by means of a kind of new idea, we consider  the $(in,ivq)$-fuzzy$h$-ideals of a hemiring.  first, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. then, a kind  of quotient hemiring  ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. moreover, the notions of generalized $varphi$-compatible$(in,ivq...

From the viewpoint of Behaviour based Control many control tasks can be divided into separate behaviour components. By defining the relevant behaviour components, the actual control action can be constructed based on the individual control actions of the component behaviours. In this case the control action is either related to an individual behaviour component or to a fusion of behaviour compo...

This material is studying MV-algebras and BL-algebras in terms of applicability in Boole algebra. Boole algebras are expanded use in fuzzy logic.

The axioms of iteration theories, or iteration categories, capture the equational properties of fixed point operations in several computationally significant categories. Iteration categories may be axiomatized by the Conway identities and identities associated with finite automata. We show that the Conway identities and the identities associated with the members of a subclass Q of finite automa...

In [1] the authors considered finitely-valued modal logics with Kripke style semantics where both propositions and the accessibility relation are valued over a finite residuated lattice. Unfortunately, the necessity operator does not satisfy in general the normality axiom (K). In this paper we focus on the case of finite chains, and we consider a different approach based on introducing a multim...

Proof systems based on rules with the property that all formulas contained in the assumptions are contained as subformulas in the conclusion as well, are particularly suitable for automated proof search. Systems of this kind were found for several well-known fuzzy logics. However, for BL (Basic Logic), the logic of continuous t-norms and their residua, the situation is less satisfactory. We con...

Quotient space theory (QST), a new granule computing tool dealing with imprecise, incomplete and uncertain knowledge, uses a triplet, including the universe, its structure and attributes, to describe a problem space or simply a space. As one of important theories of granular computing (GrC), QST is very helpful to the study of cognitive informatics (CI). This article summarizes the quotient spa...

Pseudo-MTL algebras or weak pseudo-BL algebras are non-commutative fuzzy structures which arise from pseudo-t-norms, namely, pseudo-BL algebras without the pseudo-divisibility condition. The aim of this paper is to investigate the properties of pseudo-BL algebras that also hold for pseudoMTL algebras. We will also study some classes of pseudo-MTL algebras such as good, local and Archimedean pse...