scholarly journals Multiaspect Soft Sets

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Nor Hashimah Sulaiman ◽  
Daud Mohamad
Keyword(s):  
Soft Set ◽  
Soft Sets ◽  
Basic Concepts ◽  
Novel Concept

We introduce a novel concept of multiaspect soft set which is an extension of the ordinary soft set by Molodtsov. Some basic concepts, operations, and properties of the multiaspect soft sets are studied. We also define a mapping on multiaspect soft classes and investigate several properties related to the images and preimages of multiaspect soft sets.

scholarly journals Combination of the Single-Valued Neutrosophic Fuzzy Set and the Soft Set with Applications in Decision-Making

Symmetry ◽  
2020 ◽  
Vol 12 (8) ◽  
pp. 1361 ◽  
Author(s):  
Ahmed Mostafa Khalil ◽  
Dunqian Cao ◽  
Abdelfatah Azzam ◽  
Florentin Smarandache ◽  
Wedad R. Alharbi
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Example ◽  
Fuzzy Soft Sets ◽  
Novel Concept

In this article, we propose a novel concept of the single-valued neutrosophic fuzzy soft set by combining the single-valued neutrosophic fuzzy set and the soft set. For possible applications, five kinds of operations (e.g., subset, equal, union, intersection, and complement) on single-valued neutrosophic fuzzy soft sets are presented. Then, several theoretical operations of single-valued neutrosophic fuzzy soft sets are given. In addition, the first type for the fuzzy decision-making based on single-valued neutrosophic fuzzy soft set matrix is constructed. Finally, we present the second type by using the AND operation of the single-valued neutrosophic fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example.

A new type of generalized picture fuzzy soft set and its application in decision making

2021 ◽  
pp. 1-17
Author(s):  
Hanchuan Lu ◽  
Ahmed Mostafa Khalil ◽  
W. Alharbi ◽  
M. A. El-Gayar
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Fuzzy Decision Making ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
New Type ◽  
Fuzzy Soft Sets ◽  
Novel Concept ◽  
Fuzzy Parameter

 In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Finally, we give a comparison between the picture fuzzy soft set theory and the generalized picture fuzzy soft set theory. It is shown that our proposed (i.e., generalized picture fuzzy soft set theory) is viable and provide decision makers a more mathematical insight before making decisions on their options.

scholarly journals On Fuzzy Soft Set-Valued Maps with Application

2020 ◽  
pp. 26-35
Author(s):  
Shehu Shagari Mohammed
Keyword(s):  
Fixed Point ◽  
Everyday Life ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
New Concepts ◽  
Tremendous Progress ◽  
Fuzzy Soft Sets ◽  
Novel Concept

Soft set and fuzzy soft set theories are proposed as mathematical tools for dealing with uncertainties. There has been tremendous progress concerning the extensions of these theories from different point of views of researchers so as to accommodate more robust and expressive applications in everyday life. In line with this development, in this paper, we combine the two aforementioned notions to initiate a novel concept of set-valued maps whose range set is a family of fuzzy soft sets. The later idea is employed to define Suzuki-type fuzzy soft $(e,K)$-weak contractions, thereby establishing some related fuzzy soft fixed point theorems. As a consequence, several well-known Suzuki-type fixed point theorems are derived as corollaries. Examples are also provided to validate the new concepts and to support the authenticity of the obtained results. Moreover, an application in homotopy is considered to show the usability of the obtained results.

On m-polar Diophantine fuzzy N-soft set with applications

2020 ◽  
Vol 23 ◽  
Author(s):  
Jia-Bao Liu ◽  
Shahbaz Ali ◽  
Muhammad Khalid Mahmood ◽  
Muhammad Haris Mateen
Keyword(s):  
Fuzzy Sets ◽  
Hybrid Model ◽  
Intuitionistic Fuzzy Sets ◽  
Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Proposed Model ◽  
Fuzzy Soft Sets ◽  
Novel Concept ◽  
Intuitionistic Fuzzy Soft Sets

Introduction: In this paper, we present a novel hybrid model m-polar Diophantine fuzzy N-soft set and define operations on it. Methods: We generalize the concepts of fuzzy sets, soft sets, N-soft sets, fuzzy soft sets, intuitionistic fuzzy sets, intuitionistic fuzzy soft sets, Pythagorean fuzzy sets, Pythagorean fuzzy soft sets and Pythagorean fuzzy N-soft sets by incorporating our proposed model. Additionally, we define three different sorts of complements for Pythagorean fuzzy Nsoft sets and examine few outcomes which do not hold in Pythagorean fuzzy N-soft sets complements unlike to crisp set. We further discuss about (α, β, γ) -cut of m-polar Diophantine fuzzy N-soft sets and their properties. Lastly, we prove our claim that the defined model is a generalization of soft set, N-soft set, fuzzy N-soft set, intuitionistic fuzzy N soft set and Pythagorean fuzzy N-soft set. Results: m-polar Diophantine fuzzy N-soft set is more efficient and an adaptable model to manage uncertainties as it also overcome drawbacks of existing models which are to be generalized. Conclusion: We introduced novel concept of m-polar Diophantine fuzzy N-soft sets (MPDFNS sets).

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 Generalised Interval-Valued Fuzzy Soft Set

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Abdul Razak Salleh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Decision Making Problem ◽  
Fuzzy Soft Sets ◽  
Interval Valued

We introduce the concept of generalised interval-valued fuzzy soft set and its operations and study some of their properties. We give applications of this theory in solving a decision making problem. We also introduce a similarity measure of two generalised interval-valued fuzzy soft sets and discuss its application in a medical diagnosis problem: fuzzy set; soft set; fuzzy soft set; generalised fuzzy soft set; generalised interval-valued fuzzy soft set; interval-valued fuzzy set; interval-valued fuzzy soft set.

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 On Fuzzy Soft Sets

2009 ◽  
Vol 2009 ◽  
pp. 1-6 ◽  
Author(s):  
B. Ahmad ◽  
Athar Kharal
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Fuzzy Soft Sets

We further contribute to the properties of fuzzy soft sets as defined and studied in the work of Maji et al. ( 2001), Roy and Maji (2007), and Yang et al. (2007) and support them with examples and counterexamples. We improve Proposition 3.3 by Maji et al., (2001). Finally we define arbitrary fuzzy soft union and fuzzy soft intersection and prove DeMorgan Inclusions and DeMorgan Laws in Fuzzy Soft Set Theory.

Connectedness Between Soft Sets

2018 ◽  
Vol 14 (01) ◽  
pp. 53-71 ◽  
Author(s):  
Samajh Singh Thakur ◽  
Alpa Singh Rajput
Keyword(s):  
Soft Set ◽  
Topological Spaces ◽  
Soft Sets ◽  
Continuous Mappings ◽  
Weakly Continuous

In the present paper, the concepts of soft connectedness between soft sets, soft set-connected and soft weakly continuous mappings in soft topological spaces have been introduced and studied.

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