Fuzzy Dynamic Systems and Computational Verbs Represented by Fuzzy Mathematics

Historically, fuzzy dynamic systems (FDS) were studied under different names such as dynamic fuzzy systems, fuzzy differential equations, fuzzy difference equations, fuzzy contractive maps, fuzzy systems, iterated fuzzy systems, fuzzy mappings and fuzzy logic controller. Fuzzy dynamic systems can be generated from conventional dynamic systems by using two methods. In the first method, the fuzzy extension principle can be used to transform a conventional equation into a fuzzy model. FDS generated by this method is called type-I FDS. A type-I FDS is defined by a state space of fuzzy terms and conventional evolving laws. The second method of generating FDS is to use fuzzy compositions. In this method, the corresponding FDS is called type-II FDS. In a type-II FDS, both the state space and the evolving laws are described in the form of fuzzy terms. The evolving laws can be represented as fuzzy relations. So far, almost all works on fuzzy dynamic systems(FDS) were focused on either mathematical theoretical aspects or conceptual engineering protocol, there were no work yet to address the applications of fuzzy dynamic systems to information sciences, natural language processing and artificial intelligence(AI). On the other hand, the study of computational verbs shows that to model a computational verb, we need to use dynamic systems. This opens the possibility of using FDS to model computational verbs and find applications to computational verb theory and furthermore to information sciences. As the first monograph on fuzzy dynamic systems(FDS), this timely monograph provided a systematic structure of FDS from both theoretical and applications points of view, and applies FDS to recently developed computational verb theory. This monograph can be used as a textbook or complementary materials to graduate students and researchers from nonlinear dynamic systems, fuzzy mathematics, fuzzy logic, artificial intelligent and linguistics.