scholarly journals A Novel Approach to Neutrosophic Soft Rough Set under Uncertainty

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 384 ◽  
Author(s):  
Ashraf Al-Quran ◽  
Nasruddin Hassan ◽  
Emad Marei
Keyword(s):  
Rough Set ◽  
Incomplete Data ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Novel Approach ◽  
Proposed Model ◽  
Neutrosophic Logic ◽  
Soft Rough Set ◽  
Lower And Upper Approximations

To handle indeterminate and incomplete data, neutrosophic logic/set/probability were established. The neutrosophic truth, falsehood and indeterminacy components exhibit symmetry as the truth and the falsehood look the same and behave in a symmetrical way with respect to the indeterminacy component which serves as a line of the symmetry. Soft set is a generic mathematical tool for dealing with uncertainty. Rough set is a new mathematical tool for dealing with vague, imprecise, inconsistent and uncertain knowledge in information systems. This paper introduces a new rough set model based on neutrosophic soft set to exploit simultaneously the advantages of rough sets and neutrosophic soft sets in order to handle all types of uncertainty in data. The idea of neutrosophic right neighborhood is utilised to define the concepts of neutrosophic soft rough (NSR) lower and upper approximations. Properties of suggested approximations are proposed and subsequently proven. Some of the NSR set concepts such as NSR-definability, NSR-relations and NSR-membership functions are suggested and illustrated with examples. Further, we demonstrate the feasibility of the newly rough set model with decision making problems involving neutrosophic soft set. Finally, a discussion on the features and limitations of the proposed model is provided.

scholarly journals Soft Classes and Soft Rough Classes with Applications in Decision Making

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Faruk Karaaslan
Keyword(s):  
Decision Making ◽  
Rough Set ◽  
Rough Sets ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Novel Method ◽  
Lower And Upper Approximations

Rough set was defined by Pawlak in 1982. Concept of soft set was proposed as a mathematical tool to cope with uncertainty and vagueness by Molodtsov in 1999. Soft sets were combined with rough sets by Feng et al. in 2011. Feng et al. investigated relationships between a subset of initial universe of soft set and a soft set. Feng et al. defined the upper and lower approximations of a subset of initial universe over a soft set. In this study, we firstly define concept of soft class and soft class operations such as union, intersection, and complement. Then we give some properties of soft class operations. Based on definition and operations of soft classes, we define lower and upper approximations of a soft set. Subsequently, we introduce concept of soft rough class and investigate some properties of soft rough classes. Moreover, we give a novel decision making method based on soft class and present an example related to novel method.

Modified rough bipolar soft sets

2020 ◽  
Vol 39 (3) ◽  
pp. 4259-4283
Author(s):  
Muhammad Shabir ◽  
Rizwan Gul
Keyword(s):  
Rough Set ◽  
Rough Sets ◽  
Group Decision ◽  
Soft Set ◽  
New Technique ◽  
Approximation Space ◽  
Soft Sets ◽  
Accuracy Measure ◽  
Soft Rough Set ◽  
A New Technique

Bipolar soft sets and rough sets are two different techniques to cope with uncertainty. A possible fusion of rough sets and bipolar soft sets is proposed by Karaaslan and Çağman. They introduced the notion of bipolar soft rough set. In this article, a new technique is being introduced to study roughness through bipolar soft sets. In this new technique of finding approximations of a set, flavour of both theories of bipolar soft set and rough set is retained. We call this new hybrid model modified rough bipolar soft set MRBS-set. Moreover, accuracy measure and roughness measure of modified rough bipolar soft sets are defined in MRBS-approximation space and its application in multi-criteria group decision making is presented.

Comparative Analysis of Hybrid Soft Set Methods

2014 ◽  
pp. 360-383
Author(s):  
Debadutta Mohanty
Keyword(s):  
Information System ◽  
Comparative Analysis ◽  
Set Theory ◽  
Rough Set ◽  
Rough Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Rough Set ◽  
Definition Of ◽  
The Relationship

The whole mathematical scenario has changed with the advent of the Rough Set Theory, a powerful tool to deal with uncertainty and incompleteness of knowledge in information system. With the advancement of research, the Soft Set Theory has emerged as an advanced mathematical tool to deal with data associated with uncertainty. The present chapter endeavors to forge a connection between soft set and rough set and maps a new model rough soft set to address the challenges of vagueness and impreciseness. Although the research contribution of M. Irfan Ali, Dan Meng, et al. and Feng Feng et al. had given distinct definition of rough soft set and soft rough set, the analysis explaining the genesis of these sets is not appropriate. This chapter is a new attempt to construct the relationship between a rough set, soft set, and fuzzy set to form a hybrid soft set giving a concrete comprehensive definition of rough soft set in border perspective.

