The role of fuzzy logic in the management of uncertainty in expert systems
Fuzzy Sets and Systems
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In this paper we introduce a new definition of fuzzy inclusion and equality between fuzzy subsets. The main idea is that we evaluate a fuzzy equality not only by one value, as was done up to the present, but by two ones, i.e. by a pair of numbers from the closed unit interval. Basic properties of the proposed fuzzy inclusion and equality are given. Using the new notion of fuzzy equality we next define fuzzy operations for fuzzy subsets. These operations are also characterized by a pair of numbers. All fundamental laws for fuzzy operations are listed. Some connections between lLukasiewicz logic and introduced definitions of fuzzy inclusion and equality are also described.