Distance and Similarity Measures for Generalized Hesitant Fuzzy Soft Sets

2018 ◽  
pp. 396-403 ◽  
Author(s):  
Chen Bin
Keyword(s):  
Similarity Measures ◽  
Soft Sets ◽  
Fuzzy Soft Sets

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 Similarity measures of Pythagorean fuzzy soft sets and clustering analysis

2021 ◽  
Author(s):  
Athira T M ◽  
Sunil Jacob John ◽  
Harish Garg
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Clustering Algorithm ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Pythagorean Fuzzy Set ◽  
Fuzzy Soft Sets ◽  
Membership Value

Abstract Pythagorean fuzzy set (PFS) is a broadening of intuitionistic fuzzy set that can represent the situations where the sum of membership and the non-membership values exceeds one. Adding parameterization to PFS we obtain a structure named as Pythagorean fuzzy soft set (PFSS). It has a higher capacity to deal with vagueness as it captures both the structures of a PFS and a soft set. Several practical situations demand the measure of similarity between two structures, whose sum of membership value and non-membership value exceeds one. There are no existing tools to measure the similarity between PFSS and this paper put forward similarity measures for PFSS. An axiomatic definition for similarity measure is proposed for PFSS and certain expressions for similarity measure are introduced. Further, some theorems which express the properties of similarity measures are proved. A comparative study between proposed expressions for similarity measure is carried out. Also, a clustering algorithm based on PFSS is introduced by utilizing the proposed similarity measure.

scholarly journals Similarity Measure and Entropy of Fuzzy Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhicai Liu ◽  
Keyun Qin ◽  
Zheng Pei
Keyword(s):  
Set Theory ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
The Other ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Uncertainty Measures ◽  
Fuzzy Soft Sets

Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. Recently, uncertainty measures of soft sets and fuzzy soft sets have gained attentions from researchers. This paper is devoted to the study of uncertainty measures of fuzzy soft sets. The axioms for similarity measure and entropy are proposed. A new category of similarity measures and entropies is presented based on fuzzy equivalence. Our approach is general in the sense that by using different fuzzy equivalences one gets different similarity measures and entropies. The relationships among these measures and the other proposals in the literatures are analyzed.

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

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.

Interval-valued Hesitant Fuzzy Soft Sets and their Application in Decision Making

2015 ◽  
Vol 141 (1) ◽  
pp. 71-93 ◽  
Author(s):  
Xindong Peng ◽  
Yong Yang
Keyword(s):  
Decision Making ◽  
Soft Sets ◽  
Fuzzy Soft Sets ◽  
Interval Valued
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