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.

scholarly journals An algorithm for fuzzy soft set based decision making approach

2020 ◽  
Vol 30 (1) ◽  
pp. 59-70
Author(s):  
Shehu Mohammed ◽  
Akbar Azam
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Group Decision Making ◽  
Group Decision ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Priority Table

The notion of soft set theory was initiated as a general mathematical tool for handling ambiguities. Decision making is viewed as a cognitive-based human activity for selecting the best alternative. In the present time, decision making techniques based on fuzzy soft sets have gained enormous attentions. On this development, this paper proposes a new algorithm for decision making in fuzzy soft set environment by hybridizing some existing techniques. The first novelty is the idea of absolute scores. The second concerns the concept of priority table in group decision making problems. The advantages of our approach herein are stronger power of objects discrimination and a well-determined inference.

scholarly journals A note on soft near-rings and idealistic soft near-rings

Filomat ◽  
2011 ◽  
Vol 25 (1) ◽  
pp. 53-68 ◽  
Author(s):  
Aslıhan Sezgin ◽  
Osman Atagün ◽  
Emin Aygün
Keyword(s):  
Set Theory ◽  
Theoretical Aspect ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Theoretical Approaches

Molodtsov introduced the theory of soft sets, which can be seen as an effective mathematical tool to deal with uncertainties, since it is free from the difficulties that the usual theoretical approaches have troubled. In this paper, we apply the definitions proposed by Ali et al. [M. I. Ali, F. Feng, X. Liu, W. K. Min and M. Shabir, On some new operations in soft set theory, Comput. Math. Appl. 57 (2009), 1547-1553] to the concept of soft near- rings and substructures of soft near-rings, proposed by Atag?n and Sezgin [A. O. Atag?n and A. Sezgin, Soft Near-rings, submitted] and show them with illustrating examples. Moreover, we investigate the properties of idealistic soft near-rings with respect to the near-ring mappings and we show that the structure is preserved under the near-ring epimorphisms. Main purpose of this paper is to extend the study of soft near-rings from a theoretical aspect.

scholarly journals Intuitionistic Fuzzy Soft Rough Set and Its Application in Decision Making

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Set Theory ◽  
Rough Set ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Mathematical Tool ◽  
Intuitionistic Fuzzy ◽  
Rough Approximation ◽  
Soft Rough Set

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. In this paper, we present concepts of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets, and investigate some properties of soft rough intuitionistic fuzzy sets and intuitionistic fuzzy soft rough sets in detail. Furthermore, classical representations of intuitionistic fuzzy soft rough approximation operators are presented. Finally, we develop an approach to intuitionistic fuzzy soft rough sets based on decision making and a numerical example is provided to illustrate the developed approach.

scholarly journals A new approach to bipolar soft sets and its applications

2015 ◽  
Vol 07 (04) ◽  
pp. 1550054 ◽  
Author(s):  
Faruk Karaaslan ◽  
Serkan Karataş
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Set Operations ◽  
First Results

Molodtsov [Soft set theory-first results, Comput. Math. App. 37 (1999) 19–31] proposed the concept of soft set theory in 1999, which can be used as a mathematical tool for dealing with problems that contain uncertainty. Shabir and Naz [On bipolar soft sets, preprint (2013), arXiv:1303.1344v1 [math.LO]] defined notion of bipolar soft set in 2013. In this paper, we redefine concept of bipolar soft set and bipolar soft set operations as more functional than Shabir and Naz’s definition and operations. Also we study on their basic properties and we present a decision making method with application.

scholarly journals Bipolar Soft Topological Spaces

2020 ◽  
Vol 13 (2) ◽  
pp. 227-245
Author(s):  
Asmaa Fadel ◽  
Syahida Che Dzul-Kifli
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
The Other ◽  
Topological Spaces ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Positive Information ◽  
Soft Limit ◽  
Soft Point ◽  
Soft Topological Space

Bipolar soft set theory is a mathematical tool associates between bipolarity and soft set theory, it is defined by two soft sets one of them gives us the positive information where the other gives us the negative. The goal of our paper is to define the bipolar soft topological space on a bipolar soft set and study its basic notions and properties. We also investigate the definitions of: bipolar soft interior, bipolar soft closure, bipolar soft exterior, bipolar soft boundary and establish some important properties on them. Some relations between them are also discussed. Moreover, the notions of bipolar soft point, bipolar soft limit point and the derived set of a bipolar soft set are discussed. In additions, examples are presented to illustrate our work.

scholarly journals Generalized Trapezoidal Fuzzy Soft Set and Its Application in Medical Diagnosis

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Zhang ◽  
Lan Shu ◽  
Shilong Liao
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Mathematical Tool ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets

Soft set theory is a newly emerging mathematical tool to deal with uncertain problems. In this paper, by introducing a generalization parameter, which itself is trapezoidal fuzzy, we define generalized trapezoidal fuzzy soft sets and then study some of their properties. Finally, applications of generalized trapezoidal fuzzy soft sets in a decision making problem and medical diagnosis problem are shown.

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