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Neural Computing and Applications
Erschienen in: Neural Computing and Applications 14/2020

02.11.2019 | Original Article

Modified Zhang and Xu’s distance measure for Pythagorean fuzzy sets and its application to pattern recognition problems

verfasst von: P. A. Ejegwa

Erschienen in: Neural Computing and Applications | Ausgabe 14/2020

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Abstract

The concept of distance between Pythagorean fuzzy sets (PFSs) has been proven to be relevant in the applications of PFSs as seen in the literature. The main purpose of this paper is to show that Zhang and Xu’s distance measure between PFSs fails the conditions of distance measure; hence, it is not an appropriate distance measure for PFSs. Some numerical examples are used to validate this stance. In order to remedy this shortcoming, Zhang and Xu’s distance measure for PFSs is normalised/modified to cater for the limitation by employing the technique used to normalise both Hamming and Euclidean distances between intuitionistic fuzzy sets by Szmidt and Kacprzyk. The modified Zhang and Xu’s distance measure for PFSs satisfies the conditions of the axiomatic definition of distance measure for PFSs; hence, it is an appropriate/reliable distance measure for PFSs. Finally, the modified Zhang and Xu’s distance measure for PFSs is applied to pattern recognition problems of classification of building materials and mineral fields.
Vorheriger Artikel Global dissipativity of high-order Hopfield bidirectional associative memory neural networks with mixed delays
Nächster Artikel Gated multimodal networks

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Metadaten
Titel
Modified Zhang and Xu’s distance measure for Pythagorean fuzzy sets and its application to pattern recognition problems
verfasst von
P. A. Ejegwa
Publikationsdatum
02.11.2019
Verlag
Springer London
Erschienen in
Neural Computing and Applications / Ausgabe 14/2020
Print ISSN: 0941-0643
Elektronische ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-019-04554-6

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