Intensional theory of granular computing

Abstract

This paper presents a new idea how the concept of granule can be modeled in formal fuzzy logic. The basic mathematical theory is fuzzy logic in narrow sense with evaluated syntax, which is based on Łukasiewicz algebra of truth values extended by the product. We have introduced the concepts of intension and extension of granules, internal and external operations on them, various kinds of relations, motion of granules, and others. The paper also outlines construction of some important examples of granules. At its end, we also introduce a more complex concept of association, which is formed of granules of various kinds.