Abstract-In this paper, we introduce the concept of skew semi-Heyting algebra and extend the notions of semi-Heyting algebras. We characterize a skew semi-Heyting algebra as a skew Heyting algebra interms of a unique binary operation on which an induced binary operation is defined, and some algebraic properties on it.

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.

This paper deals on boosters and β-filters in MS-almost distributive lattice M. It is proved that the set of all boosters in M is a bounded distributive lattice. Characterization of β-filters of M in terms of boosters is established and a dual homomorphism of M and the set of all boosters of M is derived. Further, it is shown that every filter in M is an e-filter and every maximal filter in M is a β-filter. Equivalent conditions on which the set of all boosters is a relatively complemented lattice are established.

In this paper, we give some results of closure fuzzy filters of decomposable MS-algebras, characterization of closure fuzzy filters, and homomorphism of closure fuzzy filters. It is observed that the class of all closure fuzzy filters of a decomposable MS-algebra forms a bounded distributive lattice. We have also characterized the class of all closure fuzzy filters of a decopmposable MS-algebra in terms of boosters. Some properties of the homomorphic images and the inverse images of closure fuzzy filters are studied.

In this paper, the space F p of fuzzy prime ideals of Heyting almost distributive lattice H is studied, and it is shown that the collection of all sets M η is a topology on F p , where η is a fuzzy ideal on H and M η = θ ∈ F p | η ⊈ θ . The only compact subset of the space F p 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 .