Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS

Pythagorean fuzzy sets (PFSs) were proposed by Yager in 2013 to treat imprecise and vague information in daily life more rigorously and efficiently with higher precision than intuitionistic fuzzy sets. In this paper, we construct new distance and similarity measures of PFSs based on the Hausdorff me...

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Veröffentlicht in:International journal of intelligent systems 2019-10, Vol.34 (10), p.2633-2654
Hauptverfasser: Hussian, Zahid, Yang, Miin‐Shen
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description Pythagorean fuzzy sets (PFSs) were proposed by Yager in 2013 to treat imprecise and vague information in daily life more rigorously and efficiently with higher precision than intuitionistic fuzzy sets. In this paper, we construct new distance and similarity measures of PFSs based on the Hausdorff metric. We first develop a method to calculate a distance between PFSs based on the Hasudorff metric, along with proving several properties and theorems. We then consider a generalization of other distance measures, such as the Hamming distance, the Euclidean distance, and their normalized versions. On the basis of the proposed distances for PFSs, we give new similarity measures to compute the similarity degree of PFSs. Some examples related to pattern recognition and linguistic variables are used to validate the proposed distance and similarity measures. Finally, we apply the proposed methods to multicriteria decision‐making by constructing a Pythagorean fuzzy Technique for Order Preference by Similarity to an Ideal Solution and then present a practical example to address an important issue related to social sector. Numerical results indicate that the proposed methods are reasonable and applicable and also that they are well suited in pattern recognition, linguistic variables, and multicriteria decision‐making with PFSs.
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subjects distance
Distance measurement
Euclidean geometry
Fuzzy sets
hasudorff metric
Intelligent systems
Metric space
multicriteria decision making
Multiple criterion
Pattern recognition
pythagorean fuzzy sets
Similarity
Similarity measures
title Distance and similarity measures of Pythagorean fuzzy sets based on the Hausdorff metric with application to fuzzy TOPSIS
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