In 1965, Zadeh [14] introduced the concept of fuzzy subsets and studied their properties on the parallel lines to set theory. In 1971, Rosenfeld [10] defined the fuzzy subgroup and gave some of its properties. Rosenfeld’s definition of a fuzzy group is a turning point for pure mathematicians. Since then, the study of fuzzy algebraic structure has been pursued in many directions such as groups, ...

In this study, firstly, we interpret the level set, support, kernel for bipolar complex fuzzy (BCF) characteristic function, and BCF point. Then, subgroup, normal conjugate, normalizer cosets, abelian factor group. Furthermore, present associated examples theorems, prove these theorems. After that, image pre-image of subgroups under homomorphism related

This section define a level subring or level ideals obtain a set of necessary and sufficient condition for the equality of two ideals and characterizes field in terms of its fuzzy ideals. It also presents a procedure to construct a fuzzy subrings (fuzzy ideals) from any given ascending chain of subring ideal. We prove that the lattice of fuzzy congruence of group G (respectively ring R) is isom...

Right ternary near-rings (RTNR) are generalization of their binary counterpart and fuzzy soft sets are generalization of soft sets which are parameterized family of subsets of a universal set. In this paper fuzzy soft Nsubgroups, quasi-ideals and bi-ideals over a right ternary near-ring N are defined. The substructures N-subgroups, quasi-ideals and bi-ideals of an RTNR are characterized in term...

There are two equivalent de nitions of a fuzzy right ideal, fuzzy left ideal, fuzzy bi-ideal or fuzzy quasi-ideal f of an ordered semigroup (or a semigroup) S in the bibliography. The rst one is based on the fuzzy subset f itself, the other on the multiplication of fuzzy sets and the greatest fuzzy subset of S. Investigations in the existing bibliography are based on the rst de nition. The pres...

The learning of a Fuzzy Rule-Based Classification System (FRBCS) by means of a supervised inductive process fundamentally implies four tasks that are complementary among them: the selection of the most informative variables to the classification problem to solve, the generation of a set of rules, the selection of the subset of rules with the best co-operation and the least redundancy, and the e...

How to approximate an arbitrary fuzzy subset by an adequate extensional one is a key question within the theory of Extensional Fuzzy Subsets. In a recent paper by the authors [19] different methods were provided to find good approximations. In this work these methods are compared in order to understand better the performance and improvement they give.

This paper defined the notion of ω , θ -complex fuzzy sets, id="M3"> subgroupoid, and id="M4"> subgroups described important examples under id="M5"> sets. Additionally, we discussed conjugacy class group with respect to id="M6"> norma...

Fuzzy tori are finite dimensional C*-algebras endowed with an appropriate notion of noncommutative geometry inherited from ergodic action a closed subgroup the torus, which meant as approximations and more generally, quantum tori. A mean to specify space is by constructing over it spectral triple. We prove in this paper that we can construct triples on fuzzy which, dimension grows infinity unde...