Abstract
In this article we introduce the notion of p-absolutely summable class of sequences of fuzzy real numbers with fuzzy metric, $\ell_p^F$,for $1 \leq p < \infty$. We study some of its properties like completeness, symmetricity, solidness and convergence free. Also we study some inclusion results.
Highlights
In this article we introduce the notion of p-absolutely summable class of sequences of fuzzy real numbers with fuzzy metric, lF∞, for 1 ≤ p < ∞
The set of all upper-semi continuous, normal, convex fuzzy real numbers is denoted by R(I)
Throughout the article, by a fuzzy real number we mean that the number belongs to R(I)
Summary
Abstract: In this article we introduce the notion of p-absolutely summable class of sequences of fuzzy real numbers with fuzzy metric, lF∞, for 1 ≤ p < ∞. If there exists t0 ∈ R such that X(t0) = 1, the fuzzy real number X is called normal. The set of all upper-semi continuous, normal, convex fuzzy real numbers is denoted by R(I). The α-level set [X]α of the fuzzy real number X, for 0 < α ≤ 1, defined as [X]α = {t ∈ R : X(t) ≥ α}. A fuzzy real number X is called non-negative if X(t) = 0, for all t < 0.
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