On Generalized Double Statistical Convergence of Order α in Intuitionistic Fuzzy Normed Spaces

Ekrem Savaş

doi:10.3390/mca21030036

Abstract

Our goal in this work is to introduce the notion V , λ ( I ) 2 -summability and ideal λ-double statistical convergence of order α with respect to the intuitionistic fuzzy norm μ , v . We also make some observations about these spaces and prove some inclusion relations.

Highlights

Intuitionistic fuzzy set (IFNS) is one of the generalizations of fuzzy set theory [1]
IFNS is characterized by a membership function and a non-membership function such that the sum of both values is less than one
We intend to use ideals to introduce the concept of Iλ-double statistical convergence of order α with respect to the intuitionistic fuzzy normed space (μ, v), and study some of its consequences

Summary

Introduction

Intuitionistic fuzzy set (IFNS) is one of the generalizations of fuzzy set theory [1]. In [26] Mohiuddine and Lohani introduced the notion of the generalized statistical convergence in intuitionistic fuzzy normed spaces. We intend to use ideals to introduce the concept of Iλ-double statistical convergence of order α with respect to the intuitionistic fuzzy normed space (μ, v), and study some of its consequences. Using the continuous t-norm and t-conorm, Saadati and Park [4] has recently introduced the concept of intuitionistic fuzzy normed space as follows. The five-tuple (X, μ, v, ∗, ♦) is said to be an intuitionistic fuzzy normed space (for short, IFNS) if X is a vector space, ∗ is a continuous t-norm, ♦ is a continuous t-conorm, and μ, v are fuzzy sets on X × (0, ∞) satisfying the following conditions for every x, y ∈ X, and s, t > 0 [4]: Math.

Iλ-Double Statistical Convergence on IFNS

Conclusions