scholarly journals Positive Implicative Ideals of BCK-Algebras Based on Intersectional Soft Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Eun Hwan Roh ◽  
Young Bae Jun
Keyword(s):  
Extension Property ◽  
Algebraic Structures ◽  
Soft Sets ◽  
Algebraic Tool

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of int-soft positive implicative ideals is introduced, and related properties are investigated. Relations between an int-soft ideal and an int-soft positive implicative ideal are established. Characterizations of an int-soft positive implicative ideal are obtained. Extension property for an int-soft positive implicative ideal is constructed. The∧-product and∨-product of int-soft positive implicative ideals are considered, and the soft intersection (resp., union) of int-soft positive implicative ideals is discussed.

scholarly journals Applications of Soft Union Sets in the Ring Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Yongwei Yang ◽  
Xiaolong Xin ◽  
Pengfei He
Keyword(s):  
Ring Theory ◽  
Algebraic Structures ◽  
Soft Sets ◽  
Quotient Rings ◽  
Isomorphism Theorems ◽  
Algebraic Tool

The aim of the paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion ofλ,μ-soft union rings which is a generalization of that of soft union rings is proposed. By introducing the notion of soft cosets, soft quotient rings based onλ,μ-soft union ideals are established. Moreover, through discussing quotient soft subsets, an approach for constructing quotient soft union rings is made. Finally, isomorphism theorems ofλ,μ-soft union rings related to invariant soft sets are discussed.

scholarly journals A Novel Approach towards Bipolar Soft Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tahir Mahmood
Keyword(s):  
Decision Making ◽  
Algebraic Structures ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Novel Approach ◽  
Operational Laws

The notion of bipolar soft sets has already been defined, but in this article, the notion of bipolar soft sets has been redefined, called T-bipolar soft sets. It is shown that the new approach is more close to the concept of bipolarity as compared to the previous ones, and further it is discussed that so far in the study of soft sets and their generalizations, the concept introduced in this manuscript has never been discussed earlier. We have also discussed the operational laws of T-bipolar soft sets and their basic properties. In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.

scholarly journals Algebraic structures of soft sets associated with new operations

2011 ◽  
Vol 61 (9) ◽  
pp. 2647-2654 ◽  
Author(s):  
Muhammad Irfan Ali ◽  
Muhammad Shabir ◽  
Munazza Naz
Keyword(s):  
Algebraic Structures ◽  
Soft Sets

On fuzzy bipolar soft sets, their algebraic structures and applications

2014 ◽  
Vol 26 (4) ◽  
pp. 1645-1656 ◽  
Author(s):  
Munazza Naz ◽  
Muhammad Shabir
Keyword(s):  
Algebraic Structures ◽  
Soft Sets

scholarly journals Characterizations of Right Weakly Regular Semigroups in Terms of Generalized Cubic Soft Sets

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 293 ◽  
Author(s):  
Muhammad Gulistan ◽  
Feng Feng ◽  
Madad Khan ◽  
Aslıhan Sezgin
Keyword(s):  
Research Direction ◽  
Ideal Theory ◽  
Characteristic Functions ◽  
Algebraic Structures ◽  
Soft Sets ◽  
Regular Semigroups ◽  
Different Types ◽  
Associative Structures ◽  
New Research ◽  
The Ideal

Cubic sets are the very useful generalization of fuzzy sets where one is allowed to extend the output through a subinterval of [ 0 , 1 ] and a number from [ 0 , 1 ] . Generalized cubic sets generalized the cubic sets with the help of cubic point. On the other hand Soft sets were proved to be very effective tool for handling imprecision. Semigroups are the associative structures have many applications in the theory of Automata. In this paper we blend the idea of cubic sets, generalized cubic sets and semigroups with the soft sets in order to develop a generalized approach namely generalized cubic soft sets in semigroups. As the ideal theory play a fundamental role in algebraic structures through this we can make a quotient structures. So we apply the idea of neutrosophic cubic soft sets in a very particular class of semigroups namely weakly regular semigroups and characterize it through different types of ideals. By using generalized cubic soft sets we define different types of generalized cubic soft ideals in semigroups through three different ways. We discuss a relationship between the generalized cubic soft ideals and characteristic functions and cubic level sets after providing some basic operations. We discuss two different lattice structures in semigroups and show that in the case when a semigroup is regular both structures coincides with each other. We characterize right weakly regular semigroups using different types of generalized cubic soft ideals. In this characterization we use some classical results as without them we cannot prove the inter relationship between a weakly regular semigroups and generalized cubic soft ideals. This generalization leads us to a new research direction in algebraic structures and in decision making theory.

scholarly journals Double-Framed Soft Sets with Applications in BCK/BCI-Algebras

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Young Bae Jun ◽  
Sun Shin Ahn
Keyword(s):  
Soft Sets ◽  
Algebraic Tool

In order to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties, the notion of double-framed soft sets is introduced, and applications in BCK/BCI-algebras are discussed. The notions of double-framed soft algebras in BCK/BCI-algebras are introduced, and related properties are investigated. Characterizations of double-framed soft algebras are considered. Product and int-uni structure of double-framed soft algebras are discussed, and several examples are provided.

scholarly journals Applications of soft intersection sets to hemirings via SI-h-bi-ideals and SI-h-quasi-ideals

Filomat ◽  
2016 ◽  
Vol 30 (8) ◽  
pp. 2295-2313
Author(s):  
Xueling Ma ◽  
Jianming Zhan ◽  
Bijan Davvaz
Keyword(s):  
Algebraic Structures ◽  
Intersection Sets ◽  
Algebraic Tool

The aim of this paper is to lay a foundation for providing a soft algebraic tool in considering many problems that contains uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of SI-h-bi-ideals and SI-h-quasi-ideals of hemirings. The relationships between these kinds of soft intersection h-ideals are established. Finally, some characterizations of h-hemiregular, h-intra-hemiregular and h-quasi-hemiregular hemirings are investigated by these kinds of soft intersection h-ideals.

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