scholarly journals A New Approach to Entropy and Similarity Measure of Vague Soft Sets

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Dan Hu ◽  
Zhiyong Hong ◽  
Yong Wang
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Uncertainty Measures

We focus our discussion on the uncertainty measures of vague soft sets. We propose axiomatic definitions of similarity measure and entropy for vague soft sets. Furthermore, we present a new category of similarity measures and entropies for vague soft sets. The basic properties of these measures are discussed and the relationships among these measures are analyzed.

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.

Some Hybrid Soft Sets and Their Application in Decision Making

2016 ◽  
pp. 86-117 ◽  
Author(s):  
Pinaki Majumdar
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Basic Properties ◽  
Two Hybrid

In this chapter the notions of two hybrid soft sets, namely fuzzy parameterized soft sets and vague soft sets has been discussed and some operations on them are defined. Some properties of these two hybrid soft sets under these operations are also studied. Application of fuzzy parameterized soft sets and vague soft sets in decision making has also been shown. Then the notion of similarity measure between two hybrid soft sets has been introduced and their basic properties are studied. Applications of these similarity measures in various problems like medical diagnosis and decision making have been shown. The idea of entropy of a fuzzy parameterized soft set has been introduced.

scholarly journals A Novel Approach towards Bipolar Soft Sets and Their Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tahir Mahmood
Keyword(s):  
Decision Making ◽  
Algebraic Structures ◽  
Soft Sets ◽  
New Approach ◽  
Basic Properties ◽  
Novel Approach ◽  
Operational Laws

The notion of bipolar soft sets has already been defined, but in this article, the notion of bipolar soft sets has been redefined, called T-bipolar soft sets. It is shown that the new approach is more close to the concept of bipolarity as compared to the previous ones, and further it is discussed that so far in the study of soft sets and their generalizations, the concept introduced in this manuscript has never been discussed earlier. We have also discussed the operational laws of T-bipolar soft sets and their basic properties. In the end, we have deliberated the algebraic structures associated with T-bipolar soft sets and the applications of T-bipolar soft sets in decision-making problems.

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 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 New Entropy-Based Similarity Measure between Interval-Valued Intuitionstic Fuzzy Sets

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 73 ◽  
Author(s):  
Saida Mohamed ◽  
Areeg Abdalla ◽  
Robert John
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
Fuzzy Decision Making ◽  
Fuzzy Decision ◽  
New Approach ◽  
Interval Valued

In this paper, we propose a new approach to constructing similarity measures using the entropy measure for Interval-Valued Intuitionistic Fuzzy Sets. In addition, we provide several illustrative examples to demonstrate the practicality and effectiveness of the proposed formula. Finally, we use the new proposed similarity measure to develop a new approach for solving problems of pattern recognition and multi-criteria fuzzy decision-making.

scholarly journals n-Valued Refined Neutrosophic Soft Sets and their Applications in Decision Making Problems and Medical Diagnosis

2018 ◽  
Vol 8 (1) ◽  
pp. 79-86 ◽  
Author(s):  
Shawkat Alkhazaleh ◽  
Ayman A. Hazaymeh
Keyword(s):  
Decision Making ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Soft Set ◽  
Soft Sets ◽  
Numerical Example

Abstract In this work we use the concept of a ‘n’-valued refined neutrosophic soft sets and its properties to solve decision making problems, Also a similarity measure between two ‘n’-valued refined neutrosophic soft sets are proposed. A medical diagnosis (MD) method is established for ‘n’-valued refined neutrosophic soft set setting using similarity measures. Lastly a numerical example is given to demonstrate the possible application of similarity measures in medical diagnosis (MD).

scholarly journals DISTANCE AND SIMILARITY MEASURES FOR SOFT SETS

2010 ◽  
Vol 06 (03) ◽  
pp. 321-334 ◽  
Author(s):  
ATHAR KHARAL
Keyword(s):  
Similarity Measure ◽  
Matrix Representation ◽  
Similarity Measures ◽  
Matching Function ◽  
Soft Sets ◽  
Fundamental Assumption ◽  
Set Operations ◽  
Erroneous Result

In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.

scholarly journals Decision making algorithmic techniques based on aggregation operations and similarity measures of possibility intuitionistic fuzzy hypersoft sets

2021 ◽  
Vol 7 (3) ◽  
pp. 3866-3895
Author(s):  
Atiqe Ur Rahman ◽  
◽  
Muhammad Saeed ◽  
Hamiden Abd El-Wahed Khalifa ◽  
Walaa Abdullah Afifi ◽  
...  
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Similarity Measures ◽  
Soft Set ◽  
Fuzzy Soft Set ◽  
Soft Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Approximate Function

<abstract><p>Soft set has limitation for the consideration of disjoint attribute-valued sets corresponding to distinct attributes whereas hypersoft set, an extension of soft set, fully addresses this scarcity by replacing the approximate function of soft sets with multi-argument approximate function. Some structures (i.e., possibility fuzzy soft set, possibility intuitionistic fuzzy soft set) exist in literature in which a possibility of each element in the universe is attached with the parameterization of fuzzy sets and intuitionistic fuzzy sets while defining fuzzy soft set and intuitionistic fuzzy soft set respectively. This study aims to generalize the existing structure (i.e., possibility intuitionistic fuzzy soft set) and to make it adequate for multi-argument approximate function. Therefore, firstly, the elementary notion of possibility intuitionistic fuzzy hypersoft set is developed and some of its elementary properties i.e., subset, null set, absolute set and complement, are discussed with numerical examples. Secondly, its set-theoretic operations i.e., union, intersection, AND, OR and relevant laws are investigated with the help of numerical examples, matrix and graphical representations. Moreover, algorithms based on AND/OR operations are proposed and are elaborated with illustrative examples. Lastly, similarity measure between two possibility intuitionistic fuzzy hypersoft sets is characterized with the help of example. This concept of similarity measure is successfully applied in decision making to judge the eligibility of a candidate for an appropriate job. The proposed similarity formulation is compared with the relevant existing models and validity of the generalization of the proposed structure is discussed.</p></abstract>

scholarly journals A New Similarity Measure of Interval-Valued Intuitionistic Fuzzy Sets Considering Its Hesitancy Degree and Applications in Expert Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-16
Author(s):  
Chong Wu ◽  
Peng Luo ◽  
Yongli Li ◽  
Xuekun Ren
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Ideal Point ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Entropy Measure ◽  
New Approach ◽  
Intuitionistic Fuzzy ◽  
Multicriteria Group Decision Making ◽  
Interval Valued

As an important content in fuzzy mathematics, similarity measure is used to measure the similarity degree between two fuzzy sets. Considering the existing similarity measures, most of them do not consider the hesitancy degree and some methods considering the hesitancy degree are based on the intuitionistic fuzzy sets, intuitionistic fuzzy values. It may cause some counterintuitive results in some cases. In order to make up for the drawback, we present a new approach to construct the similarity measure between two interval-valued intuitionistic fuzzy sets using the entropy measure and considering the hesitancy degree. In particular, the proposed measure was demonstrated to yield a similarity measure. Besides, some examples are given to prove the practicality and effectiveness of the new measure. We also apply the similarity measure to expert system to solve the problems on pattern recognition and the multicriteria group decision making. In these examples, we also compare it with existing methods such as other similarity measures and the ideal point method.

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