Similarity measures of Pythagorean fuzzy sets based on combination of cosine similarity measure and Euclidean distance measure

2018 ◽  
Author(s):  
Wan Rosanisah Wan Mohd ◽  
Lazim Abdullah
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Euclidean Distance ◽  
Distance Measure ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Pythagorean Fuzzy Sets ◽  
Euclidean Distance Measure ◽  
Cosine Similarity Measure

scholarly journals Some Similarity Measures of Neutrosophic Sets Based on the Euclidean Distance and Their Application in Medical Diagnosis

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Donghai Liu ◽  
Guangyan Liu ◽  
Zaiming Liu
Keyword(s):  
Similarity Measure ◽  
Medical Diagnosis ◽  
Euclidean Distance ◽  
Distance Measure ◽  
Multiple Criteria Decision Making ◽  
Similarity Measures ◽  
Neutrosophic Sets ◽  
Euclidean Distance Measure ◽  
The Difference ◽  
Interval Valued

Similarity measure is an important tool in multiple criteria decision-making problems, which can be used to measure the difference between the alternatives. In this paper, some new similarity measures of single-valued neutrosophic sets (SVNSs) and interval-valued neutrosophic sets (IVNSs) are defined based on the Euclidean distance measure, respectively, and the proposed similarity measures satisfy the axiom of the similarity measure. Furthermore, we apply the proposed similarity measures to medical diagnosis decision problem; the numerical example is used to illustrate the feasibility and effectiveness of the proposed similarity measures of SVNSs and IVNSs, which are then compared to other existing similarity measures.

scholarly journals Cosine Similarity Measure between Hybrid Intuitionistic Fuzzy Sets and Its Application in Medical Diagnosis

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Cosine Similarity ◽  
Individual Decision ◽  
Intuitionistic Fuzzy ◽  
Cosine Similarity Measure ◽  
The Ideal

In this paper, a cosine similarity measure between hybrid intuitionistic fuzzy sets is proposed. The aim of the paper is to investigate the cosine similarity measure with hybrid intuitionistic fuzzy information and apply it to medical diagnosis. Firstly, we construct the cosine similarity measure between hybrid intuitionistic fuzzy sets, and the relevant properties are also discussed. In order to obtain a reasonable evaluation in group decision, the weight of experts under different attributes is determined by the projection of individual decision information on the ideal decision information, where the ideal decision information is the average values of each expert’s evaluation. Furthermore, we propose a decision method for medical diagnosis based on the cosine similarity measure between hybrid intuitionistic fuzzy sets, and the patient can be diagnosed with the disease according to the values of proposed cosine similarity measure. Finally, an example is given to illustrate feasibility and effectiveness of the proposed cosine similarity measure, which is also compared with the existing similarity measures.

scholarly journals The New Similarity Measure and Distance Measure of a Hesitant Fuzzy Linguistic Term Set Based on a Linguistic Scale Function

Symmetry ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 367 ◽  
Author(s):  
Donghai Liu ◽  
Yuanyuan Liu ◽  
Xiaohong Chen
Keyword(s):  
Similarity Measure ◽  
Distance Measure ◽  
Cosine Similarity ◽  
Scale Function ◽  
Linguistic Term ◽  
Euclidean Distance Measure ◽  
Order Preference ◽  
Cosine Similarity Measure ◽  
Linguistic Scale Function ◽  
Fuzzy Linguistic

The existing cosine similarity measure for hesitant fuzzy linguistic term sets (HFLTSs) has an impediment as it does not satisfy the axiom of similarity measure. Due to this disadvantage, a new similarity measure combining the existing cosine similarity measure and the Euclidean distance measure of HFLTSs is proposed, which is constructed based on a linguistic scale function; the related properties are also given. According to the relationship between the distance measure and the similarity measure, a corresponding distance measure between HFLTSs is obtained. Furthermore, we generalize the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained distance measure of the HFLTSs. The principal advantages of the proposed method are that it cannot only effectively transform linguistic information in different semantic environments, but it can also avoid the shortcomings of existing the cosine similarity measure. Finally, a case study is conducted to illustrate the feasibility and effectiveness of the proposed method, which is compared to the existing methods.

