There have been many similarity measures introduced into literature. The ones introduced and investigated in this article can be categorized as Minkowsky metric based fuzzy logic measures. We are using normal Łukasiewicz algebra as our fuzzy structure for our classifier. The major advantage of this method is that it provides semantical information about the classification task and it allows par...

—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 intervalvalued fuzzy propositional logic that are completely analogous to those for Boolean propositional logic. Thus, determinin...

When performing set-theoretical operations, such as intersection and union, on fuzzy sets, one can opt not to consider exact formula, but to leave the results less specific (in particular, interval-valued) by using both disjunctive and conjunctive representations (normal forms) of the underlying logical operations. We investigate which De Morgan triplets are suitable for this transformation (i....

The generalization of two-valued (crisp) sets to fuzzy sets gave us a rich and powerful representation scheme within the domain of semantic uncertainty. A parallel generalization of conjunctions and disjunction is needed from tnorms and t-conorms to what we might appropriately call linguistic (fuzzy) connectives, “AND," “OR," etc. In fact a closer look at the canonical forms of the combination ...

small polygroups are multi-valued systems that satisfy group-likeaxioms. using the notion of “belonging ($epsilon$)” and “quasi-coincidence (q)” offuzzy points with fuzzy sets, the concept of ($epsilon$, $epsilon$ $vee$ q)-fuzzy subpolygroups isintroduced. the study of ($epsilon$, $epsilon$ $vee$ q)-fuzzy normal subpolygroups of a polygroupare dealt with. characterization and some of the fundam...

In this contribution, an implicative variant of the conjunctive normal form will be recalled and further studied. This normal form is an alternative to the Perfilieva’s conjunctive normal form. It will be shown that it is a suitable model for a particular case of graded fuzzy rules introduced as a generalization of classical fuzzy rules. Moreover, approximation properties of the implicative var...

The theory of fuzzy sets was inspired by Zadeh [10]. Subsequently, Rosenfeld introduced the concept of a fuzzy subgroup of a group [9]. Fuzzy cosets and fuzzy normal subgroups of a group G have been studied in [3, 5, 8]. In [4], the ring of cosets of a fuzzy ideal was constructed. Let A and B be fuzzy subgroups of G such that B ⊆ A. The purpose of this paper is to introduce the notion of fuzzy ...

In this paper, we introduce some properties of an intuitionistic normal fuzzy m-subgroup of m- group with m-homomorphism and isomorphism. We study he image, the pre-image and the inverse mapping of the intuitionistic normal fuzzy m-‎subgroups.‎