In this paper a first step in classifying the fuzzy normalsubgroups of a finite group is made. Explicit formulas for thenumber of distinct fuzzy normal subgroups are obtained in theparticular cases of symmetric groups and dihedral groups.

In the present paper, we redefine the concept of FPFS-sets in algebra systems, which is a novel way that is different from the definition of FPFS-sets in hemirings by Liu [10]. Based on the definition, we put forth FPFS-groups, FPFSnormal subgroups and FP -equivalent fuzzy soft normal subgroups of groups. Further, some properties and characterizations are investigated. Finally, aggregate fuzzy ...

The Pythagorean fuzzy set is an extension of the intuitionistic used to handle uncertain circumstances in various decisions making problems. Group theory a mathematical technique for dealing with problems symmetry. This study deals group theory. In this article, we characterize notion subgroup and examine algebraic properties concept. An extensive on cosets subgroup, normal subgroups performed....

Approximate Herbrand theorems are established for first-order fuzzy logics based on continuous t-norms, and used to provide proof-theoretic proofs of Skolemization for their Prenex fragments. Decidability and complexity results for particular fragments are obtained as consequences.

Most normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve either tautologies or contradictions which are fundamental for automatic theorem provers based on refutation methods. De Morgan implicative systems are triples like the De Morgan system, but considering fuzzy implications instead of t-conorms. These s...

In this paper, we introduce the definition of E-inversive E-semigroup with fuzzy φ-kernel normal systems. It is described that the fuzzy regular congruences on the E-inversive E-semigroup with fuzzy φ-kernel normal systems.

A new approach to normalizing fuzzy sets is introduced where it is assumed that the normalization method is compatible with a given t-norm. In this context it is proved that the most usual ways to normalize fuzzy subsets correspond to the most common t-norms. For a given fuzzy subset μ, the corresponding normalized fuzzy subset μ̂ can be viewed as the distribution of μ conditioned on the (degree...