scholarly journals Similarity measures for Fermatean fuzzy sets and its applications in group decision-making

2022 ◽  
Vol 11 (2) ◽  
pp. 167-180
Author(s):  
Laxminarayan Sahoo
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision Making ◽  
Group Decision ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Future Research ◽  
Uncertain Information

The intention of this paper is to propose some similarity measures between Fermatean fuzzy sets (FFSs). Firstly, we propose some score based similarity measures for finding similarity measures of FFSs and also propose score based cosine similarity measures between FFSs. Furthermore, we introduce three newly scored functions for effective uses of Fermatean fuzzy sets and discuss some relevant properties of cosine similarity measure. Fermatean fuzzy sets introduced by Senapati and Yager can manipulate uncertain information more easily in the process of multi-criteria decision making (MCDM) and group decision making. Here, we investigate score based similarity measures of Fermatean fuzzy sets and scout the uses of FFSs in pattern recognition. Based on different types of similarity measures a pattern recognition problem viz. personnel appointment is presented to describe the use of FFSs and its similarity measure as well as scores. The counterfeit results show that the proposed method is more malleable than the existing method(s). Finally, concluding remarks and the scope of future research of the proposed approach are given.

scholarly journals The Intuitionistic Fuzzy Linguistic Cosine Similarity Measure and Its Application in Pattern Recognition

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Intuitionistic Fuzzy ◽  
Linguistic Term ◽  
Cosine Similarity Measure ◽  
Linguistic Scale Function ◽  
Cosine Similarity Measures ◽  
Fuzzy Linguistic ◽  
Interval Valued

We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval-valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. The main advantage of the proposed cosine similarity measures is that the decision-makers can flexibly select the linguistic scale function depending on the actual semantic situation. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval-valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example.

scholarly journals Cosine Similarity Measure of Complex Fuzzy Sets and Robustness of Complex Fuzzy Connectives

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Wenping Guo ◽  
Lvqing Bi ◽  
Bo Hu ◽  
Songsong Dai
Keyword(s):  
Similarity Measure ◽  
Fuzzy Set ◽  
Fuzzy Inference ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Invariance Properties ◽  
Cosine Similarity Measure ◽  
Cosine Similarity Measures ◽  
Complex Valued ◽  
Fuzzy Connectives

Complex fuzzy set (CFS), as a generalization of fuzzy set (FS), is characterized by complex-valued membership degrees. By considering the complex-valued membership degree as a vector in the complex unit disk, we introduce the cosine similarity measures between CFSs. Then, we investigate some invariance properties of the cosine similarity measure. Finally, the cosine similarity measure is applied to measure the robustness of complex fuzzy connectives and complex fuzzy inference.

scholarly journals Modified Cosine Similarity Measure based Data Classification in Data Mining

2020 ◽  
Vol 9 (5) ◽  
pp. 649-654
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Similarity Measure ◽  
Dominant Role ◽  
Similarity Measures ◽  
Data Classification ◽  
Cosine Similarity ◽  
Machine Learning Techniques ◽  
Text Data ◽  
Cosine Similarity Measure

Text data analytics became an integral part of World Wide Web data management and Internet based applications rapidly growing all over the world. E-commerce applications are growing exponentially in the business field and the competitors in the E-commerce are gradually increasing many machine learning techniques for predicting business related operations with the aim of increasing the product sales to the greater extent. Usage of similarity measures is inevitable in modern day to day real applications. Cosine similarity plays a dominant role in text data mining applications such as text classification, clustering, querying, and searching and so on. A modified clustering based cosine similarity measure called MCS is proposed in this paper for data classification. The proposed method is experimentally verified by employing many UCI machine learning datasets involving categorical attributes. The proposed method is superior in producing more accurate classification results in majority of experiments conducted on the UCI machine learning datasets.

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