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On Asymptotically Λ-Statistical Equivalent Sequences Of Fuzzy Numbers


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

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    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 multiple L provided 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 if L = 1. In addition, we shall also present asymptotically equivalent analogs of Savas's theorems in Ref. 7.

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    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 03 (2007)
    Issue (Month): 03 ()
    Pages: 301-306

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    Handle: RePEc:wsi:nmncxx:v:03:y:2007:i:03:p:301-306

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    Keywords: Fuzzy numbers; asymptotically equivalent; asymptotically λ-statistical equivalent;


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