ON ASYMPTOTICALLY λ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

Ekrem Savaş ()
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Ekrem Savaş: Department of Mathematics, Istanbul Commerce University, Uskudar, Istanbul–Turkey, Turkey

New Mathematics and Natural Computation (NMNC), 2007, vol. 03, issue 03, 301-306

Abstract: This paper presents the following definition which is a natural combination of the definitions for asymptotically equivalent and λ-statistical convergence of fuzzy numbers. The two sequences [X] and [Y] of fuzzy numbers are said to be asymptotically λ-statistical equivalent of multipleLprovided that for every ∊ > 0\[ \lim_{n} \frac{1}{\lambda_{n}}\left |\left \{k\in I_{n}{:}\ d\left(\frac{X_{k}}{Y_{k}},L\right) \geq \epsilon \right \}\right |=0 \](denoted by$X \stackrel{S_{\lambda}^{L}(F)}{\sim} Y$) and simply asymptotically λ-statistical equivalent ifL = 1. In addition, we shall also present asymptotically equivalent analogs of Savas's theorems in Ref. 7.

Keywords: Fuzzy numbers; asymptotically equivalent; asymptotically λ-statistical equivalent (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S1793005707000781

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