Abstract
The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed (every real number r is replaced by a fuzzy number (either triangular fuzzy number or singleton fuzzy set (fuzzy point))). And then, we will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence.
Highlights
Zadeh 1 introduced the concept of fuzzy set in 1965
Z is the family of fuzzy integer numbers, where every r ∈ Z r ∈ Z is a singleton fuzzy set fuzzy point see 7–12
Q and Q are the family of fuzzy rational numbers and the family of fuzzy irrational numbers, respectively, where every r ∈ Q r ∈ Q or r ∈ Q r ∈ Q is a triangular fuzzy number and by using the representation Theorem the resolution principle
Summary
The aim of this paper is to introduce and study the fuzzy neighborhood, the limit fuzzy number, the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence on the base which is adopted by Abdul Hameed every real number r is replaced by a fuzzy number r either triangular fuzzy number or singleton fuzzy set fuzzy point. We will consider that some results respect effect of the upper sequence on the convergent fuzzy sequence, the bounded fuzzy sequence, and the Cauchy fuzzy sequence
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