Decision Method in Type-2 Fuzzy Events under Fuzzy Observed Information

Hori (né Uemura) et al. formulated the fuzzy-Bayes decision rule extension of the Wald decision function to fuzzy ORand AND-connectives with multiple subjective distributions. This decision rule maps and transforms a state of nature to fuzzy events. In this context, the map of subjective distributions is called the subjective possibility distribution and the map of utility functions is called the fuzzy utility function. The subjective possibility distribution represents the possibility of possibilities and the fuzzy utility function represents the utility of utilities, and these are OR type-2 fuzzy. This definition differs from the definition of ordinary type-2 fuzzy sets. We further incorporate the concept of time and show that so long as the state of nature follows a Markov process, the fuzzy events thus manifested also represent a Markov process. As a Monte Carlo simulation with a fuzzy transitional matrix, however, it is marked by a repeating cycle of elimination, inversion, and restoration. In the present paper, in this fuzzy-Bayes decision rule we extend the fuzzy events to type-2 fuzzy and then to pseudo OR type-3 fuzzy, and report the formulation of the Markov decision process in type-2 fuzzy events incorporating the concept of time.