Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots
In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy number...
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| Format: | Article |
| Language: | English |
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MDPI AG
2019-02-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/11/2/218 |
| _version_ | 1811187052972081152 |
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| author | Jinming Zhou Tomas Baležentis Dalia Streimikiene |
| author_facet | Jinming Zhou Tomas Baležentis Dalia Streimikiene |
| author_sort | Jinming Zhou |
| collection | DOAJ |
| description | In this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator. |
| first_indexed | 2024-04-11T13:56:43Z |
| format | Article |
| id | doaj.art-1052169e0264444b89e85d34956c7af1 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-04-11T13:56:43Z |
| publishDate | 2019-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-1052169e0264444b89e85d34956c7af12022-12-22T04:20:17ZengMDPI AGSymmetry2073-89942019-02-0111221810.3390/sym11020218sym11020218Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue RobotsJinming Zhou0Tomas Baležentis1Dalia Streimikiene2School of Mathematics and Physics, Anhui Polytechnic University, Wuhu 241000, ChinaLithuanian Institute of Agrarian Economics, V. Kudirkos Str. 18-2, LT-03105 Vilnius, LithuaniaLithuanian Institute of Agrarian Economics, V. Kudirkos Str. 18-2, LT-03105 Vilnius, LithuaniaIn this paper, Normalized Weighted Bonferroni Mean (NWBM) and Normalized Weighted Bonferroni Harmonic Mean (NWBHM) aggregation operators are proposed. Besides, we check the properties thereof, which include idempotency, monotonicity, commutativity, and boundedness. As the intuitionistic fuzzy numbers are used as a basis for the decision making to effectively handle the real-life uncertainty, we extend the NWBM and NWBHM operators into the intuitionistic fuzzy environment. By further modifying the NWBHM, we propose additional aggregation operators, namely the Intuitionistic Fuzzy Normalized Weighted Bonferroni Harmonic Mean (IFNWBHM) and the Intuitionistic Fuzzy Ordered Normalized Weighted Bonferroni Harmonic Mean (IFNONWBHM). The paper winds up with an empirical example of multi-attribute group decision making (MAGDM) based on triangular intuitionistic fuzzy numbers. To serve this end, we apply the IFNWBHM aggregation operator.https://www.mdpi.com/2073-8994/11/2/218Bonferroni harmonic meanaggregation operatorintuitionistic fuzzy setmultiple attribute group decision makingsearch and rescue robots |
| spellingShingle | Jinming Zhou Tomas Baležentis Dalia Streimikiene Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots Symmetry Bonferroni harmonic mean aggregation operator intuitionistic fuzzy set multiple attribute group decision making search and rescue robots |
| title | Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots |
| title_full | Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots |
| title_fullStr | Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots |
| title_full_unstemmed | Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots |
| title_short | Normalized Weighted Bonferroni Harmonic Mean-Based Intuitionistic Fuzzy Operators and Their Application to the Sustainable Selection of Search and Rescue Robots |
| title_sort | normalized weighted bonferroni harmonic mean based intuitionistic fuzzy operators and their application to the sustainable selection of search and rescue robots |
| topic | Bonferroni harmonic mean aggregation operator intuitionistic fuzzy set multiple attribute group decision making search and rescue robots |
| url | https://www.mdpi.com/2073-8994/11/2/218 |
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