The aim of this paper is to introduce and study the notions of fuzzy upper $e$-limit set, fuzzy lower $e$-limit set and fuzzy $e$-continuously convergent functions. Properties and basic relationships among fuzzy upper $e$-limit set, fuzzy lower $e$- limit set and fuzzy $e$-continuity are investigated via fuzzy $e$-open sets.

Reinforcement learning based on a new training method previously reported guarantees convergence and an almost complete set of rules. However, there are two shortcomings remained: first, the membership functions of the input sensor readings are determined manually and take the same form; and second, there are still a small number of blank rules needed to be manually inserted. To address these t...

In this article we introduce and investigate the notion of ∆(r)-null, ∆(r)-convergent and ∆(r)-bounded sequences of fuzzy numbers which generalize the notion of null, convergent and bounded sequence of fuzzy numbers. 2000 Mathematics Subject Classification: 40A05, 40D25.

In this paper we introduced the space of   bounded and   convergent difference sequence of fuzzy soft real numbers and the space of  lacunary   statistically convergent different sequence of fuzzy soft real numbers relating these concepts some theorem are derive. Keyword Fuzzy soft real number,   bounded,   convergent and  lacunary   statistically convergent.

In this article, we introduce the notion of statistically pre-Cauchy double sequence of fuzzy numbers. Then we present a characterization of the class of bounded statistically pre-Cauchy double sequences of fuzzy numbers with the help of Orlicz function. Further, we present a characterization of the class of bounded statistically convergent double sequences of fuzzy numbers and linked with Cesà...

We study conditions under which the solutions of a fuzzy integral equation are bounded. 1. Introduction. The concept of set-valued functions and their calculus [2] were found useful in some problems in economics [3], as well as in control theory [17]. Later on, the notion of H-differentiability was introduced by Puri and Ralesku in order to extend the differential of set-valued functions to tha...

The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72