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 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.

(α,β)-Soft Intersectional Rings and Ideals with their Applications

2019 ◽  
Vol 15 (02) ◽  
pp. 333-350 ◽  
Author(s):  
Chiranjibe Jana ◽  
Madhumangal Pal ◽  
Faruk Karaaslan ◽  
Aslihan Sezgi̇n
Keyword(s):  
Set Theory ◽  
Real Life ◽  
Ring Structure ◽  
Ring Theory ◽  
Mathematical Framework ◽  
Soft Sets ◽  
Life Problems ◽  
New Concepts ◽  
Ring Structures ◽  
Algebraic Tool

Molodtsov initiated the soft set theory, providing a general mathematical framework for handling uncertainties that we encounter in various real-life problems. The main object of this paper is to lay a foundation for providing a new soft algebraic tool for considering many problems that contain uncertainties. In this paper, we introduce a new kind of soft ring structure called [Formula: see text]-soft-intersectional ring based on some results of soft sets and intersection operations on sets. We also define [Formula: see text]-soft-intersectional ideal and [Formula: see text]-soft-intersectional subring, and investigate some of their properties using these new concepts. We obtain some results in ring theory based on [Formula: see text]-soft intersection sense and its application in ring structures. Furthermore, we provide relationships between soft-intersectional ring and [Formula: see text]-soft-intersectional ring, soft-intersectional ideal and [Formula: see text]-soft-intersectional ideal.

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.

Application of Fuzzy Soft Sets in Job Requirement Problem

2019 ◽  
Vol 10 (1) ◽  
pp. 184-189
Author(s):  
S. Sandhiya ◽  
K. Selvakumari
Keyword(s):  
Soft Sets ◽  
Fuzzy Soft Sets

Soft sets and soft topology on nearness approximation spaces

Filomat ◽  
2017 ◽  
Vol 31 (13) ◽  
pp. 4117-4125 ◽  
Author(s):  
Hatice Tasbozan ◽  
Ilhan Icen ◽  
Nurettin Bagirmaz ◽  
Abdullah Ozcan
Keyword(s):  
Soft Sets ◽  
Approximation Spaces ◽  
Soft Topology

Generalized interval-valued hesitant intuitionistic fuzzy soft sets

2021 ◽  
pp. 1-12
Author(s):  
Admi Nazra ◽  
Yudiantri Asdi ◽  
Sisri Wahyuni ◽  
Hafizah Ramadhani ◽  
Zulvera
Keyword(s):  
Hesitant Fuzzy Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Binary Operations ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Soft Sets ◽  
Comparison Table ◽  
Definition Of ◽  
Interval Valued ◽  
Intuitionistic Fuzzy Soft Sets

This paper aims to extend the Interval-valued Intuitionistic Hesitant Fuzzy Set to a Generalized Interval-valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS). Definition of a GIVHIFSS and some of their operations are defined, and some of their properties are studied. In these GIVHIFSSs, the authors have defined complement, null, and absolute. Soft binary operations like operations union, intersection, a subset are also defined. Here is also verified De Morgan’s laws and the algebraic structure of GIVHIFSSs. Finally, by using the comparison table, a different approach to GIVHIFSS based decision-making is presented.

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.

Selection principles in the context of soft sets: Menger spaces

2021 ◽  
Vol 25 (20) ◽  
pp. 12693-12702 ◽  
Author(s):  
Ljubiša D. R. Kočinac ◽  
Tareq M. Al-shami ◽  
Vildan Çetkin
Keyword(s):  
Soft Sets ◽  
Menger Spaces ◽  
Selection Principles

An algebraic approach to N-soft sets with application in decision-making using TOPSIS

2021 ◽  
pp. 1-21
Author(s):  
Muhammad Shabir ◽  
Rimsha Mushtaq ◽  
Munazza Naz
Keyword(s):  
Decision Making ◽  
Mathematical Models ◽  
Real World ◽  
Algebraic Approach ◽  
Multi Criteria Decision Making ◽  
Commutative Monoids ◽  
Soft Sets ◽  
Algebraic Properties ◽  
Different Types ◽  
Selection Of

In this paper, we focus on two main objectives. Firstly, we define some binary and unary operations on N-soft sets and study their algebraic properties. In unary operations, three different types of complements are studied. We prove De Morgan’s laws concerning top complements and for bottom complements for N-soft sets where N is fixed and provide a counterexample to show that De Morgan’s laws do not hold if we take different N. Then, we study different collections of N-soft sets which become idempotent commutative monoids and consequently show, that, these monoids give rise to hemirings of N-soft sets. Some of these hemirings are turned out as lattices. Finally, we show that the collection of all N-soft sets with full parameter set E and collection of all N-soft sets with parameter subset A are Stone Algebras. The second objective is to integrate the well-known technique of TOPSIS and N-soft set-based mathematical models from the real world. We discuss a hybrid model of multi-criteria decision-making combining the TOPSIS and N-soft sets and present an algorithm with implementation on the selection of the best model of laptop.

scholarly journals Algebraic conditions and the sparsity of spectrally arbitrary patterns

2021 ◽  
Vol 9 (1) ◽  
pp. 257-274
Author(s):  
Louis Deaett ◽  
Colin Garnett
Keyword(s):  
Major Goal ◽  
Algebraic Condition ◽  
Open Question ◽  
Algebraic Tool ◽  
General Method ◽  
Square Matrix ◽  
Spectrally Arbitrary

Abstract Given a square matrix A, replacing each of its nonzero entries with the symbol * gives its zero-nonzero pattern. Such a pattern is said to be spectrally arbitrary when it carries essentially no information about the eigenvalues of A. A longstanding open question concerns the smallest possible number of nonzero entries in an n × n spectrally arbitrary pattern. The Generalized 2n Conjecture states that, for a pattern that meets an appropriate irreducibility condition, this number is 2n. An example of Shitov shows that this irreducibility is essential; following his technique, we construct a smaller such example. We then develop an appropriate algebraic condition and apply it computationally to show that, for n ≤ 7, the conjecture does hold for ℝ, and that there are essentially only two possible counterexamples over ℂ. Examining these two patterns, we highlight the problem of determining whether or not either is in fact spectrally arbitrary over ℂ. A general method for making this determination for a pattern remains a major goal; we introduce an algebraic tool that may be helpful.

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