Hybrid vector similarity measures based on complex hesitant fuzzy sets and their applications to pattern recognition and medical diagnosis

2021 ◽  
Vol 40 (1) ◽  
pp. 625-646 ◽  
Author(s):  
Tahir Mahmood ◽  
Ubaid Ur Rehman ◽  
Zeeshan Ali ◽  
Tariq Mahmood
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Distance Measures ◽  
Hesitant Fuzzy Set ◽  
Jaccard Similarity ◽  
Special Cases ◽  
Cosine Similarity Measures ◽  
Single Set

Fuzzy set (FS) theory is one of the most important tool to deasl with complicated and difficult information in real-world. Now FS has many extensions and hesitant fuzzy set (HFS) is one of them. Further generalization of FS is complex fuzzy set (CFS), which contains only the membership grade, whose range is unit disc instead of [0, 1]. The aim of this paper is to present the idea of complex hesitant fuzzy set (CHFS) and to introduce its basic properties. Basically, CHFS is the combination of CFS and HFS to deal with two dimension information in a single set. Further, the vector similarity measures (VSMs) such as Jaccard similarity measures (JSMs), Dice similarity measures (DSMs) and Cosine similarity measures (CSMs) for CHFSs are discussed. The special cases of the proposed measures are also discussed. Then, the notion of complex hesitant fuzzy hybrid vector similarity measures are utilized in the environment of pattern recognition and medical diagnosis. Further, based on these distance measures, a decision-making method has been presented for finding the best alternative under the set of the feasible one. Illustrative examples from the field of pattern recognition as well as medical diagnosis have been taken to validate the approach. Finally, the comparison between proposed approaches with existing approaches are also discussed to find the reliability and proficiency of the elaborated measures for complex hesitant fuzzy elements.

scholarly journals A Novel Approach of Complex Dual Hesitant Fuzzy Sets and Their Applications in Pattern Recognition and Medical Diagnosis

2021 ◽  
Vol 2021 ◽  
pp. 1-31
Author(s):  
Ubaid Ur Rehman ◽  
Tahir Mahmood ◽  
Zeeshan Ali ◽  
Thammarat Panityakul
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Reliability And Validity ◽  
Hesitant Fuzzy Set ◽  
Dual Hesitant Fuzzy Set ◽  
Novel Approach ◽  
Operational Laws ◽  
Interval Valued

Complex dual hesitant fuzzy set (CDHFS) is an assortment of complex fuzzy set (CFS) and dual hesitant fuzzy set (DHFS). In this manuscript, the notion of the CDHFS is explored and its operational laws are discussed. The new methodology of the complex interval-valued dual hesitant fuzzy set (CIvDHFS) and its necessary laws are introduced and are also defensible with the help of examples. Further, the antilogarithmic and with-out exponential-based similarity measures, generalized similarity measures, and their important characteristics are also developed. These similarity measures are applied in the environment of pattern recognition and medical diagnosis to evaluate the proficiency and feasibility of the established measures. We also solved some numerical examples using the established measures to examine the reliability and validity of the proposed measures by comparing these with existing measures. To strengthen the proposed study, the comparative analysis is made and it is conferred that the proposed study is much more superior to the existing studies.

scholarly journals Some Novel Cosine Similarity Measures Based on Complex Hesitant Fuzzy Sets and Their Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Ronnason Chinram ◽  
Tahir Mahmood ◽  
Ubaid Ur Rehman ◽  
Zeeshan Ali ◽  
Aiyared Iampan
Keyword(s):  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
Cosine Function ◽  
Hesitant Fuzzy Set ◽  
Uncertain Information ◽  
Special Cases ◽  
Tangent Function ◽  
Polar Coordinate ◽  
Cosine Similarity Measures

The theory of complex hesitant fuzzy set (CHFS) is a modification technique of the complex fuzzy set (CFS) to cope with awkward and unreliable information’s in daily life issues. CHFS contains the grade of truth in the form of complex number, whose real and imaginary parts are in the form of the finite subset of the unit interval. CHFS is the mixture of hesitant fuzzy set (HFS) and CFS, which handles the complex and uncertain information in real-world issues which is compared with fuzzy sets and complex fuzzy sets. The positive membership in CHFS is in the form a polar coordinate belonging to unit disc in the complex plane. The aims of this manuscript are to explore some similarity measures (SMs), weighted SMs (WSMs) such as cosine SMs, weighted cosine SMs, SMs based on cosine function, WSMs based on cosine function, SMs based on tangent function, and WSMs based on tangent function of CHFS. Some special cases of the presented measures are discussed in detail. Moreover, we use our described SMs and weighted SMs of CHFS in the environment of medical diagnosis and pattern recognition to assess the practicality and competence of the described SMs. Finally, to find the validity and proficiency of the investigated measures based on CHFSs, the comparison between explored measures with some already defined measures and their graphical representations are also discussed in detail.

