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Many uncertainties arise in real-world problems, making them impossible to solve using conventional approaches. Researchers all over the world have developed new mathematical theories like fuzzy set theory and rough set theory to better understand the uncertainties that occur in various fields. Soft set theory, which was recently introduced, offers a novel approach to real-world problem solving by removing the need to set the membership function. This is helpful in resolving a variety of issues, and much progress is being made these days. Recently, Jun introduced the concept of a hybrid structure, which blends the concepts of a fuzzy set as well as a soft set. In this paper, we define the hybrid k-sum and hybrid k-product of k-ideals of semiring and investigate their properties. We illustrate with an example that the hybrid sum and hybrid product of two k-ideals are not always hybrid ideals. We also describe semiring regularity constraints in terms of hybrid k-ideal structures. [ABSTRACT FROM AUTHOR]

In recent years, the Fuzzy theory has emerged as the most active area of research in many branches of mathematics and engineering. This new theory was introduced by L.A. Zadeh in 1965 and since then large number of research papers have been appeared by using the concept of Fuzzy set/numbers and fuzzification of many classical theories has also been made. The object of this paper is to define the intuitionistic Fuzzy I-convergent double sequence spaces 2SI(μ,v)(T, f ) and 2SI (μ,v)0(T, f ) defined by Compact Operator and Modulus Function. We study some topological and algebraic properties of these spaces and discuss the Fuzzy topology on them. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce the concept of λ-statistical convergence of weight g of fuzzy numbers by using ideal. In addition to this concept, some inclusion theorems are also presented. [ABSTRACT FROM AUTHOR]

In this paper, our aim is to introduce and study some new spaces of lacunary I - convergence for sequence of fuzzy real number which are defined by compact operator (T) on the real space ℝ. i.e., c F I θ (T) , c F 0 I θ (T) , ℓ F ∞ I θ (T) , ℓ F ∞ θ (T) and examine some basic properties and prove some inclusions relation on these spaces. [ABSTRACT FROM AUTHOR]

In this paper, following a very recent and new approach of [1], we discuss a relation between two kinds of I-convergence of sequences, namely, I-statistical convergence of weight g and I-lacunary statistical convergence of weight g, where g : ℕ → [0,∞) is a function satisfying lim/ n→∞ g (n)=∞and n/g(n) ↛ 0 as n→ ∞ for fuzzy numbers. These methods are based on the methods of statistical convergence and lacunary statistical summability for sequences. Analogs of inclusion and consistency theorems for the sequential methods are established. [ABSTRACT FROM AUTHOR]

In this paper, we present an unified approach which defines interval valued L-fuzzy ideals of nearrings by incorporating interval valued t-norms and t-conorms. We characterize interval valued L-fuzzy ideals in terms of their level subsets. We study insertion of factors property and relate interval valued fuzzy points with interval valued fuzzy ideals. [ABSTRACT FROM AUTHOR]

In this paper, we introduce new notions, namely, ideal statistical convergence and ideal lacunary statistical convergence for fuzzy numbers, their relationship and also make some observations about these classes. [ABSTRACT FROM AUTHOR]

An ideal I is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper we introduce ideal convergent sequence spaces of fuzzy numbers using σ-bounded variation and Orlicz functions and study some basic topological and algebraic properties of these spaces. Finally we investigate the inclusions relations related to these spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of $\mathcal{I}$-statistical convergence and $\mathcal{I}$-lacunary statistical convergence with respect to the intuitionistic fuzzy norm $\left( \mu,v\right) $, investigate their relationship, and make some observations about these classes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two different stabilizers of X with respect to Y for subsets X and Y of an MV-algebra A. We show that stabilizers are ideals and we investigate the relation between stabilizers and some other ideals in MV-algebras. We also show that if I and J are ideals in an MV-algebra A, then the stabilizer of I with respect to J is the relative pseudo-complement of I with respect to J in the lattice of ideals of A. [ABSTRACT FROM AUTHOR]

In this paper we introduce some new double sequence spaces of fuzzy real numbers by combining I-convergence, Orlicz function and four dimensional matrix and we examine some properties of the resulting sequences spaces of fuzzy numbers. [ABSTRACT FROM AUTHOR]

An ideal I is a family of subsets of positive integers $\mathbb{N}$ which is closed under taking finite unions and subsets of its elements. In this paper we have introduced ideal convergent sequences of fuzzy real numbers using σ-uniform density. Furthermore, inclusion between Iσ-convergence and invariant convergence also Iσ-convergence and $[V_{\sigma}]^{F}_p$-convergence were given. [ABSTRACT FROM AUTHOR]

In this paper, using the difference operator of order m, the sequences of Orlicz functions and double lacunary sequence we introduce and study some classes of sequences of fuzzy numbers defined by I-convergence. We study some basic topological and algebraic properties of these spaces. Also we investigate the relations related to these spaces. [ABSTRACT FROM AUTHOR]