Search

In this paper, the space Fp of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets Mη is a topology on Fp, where η is a fuzzy ideal on H and Mη=θ∈Fp|η⊈θ. The only compact subset of the space Fp is given. A fuzzy congruence relation Θ on H is defined, and the homomorphism between the set of all fuzzy ideals of H and the set of all fuzzy ideals of H/Θ is established. Furthermore, we established an isomorphism between fuzzy spectrum of H and fuzzy spectrum of H/Θ.

In this paper, the concept of belligerent fuzzy GE-filter of GE-algebra is introduced. The relationship between a fuzzy GE-filter of GE-algebra and a belligerent fuzzy GE-filter of GE-algebra is given. Further, it is shown that a finite product (union) of belligerent fuzzy GE-filters of GE-algebras is a belligerent fuzzy GE-filter of the finite product (union) of GE-algebras.

In this paper, we study L-congruences and their kernel in a subclass Kn,0 of the variety of Ockham algebras A. We prove that the class of kernel L-ideals of an Ockham algebra forms a complete Heyting algebra. Moreover, for a given kernel L-ideal ξ on A, we obtain the least and the largest L-congruences on A having ξ as its kernel.

In this paper, we study fuzzy congruence relations and kernel fuzzy ideals of an Ockham algebra A,f, whose truth values are in a complete lattice satisfying the infinite meet distributive law. Some equivalent conditions are derived for a fuzzy ideal of an Ockham algebra A to become a fuzzy kernel ideal. We also obtain the smallest (respectively, the largest) fuzzy congruence on A having a given fuzzy ideal as its kernel.