Showing papers on "Fuzzy number published in 1971"

Fuzzy logic and the resolution principle

Abstract: Problem-solving systems using two-valued logic suffer from one drawback, they cannot handle fuzzy, or uncertain, information. In this paper, the author recommends the use of fuzzy logic, which is based on the concept of fuzzy sets and first order predicate calculus. It is proved that, in fuzzy logic, a set of clauses is unsatisfiable iff it is unsatisfiable in two-valued logic. It is also shown that if the most unreliable clause of a set of clauses has a truth-value a>0.5, then all the logical consequences obtained by repeatedly applying the resolution principle has truth-value never smaller than a. Implications of these results for applying fuzzy logic to problem-solving are discussed.

Pattern Classification Based on Fuzzy Relations

Abstract: A method of classifying patterns using fuzzy relations is described. To start with, we give a suitable value of the measure of subjective similarity to each pair of patterns that is taken from the population of patterns to be classified. Then a similitude between any two patterns is calculated by using the composition of a fuzzy relation. The similitude induces an equivalence relation. Consequently, we can classify the present population of the patterns into some classes by the equivalence relation. An experiment of the classification of portraits has been performed to test the method proposed here.

Some properties of fuzzy logic

Abstract: In this paper, the fuzzy set ZZadeh (1965)] is viewed as a multivalued logic with a continuum of truth values in the interval Z0, 1]. The concepts of inconsistency, validity, prime implicant and prime implicate are extended to fuzzy logic and various properties of these notions in the context of fuzzy logic are established. It is proved that a formula is valid (inconsistent) in fuzzy logic iff it is valid (inconsistent) in two-valued logic. An algorithm that generates fuzzy prime implicants (implicates) is introduced. A proof of the completeness of this algorithm is also given.

A note on fuzzy sets

Abstract: Fuzzy sets are defined as mappings from sets into Boolean lattices. The basic set theory type results for Zadeh's fuzzy sets are shown to carry over. Some results on convex fuzzy sets, star-shaped fuzzy sets, and arcwise connected fuzzy sets are given. Fuzzy sets with “holes,” bounded fuzzy sets, and connected fuzzy sets are also discussed.