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 propo...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.展开更多
In previous studies, an isosceles triangular-type possibility distribution was employed to represent the analog waves of a Gaussian Process. The model was then projected onto actual waves using Zadeh’s extension prin...In previous studies, an isosceles triangular-type possibility distribution was employed to represent the analog waves of a Gaussian Process. The model was then projected onto actual waves using Zadeh’s extension principle of mapping (Hori et al., 2019). Furthermore, by applying Vague Set and Systems theory, it was shown that the actual waves followed a Gaussian process, and that the system could be efficiently controlled via Monte Carlo simulation. However, due to the use of fuzzy OR logic in the extension principle of mapping and wave synthesis, the resulting ambiguity increased significantly. To address this issue, a Possibility Markov Chain was proposed, incorporating possibility theory to mitigate the explosion of ambiguity. In this study, we propose a novel modeling approach that utilizes a possibility transition matrix without relying on fuzzy OR logic. Additionally, we introduce the Sea-Control Algorithm, which artificially introduces system error into the system function, thereby enabling modification of the possibility transition matrix through the deliberate manipulation of possibility information within the fuzzy system.展开更多
文摘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.
文摘In previous studies, an isosceles triangular-type possibility distribution was employed to represent the analog waves of a Gaussian Process. The model was then projected onto actual waves using Zadeh’s extension principle of mapping (Hori et al., 2019). Furthermore, by applying Vague Set and Systems theory, it was shown that the actual waves followed a Gaussian process, and that the system could be efficiently controlled via Monte Carlo simulation. However, due to the use of fuzzy OR logic in the extension principle of mapping and wave synthesis, the resulting ambiguity increased significantly. To address this issue, a Possibility Markov Chain was proposed, incorporating possibility theory to mitigate the explosion of ambiguity. In this study, we propose a novel modeling approach that utilizes a possibility transition matrix without relying on fuzzy OR logic. Additionally, we introduce the Sea-Control Algorithm, which artificially introduces system error into the system function, thereby enabling modification of the possibility transition matrix through the deliberate manipulation of possibility information within the fuzzy system.
