Mathematical Modeling of Possibility Markov Chains by Possibility Theory  

作　　者：Yoshiki Uemura Takemura Kazuhisa Kenji Kita Yoshiki Uemura;Takemura Kazuhisa;Kenji Kita(Analog Image Technology Development Laboratory, Nara, Japan;Department of Psychology, Waseda University, Tokyo, Japan;MILAI Technologies, Inc., Tokushima, Japan)

机构地区：[1]Analog Image Technology Development Laboratory, Nara, Japan [2]Department of Psychology, Waseda University, Tokyo, Japan [3]MILAI Technologies, Inc., Tokushima, Japan

出　　处：《Applied Mathematics》2024年第8期499-507,共9页应用数学（英文）

摘　　要：Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.Statistical regression models are input-oriented estimation models that account for observation errors. On the other hand, an output-oriented possibility regression model that accounts for system fluctuations is proposed. Furthermore, the possibility Markov chain is proposed, which has a disidentifiable state (posterior) and a nondiscriminable state (prior). In this paper, we first take up the entity efficiency evaluation problem as a case study of the posterior non-discriminable production possibility region and mention Fuzzy DEA with fuzzy constraints. Next, the case study of the ex-ante non-discriminable event setting is discussed. Finally, we introduce the measure of the fuzzy number and the equality relation and attempt to model the possibility Markov chain mathematically. Furthermore, we show that under ergodic conditions, the direct sum state can be decomposed and reintegrated using fuzzy OR logic. We had already constructed the Possibility Markov process based on the indifferent state of this world. In this paper, we try to extend it to the indifferent event in another world. It should be noted that we can obtain the possibility transfer matrix by full use of possibility theory.

关 键 词：Possibility Markov Chain Ergodic Condition Direct Sum State Prior Indiscriminate State Posterior Discriminatory State 

分 类 号：O15[理学—数学]