scholarly journals (M,N)-Soft Intersection BL-Algebras and Their Congruences

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xueling Ma ◽  
Hee Sik Kim
Keyword(s):  
Soft Set ◽  
Algebraic Structures ◽  
Intersection Sets ◽  
Algebraic Tool

The purpose of this paper is to give a foundation for providing a new soft algebraic tool in considering many problems containing uncertainties. In order to provide these new soft algebraic structures, we discuss a new soft set-(M, N)-soft intersection set, which is a generalization of soft intersection sets. We introduce the concepts of (M, N)-SI filters of BL-algebras and establish some characterizations. Especially, (M, N)-soft congruences in BL-algebras are concerned.

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.

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 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 Closed Int Soft -Ideals and Int Soft c--Ideals

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Young Bae Jun ◽  
Kyoung Ja Lee ◽  
Eun Hwan Roh
Keyword(s):  
Algebraic Structures ◽  
Commutative Ideal ◽  
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 notions of closed intersectional soft -ideals and intersectional soft commutative -ideals are introduced, and related properties are investigated. Conditions for an intersectional soft -ideal to be closed are provided. Characterizations of an intersectional soft commutative -ideal are established, and a new intersectional soft c--ideal from an old one is constructed.

scholarly journals On (α,β)-US Sets in BCK/BCI-Algebras

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 252 ◽  
Author(s):  
Chiranjibe Jana ◽  
Madhumangal Pal
Keyword(s):  
Set Theory ◽  
Extension Property ◽  
Soft Set ◽  
Closed Ideal ◽  
Mathematical Framework ◽  
Algebraic Structures ◽  
Information Analysis ◽  
Commutative Ideal ◽  
Characterization Theorems

Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to B C K / B C I -algebras. Firstly, we introduce the notion of the ( α , β ) -Union-Soft ( ( α , β ) -US) set, with some supporting examples. Then, we discuss the soft B C K / B C I -algebras, which are called ( α , β ) -US algebras, ( α , β ) -US ideals, ( α , β ) -US closed ideals, and ( α , β ) -US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an ( α , β ) -US ideal to be an ( α , β ) -US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of ( α , β ) -unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of ( α , β ) -unions. Finally, the extension property for an ( α , β ) -US commutative ideal is established.

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

On soft set-valued maps and integral inclusions

2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Mathematical Tool ◽  
Multivalued Maps ◽  
Soft Sets ◽  
Special Cases ◽  
New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

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