In this paper, we presented 10 similarity measures between Pythagorean fuzzy sets (PFSs) based on the cosine function by considering the degree of membership, degree of nonmembership and degree of hesitation in PFSs. Then, we applied these similarity measures and weighted similarity measures between PFSs to pattern recognition and medical diagnosis. Finally, two illustrative examples are given to demonstrate the efficiency of the similarity measures for pattern recognition and medical diagnosis.

Similarity measures of Pythagorean fuzzy sets based on the cosine function and their applications

Abstract. In this paper, we presented another form of eight similarity measures between PFSs based on the cosine function between PFSs by considering the degree of positive membership, degree of neutral membership, degree of negative membership and degree of refusal membership in PFSs. Then, we applied these weighted cosine function similarity measures between PFSs to strategic decision making. Finally, an illustrative example for selecting the optimal production strategy is given to demonstrate the efficiency of the similarity measures for strategic decision making problem.

/pdf/some-cosine-similarity-measures-for-picture-fuzzy-sets-and-241sqw7oza.pdf

Some Cosine Similarity Measures for Picture Fuzzy Sets and Their Applications to Strategic Decision Making

As the extension of fuzzy set, intuitionistic fuzzy set, Pythagorean fuzzy set, and picture fuzzy set, the spherical fuzzy set is characterized by three functions expressing the positive-membership degree, the neutral-membership degree and the negative-membership degree which the sum squares of them is equal or less than 1. In this work, we shall present some novel Dice similarity measures of spherical fuzzy sets and the generalized Dice similarity measures of spherical fuzzy sets and indicates that the Dice similarity measures and asymmetric measures (projection measures) are the special cases of the generalized Dice similarity measures in some parameter values. Then, we propose the generalized Dice similarity measures-based multiple attribute group decision making models with spherical fuzzy information. Then, we apply the generalized Dice similarity measures between spherical fuzzy sets to multiple attribute group decision making. Finally, an illustrative example is given to demonstrate the efficiency of the similarity measures for selecting the desirable ERP system.

https://informatica.vu.lt/journal/INFORMATICA/article/875/file/pdf

The Generalized Dice Similarity Measures for Picture Fuzzy Sets and Their Applications

In this article, we propose another form of ten similarity measures by considering the function of membership degree, non-membership degree, and indeterminacy membership degree between the q-ROFSs on the basis of the traditional cosine similarity measures and cotangent similarity measures. Then, we utilize our presented ten similarity measures and ten weighted similarity measures between q-ROFSs to deal with multiple attribute decision-making (MADM) problems including pattern recognition and scheme selection. Finally, two numerical examples are provided to illustrate the scientific and effective of the similarity measures for pattern recognition and scheme selection.

https://www.mdpi.com/2227-7390/7/4/340/pdf

Similarity Measures of q-Rung Orthopair Fuzzy Sets Based on Cosine Function and Their Applications

This paper introduces the concept of a single valued neutrosophic multiset (SVNM) as a generalization of an intuitionistic fuzzy multiset (IFM) and some basic operational relations of SVNMs, and then proposes the Dice similarity measure and the weighted Dice similarity measure for SVNMs and investigates their properties. Finally, the Dice similarity measure is applied to a medical diagnosis problem with SVNM information. This diagnosis method can deal with the medical diagnosis problem with indeterminate and inconsistent information which cannot be handled by the diagnosis method based on IFMs.

/pdf/dice-similarity-measure-between-single-valued-neutrosophic-3h5eecdd90.pdf

Dice Similarity Measure between Single Valued Neutrosophic Multisets and Its Application in Medical Diagnosis

In this paper, the Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) based on Cotangent function is presented and analyzed. The properties of the similarity measure are proved and verified using the numerical evaluation of the proposed similarity measure. The unique feature of this proposed method is that it considers multi membership and non membership for the same element. As the proposed method is mathematically valid, it can be applied to any decision making problems, medical diagnosis, engineering problems, pattern recognition, etc. Finally, the application of medical diagnosis shows that the proposed similarity measures are much simpler, well suited one to use with linguistic variables.

/pdf/intuitionistic-fuzzy-multi-similarity-measure-based-on-33sikoldsd.pdf

Intuitionistic Fuzzy Multi Similarity Measure Based on Cotangent Function

In this paper, three distance measures and their corresponding similarity measures of Intuitionistic Fuzzy Multi sets (IFMS) are introduced and compared. The measures are based on Hausdroff distance measure, Geometric distance measure and the Normalized distance measure.

/pdf/on-distance-and-similarity-measures-of-intuitionistic-fuzzy-dxgbofwbs3.pdf

On Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set

In this paper, the Correlation measure of Intuitionistic Fuzzy Multi sets (IFMS) is proposed. The concept of this Correlation measure of IFMS is the extension of Correlation measure of IFS. Using the Correlation of IFMS measure, the application of medical diagnosis and pattern recognition are presented. The new method also shows that the correlation measure of any two IFMS equals one if and only if the two IFMS are the same.

/pdf/correlation-measure-for-intuitionistic-fuzzy-multi-sets-3hkw907k5l.pdf

Correlation measure for intuitionistic fuzzy multi sets

The Normalized Geometric and Normalized Hamming distance measures of Intuitionistic Fuzzy Multi sets (IFMS) are presented in depth in this paper. Due to the wide applications in various fields, the distance measure plays a vital role in Intuitionistic Fuzzy sets (IFS). We extend the distance measure of IFS to IFMS as there are possibilities of multi membership, non membership for the same element. To demonstrate the efficiency of the proposed measures, the properties of distance measures are analysed. As the proposed method is mathematically valid, it can be applied to any decision making problems, medical diagnosis, engineering problems, pattern recognition, etc. The application of medical diagnosis and pattern recognition shows that the proposed distance measures are much simpler, well suited one to use with linguistic variables.

https://www.ijsr.net/archive/v2i11/MDIwMTMzMzg=.pdf

A Study of Normalized Geometric and Normalized Hamming Distance Measures in Intuitionistic Fuzzy Multi Sets

As Similarity measure for fuzzy sets is one of the important research topics of fuzzy set theory, there are several methods to measure similarity between two fuzzy sets (FS), Intuitionistic fuzzy sets (IFS) and Intuitionistic fuzzy multi sets (IFMS). In this paper, the Normalized Hamming Similarity measure of Intuitionistic Fuzzy Multi sets (IFMS) is introduced. This new measure for IFMS is based on the geometrical interpretation of IFS which involves both similarity and dissimilarity. Using this measure, the application of medical diagnosis and pattern recognition are shown.

/pdf/normalized-hamming-similarity-measure-for-intuitionistic-1wq3uwnvs9.pdf

P. Rajarajeswari

Papers

Intuitionistic Fuzzy Multi Similarity Measure Based on Cotangent Function

On Distance and Similarity Measures of Intuitionistic Fuzzy Multi Set

Correlation measure for intuitionistic fuzzy multi sets

A Study of Normalized Geometric and Normalized Hamming Distance Measures in Intuitionistic Fuzzy Multi Sets

Normalized Hamming Similarity Measure for Intuitionistic Fuzzy Multi Sets and Its Application in Medical diagnosis