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In this paper, we study the notion of derivation on hoop algebras and also the (isotone, contractive, ideal, regular, idempotent and perfect) derivation on hoop algebras. We state and prove some theorems, which determine the relationship between these notions and other types of derivations on hoop algebra. We also find the equivalent condition for isotone derivation. The notion of derivations by introducing the notion of generalized derivation is extended. Also, some results on generalized derivation in hoop algebras are discussed and some equivalent conditions are given. We study some properties of new derivation and investigate some related properties of them and show that the fixed point set of a good generalized ideal derivation is a hoop algebra. [ABSTRACT FROM AUTHOR]

In this paper, the notion of fuzzy pseudo-CI-filter in a pseudo-CI-algebra is introduced and its elementary properties are investigated. With the upper level set, the relationship between pseudo-CI-filter and fuzzy pseudo-CI-filter is shown and this relationship is illustrated with an example. Some type of fuzzy pseudo-CI-filters and the relationships between them and the fuzzy pseudo-CI-filter are checked. We study generated fuzzy pseudo-CI-filter by a fuzzy set. In addition, the properties of fuzzy pseudo-CI-filter are studied in Noetherian and Artinian pseudo-CI-algebra. We construct a fuzzy pseudo-CI-filter by a strictly ascending sequence of pseudo-CI-filter of pseudo-CI-algebra and any strictly decreasing sequence in (0 , 1). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of hesitant fuzzy subsemiring, hesitant fuzzy ideals, hesitant fuzzy (bi, quasi, interior) ideals of (ordered) Γ -semiring. We characterize simple and regular (ordered) Γ -semiring by using hesitant fuzzy ideals. [ABSTRACT FROM AUTHOR]