𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Normal forms and truth tables for fuzzy logics

✍ Scribed by Mai Gehrke; Carol L. Walker; Elbert A. Walker

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
421 KB
Volume
138
Category
Article
ISSN
0165-0114

No coin nor oath required. For personal study only.

✦ Synopsis

In this paper, we examine and compare De Morgan-, Kleene-, and Boolean-disjunctive and conjunctive normal forms and consider their role in fuzzy settings. In particular, we show that there are normal forms and truth tables for classical fuzzy propositional logic and interval-valued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determining logical equivalence of two expressions in fuzzy propositional logic is a ΓΏnite problem, and similarly for the interval-valued case. Turksen's work on interval-valued fuzzy sets is examined in light of these results.

πŸ“œ SIMILAR VOLUMES

Truth and logical form
Truth and logical form
✍ Robert Cummins πŸ“‚ Article πŸ“… 1975 πŸ› Springer Netherlands 🌐 English βš– 939 KB
Which truth values in fuzzy logics are d
Which truth values in fuzzy logics are definable?
✍ Hung T. Nguyen; Vladik Kreinovich; Antonio Di Nola πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 89 KB

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0, 1]. There are only denumerable many words and phrases and continuum many real numbers; thus, not every real number corresponds to some common sense degree of uncertainty. In this article

Minimization of disjunctive normal forms
Minimization of disjunctive normal forms of fuzzy logic functions
✍ Kabekode V.S. Bhat πŸ“‚ Article πŸ“… 1981 πŸ› Elsevier Science 🌐 English βš– 977 KB

In this paper, we present a consistent theory for the minimization of fuzzy functions given in disjunctive normal form by studying the structure of such functions. An O(N\*) time algorithm is given for minimization of a fuzzy function consisting entirely of elementary phrases. The minimal form in th