Algebraic structures especially an ordered semigroups play a prominent role in mathematics with wide ranging applications in many disciplines such as control engineering, computer arithmetics, coding theory, sequential machines and formal languages. A theory of fuzzy sets in terms of fuzzy points on ordered semigroups can be developed. In this paper, we generalize the concept of (α, β)-fuzzy le...

Algebraic properties and structures of intuitionistic $$L-$$ fuzzy multiset finite automata (ILFMA) are discussed through congruences on a semigroup in this paper. Firstly, we put forward the notion compatible relation, monoid associated with relation can be effectively constructed, construct two monoids different congruence relations given ILFMA, then prove that they isomorphic. Furthermore, u...

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In this paper, our approach is to study properties of approximations on nearness approximation spaces. Afterwards, our aim is to define near semigroups and near ideals on near approximation spaces. We introduce some properties of these near structures. The nearness of sets and, in particular, the nearness of algebraic structures on nearness approximation spaces fits within the milieu of fuzzy s...

following the categorical approach to universal algebra through algebraic theories, proposed by f.~w.~lawvere in his phd thesis, this paper aims at introducing a similar setting for general topology. the cornerstone of the new framework is the notion of emph{categorically-algebraic} (emph{catalg}) emph{topological theory}, whose models induce a category of topological structures. we introduce t...

Fuzzy spaces are obtained by quantizing adjoint orbits of compact semi-simple Lie groups. Fuzzy spheres emerge from quantizing S and are associated with the group SU(2) in this manner. They are useful for regularizing quantum field theories and modeling spacetimes by non-commutative manifolds. We show that fuzzy spaces are Hopf algebras and in fact have more structure than the latter. They are ...

in this paper, we study fuzzy substructures in connection withhv-structures. the original idea comes from geometry, especially from thetwo dimensional euclidean vector space. using parameters, we obtain a largenumber of hyperstructures of the group-like or ring-like types. we connect,also, the mentioned hyperstructures with the theta-operations to obtain morestrict hyperstructures, as hv-groups...

in this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. we also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

This paper belongs to our series of works on algebraic geometry over arbitrary structures. In this one, there will be investigated seven equivalences (namely: geometric, universal quasi-equational, universal, elementary, and combinations thereof) in specific classes structures (equationally Noetherian, qω-compact, uω-compact, equational domains, co-domains, etc.). The main questions are the fol...