Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making
The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vaguene...
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| Language: | English |
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Wiley
2018-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2018/2832839 |
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| author | Miin-Shen Yang Zahid Hussain |
| author_facet | Miin-Shen Yang Zahid Hussain |
| author_sort | Miin-Shen Yang |
| collection | DOAJ |
| description | The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In the present paper, we have used both probabilistic and nonprobabilistic types to calculate fuzzy entropy of PFSs. Firstly, a probabilistic-type entropy measure for PFSs is proposed and then axiomatic definitions and properties are established. Secondly, we utilize a nonprobabilistic-type with distances to construct new entropy measures for PFSs. Then a min–max operation to calculate entropy measures for PFSs is suggested. Some examples are also used to demonstrate suitability and reliability of the proposed methods, especially for choosing the best one/ones in structured linguistic variables. Furthermore, a new method based on the chosen entropies is presented for Pythagorean fuzzy multicriterion decision making to compute criteria weights with ranking of alternatives. A comparison analysis with the most recent and relevant Pythagorean fuzzy entropy is conducted to reveal the advantages of our developed methods. Finally, this method is applied for ranking China-Pakistan Economic Corridor (CPEC) projects. These examples with applications demonstrate practical effectiveness of the proposed entropy measures. |
| format | Article |
| id | doaj-art-b0f6e4e6df9e45518c8636d97734b811 |
| institution | OA Journals |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b0f6e4e6df9e45518c8636d97734b8112025-08-20T02:23:36ZengWileyComplexity1076-27871099-05262018-01-01201810.1155/2018/28328392832839Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision MakingMiin-Shen Yang0Zahid Hussain1Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, TaiwanDepartment of Applied Mathematics, Chung Yuan Christian University, Chung-Li 32023, TaiwanThe concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In the present paper, we have used both probabilistic and nonprobabilistic types to calculate fuzzy entropy of PFSs. Firstly, a probabilistic-type entropy measure for PFSs is proposed and then axiomatic definitions and properties are established. Secondly, we utilize a nonprobabilistic-type with distances to construct new entropy measures for PFSs. Then a min–max operation to calculate entropy measures for PFSs is suggested. Some examples are also used to demonstrate suitability and reliability of the proposed methods, especially for choosing the best one/ones in structured linguistic variables. Furthermore, a new method based on the chosen entropies is presented for Pythagorean fuzzy multicriterion decision making to compute criteria weights with ranking of alternatives. A comparison analysis with the most recent and relevant Pythagorean fuzzy entropy is conducted to reveal the advantages of our developed methods. Finally, this method is applied for ranking China-Pakistan Economic Corridor (CPEC) projects. These examples with applications demonstrate practical effectiveness of the proposed entropy measures.http://dx.doi.org/10.1155/2018/2832839 |
| spellingShingle | Miin-Shen Yang Zahid Hussain Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making Complexity |
| title | Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making |
| title_full | Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making |
| title_fullStr | Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making |
| title_full_unstemmed | Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making |
| title_short | Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making |
| title_sort | fuzzy entropy for pythagorean fuzzy sets with application to multicriterion decision making |
| url | http://dx.doi.org/10.1155/2018/2832839 |
| work_keys_str_mv | AT miinshenyang fuzzyentropyforpythagoreanfuzzysetswithapplicationtomulticriteriondecisionmaking AT zahidhussain fuzzyentropyforpythagoreanfuzzysetswithapplicationtomulticriteriondecisionmaking |