Fuzzy n-ary groups as a generalization of Rosenfeld's fuzzy groups

The notion of an $n$-ary group is a natural generalization of the notion of a group and has many applications in different branches. In this paper, the notion of (normal) fuzzy $n$-ary subgroup of an $n$-ary group is introduced and some related properties are investigated. Characterizations of fuzzy $n$-ary subgroups are given

Characterizations of LA-semigroups by new types of fuzzy ideals

In this article, we give some characterization results offuzzy left(right) ideals, fuzzy generalized bi-ideals and -fuzzy bi-ideals of an LA-semigroup. We also give some characterizations of LA-semigroups by the properties of fuzzy ideals.Comment: arXiv admin note: substantial text overlap with arXiv:1210.651

A New Type of Interval Valued Fuzzy Normal Subgroups of Groups

In this paper we are using the notions of not belonging and non quasi- -coincidence of an interval valued fuzzy point with an interval valued fuzzy set, we define the concepts of interval valued -fuzzy normal subgroups and interval valued -fuzzy cosets which is a generalizati on of fuzzy normal subgroups, fuzzy coset, interval valued fuzzy normal subgroups, interval valued fuzzy coset, interval valued -fuzzy normal subgroups and interval valued -fuzzy cosets. We give some characterizations of an interval valued -fuzzy normal subgroup and interval valued -fuzzy coset, and deal with several related properties. The important achievement of the study with an interval valued -fuzzy normal subgroup and interval valued -fuzzy cosets is the generalization of that the notions of fuzzy normal subgroups, fuzzy coset, interval valued fuzzy normal subgroups, interval valued fuzzy coset, interval valued -fuzzy normal subgroups and interval valued -fuzzy cosets. We prove that the set of all interval valued -fuzzy cosets of is a group, where the multiplication is defined by for all If is defined by for all Then is an interval valued -fuzzy normal subgroup o

On the converse of Fuzzy Lagrange's Theorem

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 groups

Characterizations of Fuzzy Fated Filters of R0R_0-algebras Based on Fuzzy Points

The most general form of the notion of quasi-coincidence of a fuzzy point with a fuzzy subset is considered, and generalization of fuzzy fated of $R_0$-algebras is discussed. The notion of an $(\epsilon , \epsilon \vee q_k)$-fuzzy fated filter in an $R_0$-algebra is introduced, and several properties are investigated. Characterizations of an $(\epsilon ,\epsilon \vee q_k)$-fuzzy fated filter in an $R_0$-algebra are discussed. Using a collection of fated filters, a $(\epsilon ,\epsilon \vee q_k)$-fuzzy fated filter is established.Comment: 6 page

A new generalization of fuzzy ideals in LA-semigroups

In this article, the concept of generalized fuzzy ideals in LA-semigroups. We introduced different types of generalized fuzzy ideals like bi-ideals, interior ideals and quasi ideals in LA-semigroup

Intra-regular Abel-Grassmann's groupoids

We characterize intra-regular Abel-Grassmann's groupoids by the properties of their ideals and $(\in ,\in!\vee q_{k})$-fuzzy ideals of various types

Soft MTL-algebras based on fuzzy sets

In this paper, we deal with soft MTL-algebras based on fuzzy sets. By means of $\in$-soft sets and q-soft sets, some characterizations of (Boolean, G- and MV-) filteristic soft MTL-algebras are investigated. Finally, we prove that a soft set is a Boolean filteristic soft MTL-algebra if and only if it is both a G-filteristic soft MTL-algebra and an MV-filteristic soft MTL-algebra

On lacunary statistically quasi-Cauchy sequences

The main object of this paper is to investigate lacunary statistically ward continuity. We obtain some relations between this kind of continuity and some other kinds of continuities. It turns out that any lacunary statistically ward continuous real valued function on a lacunary statistically ward compact subset $E\subset{\textbf{R}}$ is uniformly continuous.Comment: 20 page

A new variation on statistical ward continuity

A real valued function defined on a subset $E$ of $\mathbb{R}$, the set of real numbers, is $\rho$-statistically downward continuous if it preserves $\rho$-statistical downward quasi-Cauchy sequences of points in $E$, where a sequence $(\alpha_{k})$ of real numbers is called ${\rho}$-statistically downward quasi-Cauchy if $\lim_{n\rightarrow\infty}\frac{1}{\rho_{n} }|\{k\leq n: \Delta \alpha_{k} \geq \varepsilon\}|=0$ for every $\varepsilon>0$, in which $(\rho_{n})$ is a non-decreasing sequence of positive real numbers tending to $\infty$ such that $\limsup _{n} \frac{\rho_{n}}{n}<\infty$, $\Delta \rho_{n}=O(1)$, and $\Delta \alpha _{k} =\alpha _{k+1} - \alpha _{k}$ for each positive integer $k$. It turns out that a function is uniformly continuous if it is $\rho$-statistical downward continuous on an above bounded set.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1710.0051