Some Results of Anti Fuzzy Subrings Over t-Conorms

In this paper, we define anti fuzzy subrings by using t-conorm C and study some of their algebraic properties. We consider properties of intersection, direct product and homomorphisms for anti fuzzy subbrings with respect to t-conorm C. Thereafter, we define anti fuzzy quotient subrings over t-conorm C

Inverse System in The Category of Intuitionistic Fuzzy Soft Modules

This paper begins with the basic concepts of soft module. Later, we introduce inverse system in the category of intutionistic fuzzy soft modules and prove that its limit exists in this category. Generally, limit of inverse system of exact sequences of intutionistic fuzzy soft modules is not exact. Then we define the notion  which is first derived functor of the inverse limit functor. Finally, using methods of homology algebra, we prove that the inverse system limit of exact sequence of intutionistic fuzzy soft modules is exact

The Universal Coefticient Theorem in the Category of Fuzzy Soft Modules

This paper begins with the basic concepts of chain comlexes of fuzzy soft modules. Later, we introduce short exact sequence of fuzzy soft modules and prove that split short exact sequence of fuzzy soft chain complex. Naturally, we want to investigate whether or not the universal coefficient theorems are satisfied in category of fuzzy soft chain complexes. However, in the proof of these theorems in the category of chain complexes, exact sequence of homology modules of chain complexes is used. Generally, sequence of fuzzy soft homology modules is not exact in fuzzy chain complexes. Therefore in this study, we construct exact sequence of fuzzy soft homology modules under some conditions. Universal coefficients theorem is proven by making use of this idea

Gradual and Fuzzy Modules: Functor Categories

The categorical treatment of fuzzy modules presents some problems, due to the well known fact that the category of fuzzy modules is not abelian, and even not normal. Our aim is to give a representation of the category of fuzzy modules inside a generalized category of modules, in fact, a functor category, Mod-P, which is a Grothendieck category. To do that, first we consider the preadditive category P, defined by the interval P = (0,1], to build a torsionfree class J in Mod-P, and a hereditary torsion theory in Mod-P, to finally identify equivalence classes of fuzzy submodules of a module M with F-pair, which are pair (G, F), of decreasing gradual submodules of M, where G belongs to J, satisfying G = F-d, and U alpha F (alpha) is a disjoint union of F(1) and F(alpha)\G(alpha), where alpha is running in (0, 1].Programa Operativo FEDER 2014-2020 A-FQM-394-UGR20Consejeria de Economia, Conocimiento, Empresas y Universidad de la Junta de Andalucia (Spain

NeutroAlgebra Theory, volume I

Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more