed point of the contractive mapping. Moreover, the optimality equation for the fuzzy decision model is derived under some continuity conditions. Also, an illustrated example is given to explain the theoretical results and the computation in the paper. |
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