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.

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.

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 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.

scholarly journals Data Analysis Approach for Incomplete Interval-Valued Intuitionistic Fuzzy Soft Sets

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1061
Author(s):  
Hongwu Qin ◽  
Huifang Li ◽  
Xiuqin Ma ◽  
Zhangyun Gong ◽  
Yuntao Cheng ◽  
...  
Keyword(s):  
Missing Data ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Intuitionistic Fuzzy ◽  
Degree Of Membership ◽  
Filling Method ◽  
Fuzzy Soft Sets ◽  
Interval Valued ◽  
Intuitionistic Fuzzy Soft Sets

The model of interval-valued intuitionistic fuzzy soft sets is a novel excellent solution which can manage the uncertainty and fuzziness of data. However, when we apply this model into practical applications, it is an indisputable fact that there are some missing data in many cases for a variety of reasons. For the purpose of handling this problem, this paper presents new data processing approaches for an incomplete interval-valued intuitionistic fuzzy soft set. The missing data will be ignored if percentages of missing degree of membership and nonmember ship in total degree of membership and nonmember ship for both the related parameter and object are below the threshold values; otherwise, it will be filled. The proposed filling method fully considers and employs the characteristics of the interval-valued intuitionistic fuzzy soft set itself. A case is shown in order to display the proposed method. From the results of experiments on all thirty randomly generated datasets, we can discover that the overall accuracy rate is up to 80.1% by our filling method. Finally, we give one real-life application to illustrate our proposed method.

scholarly journals Object–Parameter Approaches to Predicting Unknown Data in an Incomplete Fuzzy Soft Set

2017 ◽  
Vol 27 (1) ◽  
pp. 157-167 ◽  
Author(s):  
Yaya Liu ◽  
Keyun Qin ◽  
Chang Rao ◽  
Mahamuda Alhaji Mahamadu
Keyword(s):  
Similarity Measures ◽  
Soft Set ◽  
Data Sets ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Forecasting Accuracy ◽  
Fuzzy Soft Sets ◽  
Object Parameter ◽  
Parameter Approach ◽  
Exchange Data

Abstract The research on incomplete fuzzy soft sets is an integral part of the research on fuzzy soft sets and has been initiated recently. In this work, we first point out that an existing approach to predicting unknown data in an incomplete fuzzy soft set suffers from some limitations and then we propose an improved method. The hidden information between both objects and parameters revealed in our approach is more comprehensive. Furthermore, based on the similarity measures of fuzzy sets, a new adjustable object-parameter approach is proposed to predict unknown data in incomplete fuzzy soft sets. Data predicting converts an incomplete fuzzy soft set into a complete one, which makes the fuzzy soft set applicable not only to decision making but also to other areas. The compared results elaborated through rate exchange data sets illustrate that both our improved approach and the new adjustable object-parameter one outperform the existing method with respect to forecasting accuracy.

scholarly journals MCGDM Based on VIKOR and TOPSIS Methods Using Spherical Interval Valued Fuzzy Soft With Aggregation Operators

2021 ◽  
Author(s):  
ARULMOZHI K ◽  
Palanikumar M
Keyword(s):  
Score Function ◽  
Soft Set ◽  
Point Of View ◽  
Ideal Solution ◽  
Fuzzy Soft Set ◽  
Decision Matrix ◽  
Soft Sets ◽  
Strong Point ◽  
Fuzzy Soft Sets ◽  
Interval Valued

Abstract Spherical interval valued fuzzy soft set (SIVFS set) has much stronger ability than Pythagorean interval valued fuzzy soft set and interval valued intuitionistic fuzzy soft set. Now, we talk about aggregated operation for aggregating SIVFS decision matrix. TOPSIS and VIKOR methods are strong point of view for multi criteria group decision making (MCGDM), which is a various extensions of interval valued fuzzy soft sets. We talk through a score function based on aggregating TOPSIS and VIKOR method to the SIVFS-positive ideal solution and the SIVFSnegative ideal solution. Also TOPSIS and VIKOR methods are provides the weights of decision makings. To nd out the optimal alternative under closeness is introduced.

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