Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems
In this paper, a generalized picture fuzzy soft set is proposed, which is an extension of the picture fuzzy soft sets. We investigate the basic properties of picture fuzzy soft sets and define an F-subset, M-subset, extended union, extended intersection, restricted union, restricted intersection and...
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doaj-eb192ebaa43f4d8e8d40f39db3fe7af82020-11-25T00:55:53ZengMDPI AGSymmetry2073-89942019-03-0111341510.3390/sym11030415sym11030415Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support SystemsMuhammad Jabir Khan0Poom Kumam1Shahzaib Ashraf2Wiyada Kumam3KMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandKMUTT Fixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Abdul wali Khan University, Mardan 23200, PakistanProgram in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, ThailandIn this paper, a generalized picture fuzzy soft set is proposed, which is an extension of the picture fuzzy soft sets. We investigate the basic properties of picture fuzzy soft sets and define an F-subset, M-subset, extended union, extended intersection, restricted union, restricted intersection and also prove the De Morgan’s laws for picture fuzzy soft information. We investigate upper and lower substitution for both picture fuzzy sets and generalized picture fuzzy soft sets. Meanwhile, the related proofs are given in detail. Finally, we propose an algorithm to deal with generalized picture fuzzy soft information. To show the supremacy and effectiveness of the proposed technique, we illustrate a descriptive example using generalized picture fuzzy soft information. Results indicate that the proposed technique is more generalized and effective over all the existing structures of fuzzy soft sets.https://www.mdpi.com/2073-8994/11/3/415picture fuzzy setspicture fuzzy soft setspicture fuzzy Dombi weighted average operatorpicture fuzzy weighted averaging operator |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Muhammad Jabir Khan Poom Kumam Shahzaib Ashraf Wiyada Kumam |
spellingShingle |
Muhammad Jabir Khan Poom Kumam Shahzaib Ashraf Wiyada Kumam Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems Symmetry picture fuzzy sets picture fuzzy soft sets picture fuzzy Dombi weighted average operator picture fuzzy weighted averaging operator |
author_facet |
Muhammad Jabir Khan Poom Kumam Shahzaib Ashraf Wiyada Kumam |
author_sort |
Muhammad Jabir Khan |
title |
Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems |
title_short |
Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems |
title_full |
Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems |
title_fullStr |
Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems |
title_full_unstemmed |
Generalized Picture Fuzzy Soft Sets and Their Application in Decision Support Systems |
title_sort |
generalized picture fuzzy soft sets and their application in decision support systems |
publisher |
MDPI AG |
series |
Symmetry |
issn |
2073-8994 |
publishDate |
2019-03-01 |
description |
In this paper, a generalized picture fuzzy soft set is proposed, which is an extension of the picture fuzzy soft sets. We investigate the basic properties of picture fuzzy soft sets and define an F-subset, M-subset, extended union, extended intersection, restricted union, restricted intersection and also prove the De Morgan’s laws for picture fuzzy soft information. We investigate upper and lower substitution for both picture fuzzy sets and generalized picture fuzzy soft sets. Meanwhile, the related proofs are given in detail. Finally, we propose an algorithm to deal with generalized picture fuzzy soft information. To show the supremacy and effectiveness of the proposed technique, we illustrate a descriptive example using generalized picture fuzzy soft information. Results indicate that the proposed technique is more generalized and effective over all the existing structures of fuzzy soft sets. |
topic |
picture fuzzy sets picture fuzzy soft sets picture fuzzy Dombi weighted average operator picture fuzzy weighted averaging operator |
url |
https://www.mdpi.com/2073-8994/11/3/415 |
work_keys_str_mv |
AT muhammadjabirkhan generalizedpicturefuzzysoftsetsandtheirapplicationindecisionsupportsystems AT poomkumam generalizedpicturefuzzysoftsetsandtheirapplicationindecisionsupportsystems AT shahzaibashraf generalizedpicturefuzzysoftsetsandtheirapplicationindecisionsupportsystems AT wiyadakumam generalizedpicturefuzzysoftsetsandtheirapplicationindecisionsupportsystems |
_version_ |
1725229148565143552 |