in this paper, we use parametric form of fuzzy number and we converta fuzzy linear system to two linear system in crisp case. conditions for the existence of a minimal solution to $mtimes n$ fuzzy linear equation systems are derived and a numerical procedure for calculating the minimal solution is designed. numerical examples are presented to illustrate the proposed method.

State minimization is a fundamental problem in automata theory. The problem is also of great importance in the study of fuzzy automata. However, most work in the literature considered only state reduction of fuzzy automata, whereas the state minimization problem is almost untouched for fuzzy automata. Thus in this paper we focus on the latter problem. Formally, the decision version of the minim...

This work is towards the study of the relationship between fuzzy preordered sets and Alexandrov (left/right) fuzzy topologies based on generalized residuated lattices here the fuzzy sets are equipped with generalized residuated lattice in which the commutative property doesn't hold. Further, the obtained results are used in the study of fuzzy automata theory.

In this thesis, we consider minimality and size reduction issues of one-tape and multitape automata. Although the topic of minimization of one-tape automata has been widely studied for many years, it seems that some issues have not gained attention. One of these issues concerns finding specific conditions on automata that imply their minimality in the class of nondeterministic finite automata (...

We give a new version of fuzzy alternating Büchi automata over distributive lattices: weights are putting in every leaf node of run trees rather than along with edges from every node to its children. Such settings are great benefit to obtain complement just by taking dual operation and replacing each final weight with its complement. We prove that L-fuzzy nondeterministic Büchi automata have th...

We generalize the previous results that were obtained by Kohout for relations based on fuzzy Basic Logic systems (BL) of Hájek and also for relational systems based on left-continuous tnorms. The present paper extends generalized morphisms into the realm of Monoidal Fuzzy Logics by first proving and then using relational inequalities over pseudo-associative BK-products of relations in these log...

This paper is a contribution to the discussion of the problem, whether there is a fuzzy logic that can be considered as the real fuzzy logic. We give reasons for taking IMTL, BL, LΠ and Ev L (fuzzy logic with evaluated syntax) as those fuzzy logics that should be indeed taken as the real fuzzy logics.