Vague controller: a generalization of fuzzy logic controller

In this research, a vague controller (VC) is synthesized by using the notion of vague sets, which are a generalization of fuzzy sets and characterized by a truth-membership function and a falsity-membership function. The vague sets follow the basic set operations and logic operations defined for fuzzy sets, and are superior to fuzzy sets in that they could deal with the uncertainty encountered in real-world applications in a move natural way. Depending on the vague sets, the VC is developed as a generalization of fuzzy logic controller (FLC). The design procedures of the VC, which allow an arbitrary number of input variables, and each variable could have a distinct number of linguistic values, are outlined in this paper. In order to compensate the effort in constructing two series of membership functions for vague sets and to ease the difficulties in designing VCs, a new means of designating membership functions for VCs is also presented in this article. This method constructs a set of membership functions systematically by using only two parameters: number of linguistic values of a linguistic variable and shrinking factor. The membership functions generated by this method, shrinking-span membership functions (SSMFs), have different spans over the universe of discourse and, therefore, ave more rational and more practical from the human expert's point of view.