Abstract
In the present paper, we introduce and study ideal convergence of some fuzzy sequence spaces via lacunary sequence, infinite matrix and Orlicz function. We study some topological and algebraic properties of these spaces. We also make an effort to show that these spaces are normal as well as monotone. Further, it is very interesting to show that if $I$ is not maximal ideal then these spaces are not symmetric.
Highlights
Introduction and preliminariesThe concept of ordinary convergence of a sequence of fuzzy numbers was introduced by Matloka [18] and proved some basic theorems for sequences of fuzzy numbers
13 (5) (2020), 1131-1148 and Savas [30] studied statistical convergence and statistically Cauchy for sequence of fuzzy numbers. They proved that a sequence of fuzzy numbers is statistically convergent if and only if it is statistically Cauchy
Esi et al [5] and Tripathy et al [40] have introduced a new type of generalized difference operators and unified those as follows: Let ν, m be non-negative integers, for Z a given sequence space, we have
Summary
Introduction and preliminariesThe concept of ordinary convergence of a sequence of fuzzy numbers was introduced by Matloka [18] and proved some basic theorems for sequences of fuzzy numbers. Let L(R) denotes the set of all fuzzy numbers. Lindenstrauss and Tzafriri [17] used the idea of Orlicz function to define the following sequence space
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