New distance and similarity measures for hesitant fuzzy sets and their application in hierarchical clustering

2020 ◽  
Vol 39 (3) ◽  
pp. 4349-4360
Author(s):  
Kamran Rezaei ◽  
Hassan Rezaei
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
The Other ◽  
Hesitant Fuzzy Set ◽  
Membership Degree ◽  
Hesitant Fuzzy Sets ◽  
Variation Range

The hesitant fuzzy sets (HFSs) are an extension of the classical fuzzy sets. The membership degree of each element in a hesitant fuzzy set can be a set of possible values in the interval [0,1]. On the other hand, distance and similarity measures are important tools in several applications such as pattern recognition, clustering, medical diagnosis, etc. Hence, numerous studies have focused on investigating distance and similarity measures for HFSs. In this paper, some improved distance and similarity measures are introduced for the HFSs, considering the variation range as a hesitance degree for these sets. Comparing the proposed measures to some available distance and similarity measures indicated the better results of the proposed measures. Finally, the application of the proposed measures was investigated in the clustering.

Multi-criteria decision making and pattern recognition based on similarity measures for Fermatean fuzzy sets

2021 ◽  
pp. 1-17
Author(s):  
Changlin Xu ◽  
Juhong Shen
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
New Method ◽  
Fuzzy Decision Making ◽  
Multi Criteria Decision Making

 Higher-order fuzzy decision-making methods have become powerful tools to support decision-makers in solving their problems effectively by reflecting uncertainty in calculations better than crisp sets in the last 3 decades. Fermatean fuzzy set proposed by Senapati and Yager, which can easily process uncertain information in decision making, pattern recognition, medical diagnosis et al., is extension of intuitionistic fuzzy set and Pythagorean fuzzy set by relaxing the restraint conditions of the support for degrees and support against degrees. In this paper, we focus on the similarity measures of Fermatean fuzzy sets. The definitions of the Fermatean fuzzy sets similarity measures and its weighted similarity measures on discrete and continuous universes are given in turn. Then, the basic properties of the presented similarity measures are discussed. Afterward, a decision-making process under the Fermatean fuzzy environment based on TOPSIS method is established, and a new method based on the proposed Fermatean fuzzy sets similarity measures is designed to solve the problems of medical diagnosis. Ultimately, an interpretative multi-criteria decision making example and two medical diagnosis examples are provided to demonstrate the viability and effectiveness of the proposed method. Through comparing the different methods in the multi-criteria decision making and the medical diagnosis application, it is found that the new method is as efficient as the other methods. These results illustrate that the proposed method is practical in dealing with the decision making problems and medical diagnosis problems.

Using the Similarity Measure Between Intuitionistic Fuzzy Sets for the Application on Pattern Recognitions

2018 ◽  
pp. 972-985
Author(s):  
Lixin Fan
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Definition Of

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

scholarly journals Distance and Similarity Measures for Spherical Fuzzy Sets and Their Applications in Selecting Mega Projects

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 519 ◽  
Author(s):  
Muhammad Jabir Khan ◽  
Poom Kumam ◽  
Wejdan Deebani ◽  
Wiyada Kumam ◽  
Zahir Shah
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Similarity Measures ◽  
Developed Countries ◽  
Distance Measures ◽  
Membership Functions ◽  
Pythagorean Fuzzy Set ◽  
Picture Fuzzy Set

A new condition on positive membership, neutral membership, and negative membership functions give us the successful extension of picture fuzzy set and Pythagorean fuzzy set and called spherical fuzzy sets ( SFS ) . This extends the domain of positive membership, neutral membership, and negative membership functions. Keeping in mind the importance of similarity measure and application in data mining, medical diagnosis, decision making, and pattern recognition, several studies on similarity measures have been proposed in the literature. Some of those, however, cannot satisfy the axioms of similarity and provide counter-intuitive cases. In this paper, we proposed the set-theoretic similarity and distance measures. We provide some counterexamples for already proposed similarity measures in the literature and shows that how our proposed method is important and applicable to the pattern recognition problems. In the end, we provide an application of a proposed similarity measure for selecting mega projects in under developed countries.

