Linguistic Dynamic Systems Theory And Application Of Type-2Fuzzy Sets Under Time-varying Universe Of Discourse

In order to effective use perception information which expressed by natural language to solve the problems of human behavior related to the complex systems, based on type-2fuzzy sets, theories and applications of linguistic dynamic systems under time-varying universe of discourse are researched in this paper. Possible routes and methods are provided to solve problems of perception information processing and modeling and analysis of complex systems.At first, the definition and the basic computing method of type-1and type-2fuzzy set are introduced in this paper. According to the conventional mathematical model of research objects being built or not, linguistic dynamic systems are divided into type-Ⅰ and type-Ⅱ Linguistic dynamic systems, the corresponding methods of the computing with words are also divided into type-Ⅰ and type-Ⅱ computing with words. Their numerical calculation methods are given in this paper.Subsequently, five different kinds of representations of type-2fuzzy sets are discussed. The definition of footprint of uncertainty of type-2fuzzy set is introduced and analyzed and its error form is revised. Numerical examples are used to compare the right and wrong representations of footprint of uncertainty.Extension principle of interval type-2fuzzy sets are used to convert Mealy automata to interval type-2fuzzy Mealy automata (IT2FMA), IT2FMA as the formal model of computing with words is for studying linguistic dynamic systems, the relation of time complexity for a IT2FMA computing strings of words in comparison to computing strings of symbols are analyzed, then study the linguistic dynamic orbits based on IT2MFA.At last, time-varying universe of discourse can be divided into continuous time-varying universe of discourse and discrete time-varying universe of discourse according to the characteristics of the objects of study(whether the universe of discourse continuous or not). Based on the interval type-2fuzzy sets, linguistic dynamic systems under continuous time-varying universe of discourse and discrete time-varying universe of discourse are discussed in this paper respectively. They are applied to research the house price change trend and the universities’ library booksmanagement system.