Reasoning about mathematical fuzzy logic and its future

Abstract

This paper is devoted to reasoning about fuzzy logic which is based on various personal observations of the author. Our goal is to think of the state of the art in mathematical fuzzy logic (MFL) and to outline some of the tasks on which, in the author's opinion, MFL should focus in the future. In our discussion, we will mention not only the basic theory, but also its extension called fuzzy logic in broader sense (FLb). The paradigm of the latter is to be the logic of natural human reasoning, whose most essential characteristic is the use of natural language. Besides brief description of FLb, we will also mention some of its applications. On the basis of that, we will ponder on other possible directions for research, namely the possibility of using FLn as a metatheory of fuzzy mathematics, as a proper tool for modeling of the main manifestations of the phenomenon of vagueness, and as a reasonable tool for developing models of linguistic semantics.