Using the Similarity Measure between Intuitionistic Fuzzy Sets for the Application on Pattern Recognitions

2015 ◽  
Vol 9 (2) ◽  
pp. 24-36 ◽  
Author(s):  
Lixin Fan
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Definition Of

The measurement of uncertainty is an important topic for the theories dealing with uncertainty. The definition of similarity measure between two IFSs is one of the most interesting topics in IFSs theory. A similarity measure is defined to compare the information carried by IFSs. Many similarity measures have been proposed. A few of them come from the well-known distance measures. In this work, a new similarity measure between IFSs was proposed by the consideration of the information carried by the membership degree, the non-membership degree, and hesitancy degree in intuitionistic fuzzy sets (IFSs). To demonstrate the efficiency of the proposed similarity measure, various similarity measures between IFSs were compared with the proposed similarity measure between IFSs by numerical examples. The compared results demonstrated that the new similarity measure is reasonable and has stronger discrimination among them. Finally, the similarity measure was applied to pattern recognition and medical diagnosis. Two illustrative examples were provided to show the effectiveness of the pattern recognition and medical diagnosis.

scholarly journals New similarity measures for single-valued neutrosophic sets with applications in pattern recognition and medical diagnosis problems

2020 ◽  
Author(s):  
Jia Syuen Chai ◽  
Ganeshsree Selvachandran ◽  
Florentin Smarandache ◽  
Vassilis C. Gerogiannis ◽  
Le Hoang Son ◽  
...  
Keyword(s):  
Pattern Recognition ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Rank Correlation ◽  
Distance Measures ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Numerical Examples ◽  
Information Measures ◽  
Comparison Results

AbstractThe single-valued neutrosophic set (SVNS) is a well-known model for handling uncertain and indeterminate information. Information measures such as distance measures, similarity measures and entropy measures are very useful tools to be used in many applications such as multi-criteria decision making (MCDM), medical diagnosis, pattern recognition and clustering problems. A lot of such information measures have been proposed for the SVNS model. However, many of these measures have inherent problems that prevent them from producing reasonable or consistent results to the decision makers. In this paper, we propose several new distance and similarity measures for the SVNS model. The proposed measures have been verified and proven to comply with the axiomatic definition of the distance and similarity measure for the SVNS model. A detailed and comprehensive comparative analysis between the proposed similarity measures and other well-known existing similarity measures has been done. Based on the comparison results, it is clearly proven that the proposed similarity measures are able to overcome the shortcomings that are inherent in existing similarity measures. Finally, an extensive set of numerical examples, related to pattern recognition and medical diagnosis, is given to demonstrate the practical applicability of the proposed similarity measures. In all numerical examples, it is proven that the proposed similarity measures are able to produce accurate and reasonable results. To further verify the superiority of the suggested similarity measures, the Spearman’s rank correlation coefficient test is performed on the ranking results that were obtained from the numerical examples, and it was again proven that the proposed similarity measures produced the most consistent ranking results compared to other existing similarity measures.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

scholarly journals Algorithm for Probabilistic Dual Hesitant Fuzzy Multi-Criteria Decision-Making Based on Aggregation Operators With New Distance Measures

Mathematics ◽  
2018 ◽  
Vol 6 (12) ◽  
pp. 280 ◽  
Author(s):  
Harish Garg ◽  
Gagandeep Kaur
Keyword(s):  
Decision Making ◽  
Fuzzy Set ◽  
Weight Vector ◽  
Aggregation Operators ◽  
Distance Measures ◽  
Weighted Averaging ◽  
Hesitant Fuzzy Set ◽  
Maximum Deviation ◽  
Dual Hesitant Fuzzy Set ◽  
Deviation Method

Probabilistic dual hesitant fuzzy set (PDHFS) is an enhanced version of a dual hesitant fuzzy set (DHFS) in which each membership and non-membership hesitant value is considered along with its occurrence probability. These assigned probabilities give more details about the level of agreeness or disagreeness. By emphasizing the advantages of the PDHFS and the aggregation operators, in this manuscript, we have proposed several weighted and ordered weighted averaging and geometric aggregation operators by using Einstein norm operations, where the preferences related to each object is taken in terms of probabilistic dual hesitant fuzzy elements. Several desirable properties and relations are also investigated in details. Also, we have proposed two distance measures and its based maximum deviation method to compute the weight vector of the different criteria. Finally, a multi-criteria group decision-making approach is constructed based on proposed operators and the presented algorithm is explained with the help of the numerical example. The reliability of the presented decision-making method is explored with the help of testing criteria and by comparing the results of the example with several prevailing studies.

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