Showing papers on "Fuzzy logic 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.

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.

Automated interpretation and editing of fuzzy line drawings

Abstract: One of the problems in automated line drawing analysis is to construct a cleaner drawing from the original drawing. For example, a chemist using an interactive chemical structure analysis system will usually draw a rough sketch of a chemical structure on a display device or a tablet. It is desirable to obtain a cleaner version of the rough sketch so that the cleaner drawing can be redisplayed. Moreover, the cleaner drawing can then be used to generate hard-copy output through a plotter, a magnetic film recorder or a photocomposer. Such an automated line drawing editing program can enhance the usefulness of an interactive system and is also of value in itself.