Related papers: A new equivalence relation to classify the fuzzy s…
This article computes the number of fuzzy subgroups of symmetric group $S_5$. First, an equivalence relation on the set of all fuzzy subgroups of a group G is defined.Without any equivalence relation on fuzzy subgroups of group G, the…
Preferential equality is an equivalence relation on fuzzy subsets of finite sets and is a generalization of classical equality of subsets. In this paper we introduce a tightened version of the preferential equality on fuzzy subsets and…
By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize those pairs of fuzzy sets which form fuzzy rough sets w.r.t. a t-similarity relation…
We study infinite approximate subgroups of soluble Lie groups. Generalising a theorem of Fried and Goldman we show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building up on this result we…
The purpose of this paper is to determine the number of fuzzy subgroups of a finite abelian group of order $p^{n}q^{m}$. As an application of our main result, explicit formulas for the number of fuzzy subgroups of…
In these notes we will survey recent results on various finitary approximation properties of infinite groups. We will discuss various restrictions on groups that are approximated for example by finite solvable groups or finite-dimensional…
Since categories are graphs with additional "structure", one should start from fuzzy graphs in order to define a theory of fuzzy categories. Thus is makes sense to introduce categories whose morphisms are associated with a plausibility…
In fuzzy theory of sets and groups, the use of $\alpha$--levels is a standard to translate problems from the fuzzy to the crisp framework. Using strong $\alpha$--levels, it is possible to establish a one to one correspondence which makes…
We investigate classifications of quasitrivial semigroups defined by certain equivalence relations. The subclass of quasitrivial semigroups that preserve a given total ordering is also investigated. In the special case of finite semigroups,…
In this paper, we have tried to apply the concepts of fuzzy sets to Lie groups and its relative concepts. First, we define a ${\cal C}^1$ fuzzy submanifold after reviewing ${\cal C}^1-$fuzzy manifold definition. In main section, we defined…
We give a brief introduction to the notion of an 'approximate group' and some of its numerous applications.
In fuzzy group theory many versions of the well-known Lagrange's theorem have been studied. The aim of this article is to investigate the converse of one of those results. This leads to an interesting characterization of finite cyclic…
We classify all finite groups with five relative commutativity degrees. Also, we give a partial answer to our previous conjecture on a lower bound of the number of relative commutativity degrees of finite groups.
We give some inclusion relations for arbitrary fuzzy sets with reference to famous inequalities. In particular, we can know that the bounded sum and the algebraic product go well together. We would like to propose the concept of `Fuzzy Set…
We give new characterizations of sofic groups: -- A group $G$ is sofic if and only if it is a subgroup of a quotient of a direct product of alternating or symmetric groups. -- A group $G$ is sofic if and only if any system of equations…
In this paper we introduce and study the concept of distinct fuzzy subgroups commutativity degree of a finite group G. This quantity measures the probability of two random distinct fuzzy subgroups of G commuting. We determine distinct fuzzy…
In this paper we introduce and study the poset of equivalence classes of subgroups of a finite group $G$, induced by the isomorphism relation. This contains the well-known lattice of solitary subgroups of $G$. We prove that in several…
The theory of fuzzy semigroups is a branch of mathematics that arose in early 90's as an effort to characterize properties of semigroups by the properties of their fuzzy subsystems which include, fuzzy subsemigroups and their alike, fuzzy…
In this article we introduce and study a class of finite groups for which the orders of normal subgroups satisfy a certain inequality. It is closely connected to some well-known arithmetic classes of natural numbers.
We introduced and study fuzzy gamma-hypersemigroups, according to fuzzy semihyper- groups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy…