We introduce the notion of hypergroupoids HBinX, , and show that HBinX, is a super-semigroup of the semigroup BinX, via the identification x ↔ {x}. We prove that HBin * X, , ∅ is a BCK-algebra, and obtain several properties of HBin * X, .

Using the notion of anti fuzzy points and its besideness to and non-quasi-coincidence with a fuzzy set, new concepts of an anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their inter-relations and related properties are investigated in [3]. The notion of the new fuzzy subalgebra with thresholds are introduced and relationship between this notion and the new fuzzy subalgebra of a B...

Based on fuzzy set theory, extensions, translations and multiplications of ideals in BCK/BCI-algebras are discussed. Relations among fuzzy translations, fuzzy extensions and fuzzy multiplications of fuzzy ideals are investigated.

In this paper, we introduce the concept of doubt fuzzy H-ideals in BCKalgebras and study its some properties. Moreover, we provide characterizations of H-Artin BCK-algebras in terms of doubt fuzzy H-ideals.

We propose a method for explicit computation of the Chern character form of a holomorphic Hermitian vector bundle (E, h) over a complex manifold X in a local holomorphic frame. First, we use the descent equations arising in the double complex of (p, q)-forms on X and find the explicit degree decomposition of the Chern–Simons form csk associated to the Chern character form chk of (E, h). Second,...

Using the notion of anti fuzzy points and its besideness to and nonquasi-coincidence with a fuzzy set, new concepts in anti fuzzy subalgebras in BCK/BCI-algebras are introduced and their properties and relationships are investigated.