Study of Weak Fuzzy Automaton Homomorphisms on Single Input Fuzzy Automata

In this paper we have defined input-connected fuzzy automaton and established that in an input connected fuzzy automaton, element of an orbit maps to an element of the orbit under the weak fuzzy automaton endomorphism. Further, if an input x is unicore in the fuzzy automaton, then the number of weak fuzzy automaton endomorphisms of A(x) is equal to the number of states.

Minimization of Hesitant L-Fuzzy Automaton

In this paper, we study a new generalization for the notion of fuzzy automata, which we called hesitant L-fuzzy automaton (HLFA). We present the formulations of the mathematics framework for the theory of HLFA. Moreover, we present the concepts of hesitant L-fuzzy behavior and inverse hesitant L-fuzzy behavior recognized by a type of HLFA. After that, for any hesitant L-fuzzy language we present a minimal complete accessible deterministic hesitant L-fuzzy automaton recognizing that. Finally, we present an algorithm, which determines states of the minimal hesitant L-fuzzy automaton and we present the time complexity of the algorithm.

New directions in LB-valued general fuzzy automata: A topological view

In the current study, we define the different L-valued operators on LB-valued general fuzzy automata or simply LB-valued GFA, where B is considered as a complete infinitely distributive lattice of propositions about the GFA. In particular, this study demonstrates that the L-valued successor and predecessor operators induce L-valued co-topologies while the L-valued residuated and approximation operators induce L-valued topologies on the state set of given LB-valued GFA. Further, we show that the continuity and separation properties of such LB-valued general fuzzy automaton can be examined in terms of these topologies. Moreover, we study and explicate the LB-valued GFA structure space and LB-valued GFA homotopy in more details.

On Algebraic Properties of Inverse Fuzzy Languages

Aims/Objectives: In this paper, we investigate some of the algebraic properties of inverse fuzzy languages. We proved that a fuzzy automaton is inverse if and only if the transition monoid is an inverse monoid. A fuzzy language is an inverse fuzzy language if the minimal fuzzy automaton recognizing that fuzzy language is an inverse fuzzy automaton. We also discuss some more properties of an inverse fuzzy language based on the fact that an inverse monoid is one which is regular and idempotent commute.

The Relationship Among Fuzzy Languages, Upper Sets and Fuzzy Ordered Monoids

The concept of recognizability of a fuzzy language by crisp deterministic fuzzy automaton and monoid is well known. The purpose of the present work is to study the recognizability of fuzzy languages by fuzzy ordered monoids. We show that the upper sets of a given fuzzy ordered monoid play a nice role in such studies. Also, we introduce the syntactic fuzzy ordered monoid of an upper set which recognizes this upper set.