114 research outputs found
Interval valued intuitionistic -fuzzy -submodules
On the basis of the concept of the interval valued intuitionistic fuzzy sets
introduced by K.Atanassov, the notion of interval valued intuitionistic fuzzy
-submodules of an -module with respect to -norm and -norm
is given and the characteristic properties are described. The homomorphic
image and the inverse image are investigated.In particular, the connections
between interval valued intuitionistic -fuzzy -submodules and
interval valued intuitionistic -fuzzy submodules are discussed
Interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras
We introduce the concept of quasi-coincidence of a fuzzy interval value with
an interval valued fuzzy set. By using this new idea, we introduce the notions
of interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras and
investigate some of their related properties. Some characterization theorems of
these generalized interval valued fuzzy filters are derived. The relationship
among these generalized interval valued fuzzy filters of pseudo -algebras
is considered. Finally, we consider the concept of implication-based interval
valued fuzzy implicative filters of pseudo -algebras, in particular, the
implication operators in Lukasiewicz system of continuous-valued logic are
discussed
Characterizations of ordered semigroups in terms of (â, â â¨q)-fuzzy interior ideals
In this paper, we give characterizations of ordered semigroups in terms of (â, â â¨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (â, â â¨q)-fuzzy interior ideals (resp. (â, â â¨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (â, â â¨q)-fuzzy ideals and (â, â â¨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (â, â â¨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (â, â â¨q)-fuzzy ideals (resp. (â, â â¨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed
2-Absorbing Vague Weakly Complete Î-Ideals in Î-Rings
The aim of this study is to provide a generalization of prime vague Î-ideals in Î-rings by introducing non-symmetric 2-absorbing vague weakly complete Î-ideals of commutative Î-rings. A novel algebraic structure of a primary vague Î-ideal of a commutative Î-ring is presented by 2-absorbing weakly complete primary ideal theory. The approach of non-symmetric 2-absorbing K-vague Î-ideals of Î-rings are examined and the relation between a level subset of 2-absorbing vague weakly complete Î-ideals and 2-absorbing Î-ideals is given. The image and inverse image of a 2-absorbing vague weakly complete Î-ideal of a Î-ring and 2-absorbing K-vague Î-ideal of a Î-ring are studied and a 1-1 inclusion-preserving correspondence theorem is given. A vague quotient Î-ring of R induced by a 2-absorbing vague weakly complete Î-ideal of a 2-absorbing Î-ring is characterized, and a diagram is obtained that shows the relationship between these concepts with a 2-absorbing Î-ideal
Homomorphism and quotient of fuzzy k-hyperideals
In [15], we introduced the notion of weak (resp. strong) fuzzy k- hyperideal. In this note we investigate the behavior of them under homomorphisms of semihyperrings. Also we define the quotient of fuzzy weak (resp. strong) k-hyperideals by a regular relation of semihyperring and obtain some results
History and new possible research directions of hyperstructures
We present a summary of the origins and current developments of the theory of algebraic hyperstructures. We also sketch some possible lines of research
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