Abstract
The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (λ, μ)-ideal statistical convergence and strongly weighted (λ, μ)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.
Highlights
In 1965, Zadeh [1], an expert in cybernetics at University of California, first proposed the concept of fuzzy set theory
Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers
We have examined relevant inclusion relations concerning weighted (λ, μ ) -ideal statistical convergence and strongly weighted (λ, μ ) -ideal convergence of double sequences of fuzzy numbers
Summary
In 1965, Zadeh [1], an expert in cybernetics at University of California, first proposed the concept of fuzzy set theory. Fuzzy set theory and its applications have been attracting the attention of researchers from various areas of science, engineering and technology. The practical problems we have to solve often involve uncertainty, which can be expressed by fuzzy number [2]. In the following research work, the convergence problem of sequences of fuzzy numbers is important.
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