ON ASYMPTOTICALLY λ-STATISTICAL EQUIVALENT SEQUENCES OF FUZZY NUMBERS

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.