Notes on implementing fuzzy sets in Prolog

Abstract

Due to its unique characteristics, Prolog requires special techniques for implementing ordinary as well as fuzzy sets. This article presents a comparative overview of various strategies of representing and manipulating fuzzy sets in Prolog. There are two major approaches to implement fuzzy sets in Prolog. One is to incorporate fuzzy representations and operations on top of an existing Prolog. The second way is to develop a new extended Prolog language. This article discusses various methods based primarily on the first approach. The choice of a method depends on many factors, such as whether a database for fuzzy sets already exists, the type of applications, the type of fuzzy set operations performed, whether an implicit description of the elements is possible, the size of the database, and the required computation time. The following methods are discussed in this article: explicit description (finite), using lists; explicit description (finite), using a fact for every element; implicit description (finite, infinite); and other methods and extensions.