A family of subsets of an n–set is k–locally thin if for every k of its member sets the ground set has at least one element contained in exactly 1 of them. We derive new asymptotic upper bounds for the maximum cardinality of locally thin set families for every even k. This improves on previous results of two of us with Monti. ∗Research supported in part by a USA Israeli BSF grant and by a grant...

A simple easy to implement algorithm is proposed to address wall tracking task of an autonomous robot. The robot should navigate in unknown environments, find the nearest wall, and track it solely based on locally sensed data. The proposed method benefits from coupling fuzzy logic and Q-learning to meet requirements of autonomous navigations. Fuzzy if-then rules provide a reliable decision maki...

The backing of the fuzzy ideal is normal ideal in some ring and in same time there fuzzy set whose is not fuzzy ideal and it backing set is ideal, i.e., it crisp is normal ideal. Consequently, in this paper we constructing a fuzziness function which defined on fuzzy sets and assigns membership grade for every fuzzy set whose it backing set are crisp ideal. Now, Let  be collection of all fuzzy s...

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.