Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making
The overlap function, a continuous aggregation function, is widely used in classification, decision-making, image processing, etc. Compared to applications, overlap functions have also achieved fruitful results in theory, such as studies on the fundamental properties of overlap functions, various ge...
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2024-11-01
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| author | Mei Jing Jingqian Wang Mei Wang Xiaohong Zhang |
| author_facet | Mei Jing Jingqian Wang Mei Wang Xiaohong Zhang |
| author_sort | Mei Jing |
| collection | DOAJ |
| description | The overlap function, a continuous aggregation function, is widely used in classification, decision-making, image processing, etc. Compared to applications, overlap functions have also achieved fruitful results in theory, such as studies on the fundamental properties of overlap functions, various generalizations of the concept of overlap functions, and the construction of additive and multiplicative generators based on overlap functions. However, most of the research studies on the overlap functions mentioned above contain commutativity and continuity, which can limit their practical applications. In this paper, we remove the symmetry and continuity from overlap functions and define discrete pseudo-quasi overlap functions on finite chains. Meanwhile, we also discuss their related properties. Then, we introduce pseudo-quasi overlap functions on sub-chains and construct discrete pseudo-quasi overlap functions on finite chains using pseudo-quasi overlap functions on these sub-chain functions. Unlike quasi-overlap functions on finite chains generated by the ordinal sum, discrete pseudo-quasi overlap functions on finite chains constructed through pseudo-quasi overlap functions on different sub-chains are dissimilar. Eventually, we remove the continuity from pseudo-automorphisms and propose the concept of pseudo-quasi-automorphisms. Based on this, we utilize pseudo-overlap functions, pseudo-quasi-automorphisms, and integral functions to obtain discrete pseudo-quasi overlap functions on finite chains, moreover, we apply them to fuzzy multi-attribute group decision-making. The results indicate that compared to overlap functions and pseudo-overlap functions, discrete pseudo-quasi overlap functions on finite chains have stronger flexibility and a wider range of practical applications. |
| format | Article |
| id | doaj-art-ad71e52bfda440b4958a3c6e8963a8b6 |
| institution | DOAJ |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-ad71e52bfda440b4958a3c6e8963a8b62025-08-20T02:48:06ZengMDPI AGMathematics2227-73902024-11-011222356910.3390/math12223569Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-MakingMei Jing0Jingqian Wang1Mei Wang2Xiaohong Zhang3School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, ChinaSchool of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, ChinaThe overlap function, a continuous aggregation function, is widely used in classification, decision-making, image processing, etc. Compared to applications, overlap functions have also achieved fruitful results in theory, such as studies on the fundamental properties of overlap functions, various generalizations of the concept of overlap functions, and the construction of additive and multiplicative generators based on overlap functions. However, most of the research studies on the overlap functions mentioned above contain commutativity and continuity, which can limit their practical applications. In this paper, we remove the symmetry and continuity from overlap functions and define discrete pseudo-quasi overlap functions on finite chains. Meanwhile, we also discuss their related properties. Then, we introduce pseudo-quasi overlap functions on sub-chains and construct discrete pseudo-quasi overlap functions on finite chains using pseudo-quasi overlap functions on these sub-chain functions. Unlike quasi-overlap functions on finite chains generated by the ordinal sum, discrete pseudo-quasi overlap functions on finite chains constructed through pseudo-quasi overlap functions on different sub-chains are dissimilar. Eventually, we remove the continuity from pseudo-automorphisms and propose the concept of pseudo-quasi-automorphisms. Based on this, we utilize pseudo-overlap functions, pseudo-quasi-automorphisms, and integral functions to obtain discrete pseudo-quasi overlap functions on finite chains, moreover, we apply them to fuzzy multi-attribute group decision-making. The results indicate that compared to overlap functions and pseudo-overlap functions, discrete pseudo-quasi overlap functions on finite chains have stronger flexibility and a wider range of practical applications.https://www.mdpi.com/2227-7390/12/22/3569fuzzy logicinformation fusionoverlap functionfuzzy multi-attribute group decision-making |
| spellingShingle | Mei Jing Jingqian Wang Mei Wang Xiaohong Zhang Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making Mathematics fuzzy logic information fusion overlap function fuzzy multi-attribute group decision-making |
| title | Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making |
| title_full | Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making |
| title_fullStr | Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making |
| title_full_unstemmed | Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making |
| title_short | Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making |
| title_sort | discrete pseudo quasi overlap functions and their applications in fuzzy multi attribute group decision making |
| topic | fuzzy logic information fusion overlap function fuzzy multi-attribute group decision-making |
| url | https://www.mdpi.com/2227-7390/12/22/3569 |
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