In this paper, we have developed an algebraic theory, suitable for the analysis of fuzzy systems. We have used the notions of semiring and semimodule, introduced the notion of semilinear space and gave numerous examples of them and defined also the notions of linear dependence and independence. Then, we have shown that the composition operation, which plays an essential role in the analysis of ...

Recently, fuzzy multi-sets have come to the forefront of scientists’ interest and been used in algebraic structures such as multi-groups, multi-rings, anti-fuzzy multigroup (α, γ)-anti-fuzzy subgroups. In this paper, we first summarize knowledge about structure γ)-anti-multi-fuzzy a way, notion is an application multi sets theory group. The concept complement set that generalizes both theories ...

Fuzzy Description Logics have been widely studied as a formalism for representing and reasoning withvague knowledge. One of the most basic reasoning tasks in (fuzzy) Description Logics is to decide whetheran ontology representing a knowledge domain is consistent. Surprisingly, not much is known about thecomplexity of this problem for semantics based on complete De Morgan lattices. T...

An important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic, is that of a filter. Filters can be used, amongst others, to define congruence relations. Specific kinds of filters include Boolean filters and prime filters. In this paper, we define several different filters of residuated lattices and triangle algebras and examine their mutual...

We provide a generalization of one-sided (crisp-fuzzy) concept lattices, based on Galois connections. Our approach allows analysis of object-attribute models with different structures for truth values of attributes. Moreover, we prove that this method of creating one-sided concept lattices is the most general one, i.e., with respect to the set of admissible formal contexts, it produces all Galo...

The aim of this paper is to study the actions of the groups on lattices and to give some connections between the structure of a group and the structure of its subgroup lattice. Moreover, we shall introduce the concept of direct ∨-sum of G-sublattices and we shall present a generalization of a result about finite nilpotent groups. 1 Preliminaries Let (G, ·, e) be a monoid and L be a G–set (relat...

this paper continues the investigation of the rst author begun in part one. the hereditary properties of n-homomorphism amenability for banach algebras are investigated and the relations between n-homomorphism amenability of a banach algebra and its ide- als are found. analogous to the character amenability, it is shown that the tensor product of two unital banach algebras is n-homomorphism am...

In our real life, bipolar fuzzy theory is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. In this paper, we provide a general algebraic framework for handling bipolar information by combining the theory of bipolar fuzzy sets with hemirings. First, we present the concepts of b...