In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

In this paper, a new concept of anti-homomorphism between two fuzzy groups G and G‫׀‬ is defined many results analogous to homomorphism of groups are established

Abstract. Studied is the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modeling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (PortRoyal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...

In this paper, the concept of fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) of an ordered group (resp. lattice-ordered group) is introduced and some properties, characterizations and related results are given. Also, the fuzzy convex subgroup (resp. fuzzy convex lattice-ordered subgroup) generated by a fuzzy subgroup (resp. fuzzy subsemigroup) is characterized. Furthermore,...

This paper studies the issue of similarity relations in fuzzy concept lattices. Fuzzy concepts and fuzzy concept lattices represent a formal approach to the modelling of non-sharp (fuzzy) concepts and conceptual structures in the sense of traditional (Port-Royal) logic. Applications of concept lattices are in representation of conceptual knowledge and in conceptual analysis of (fuzzy) data. Sim...

In this work we present constructions of algebraic lattices in Euclidean space with optimal center density in dimensions 2, 3, 4, 6, 8 and 12, which are rotated versions of the lattices 3n , for n = 2, 3, 4, 6, 8 and K12. These algebraic lattices are constructed through twisted canonical homomorphism via ideals of a ring of algebraic integers. Mathematical subject classification: 18B35, 94A15, ...