Quotient is a basic operation of formal languages, which plays key role in the construction minimal deterministic finite automata (DFA) and universal automata. In this paper, we extend to power series systemically investigate its implications study weighted particular, define two quotient operations for are called (left or right) quotients residuals respectively. Algebraic properties closure (w...

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.

Recently, Yamamoto presented a new method for the conversion from regular expressions (REs) to non-deterministic finite automata (NFA) based on the Thompson ε-NFA (AT). The AT automaton has two quotients discussed: the suffix automaton Asuf and the prefix automaton, Apre. Eliminating ε-transitions in AT, the Glushkov automaton (Apos) is obtained. Thus, it is easy to see that Asuf and the partia...

BL-algebras, introduced by P.Hájek, form an algebraic counterpart of the basic fuzzy logic. In the paper it is shown that BL-algebras are the duals of bounded representable DRl-monoids. This duality enables us to describe some structure properties of BL-algebras.

For a given reachable automaton A, we prove that the (state-)endomorphism monoid End(A) divides its characteristic monoid M(A). Hence so does its (state-)automorphism group Aut(A), and, for finite A, Aut(A) is a homomorphic image of a subgroup of the characteristic monoid. It follows that in the presence of a (state-) automorphism group G of A, a finite automaton A (and its transformation monoi...

In this paper, we deal with Molaei’s generalized groups. We definethe notion of a fuzzy generalized subgroup with respect to a t-norm (orT-fuzzy generalized subgroup) and give some related properties. Especially,we state and prove the Representation Theorem for these fuzzy generalizedsubgroups. Next, using the concept of continuity of t-norms we obtain a correspondencebetween TF(G), the set of ...

The aim of this paper is to define a new kind of fuzzy gamma ring. So the concepts of fuzzy gamma ring, fuzzy ideal, fuzzy quotient gamma ring, and fuzzy gamma homomorphism are introduced.

We study the norm induced by the supremum metric on the space of fuzzy numbers. And then we propose a method for constructing a norm on the quotient space of fuzzy numbers. This norm is very natural and works well with the induced metric on the quotient space.