Discrete Pseudo-Quasi Overlap Functions and Their Applications in Fuzzy Multi-Attribute Group Decision-Making

Mei Jing, Jingqian Wang, Mei Wang and Xiaohong Zhang ()
Additional contact information
Mei Jing: School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China
Jingqian Wang: School of Mathematics and Data Science, Shaanxi University of Science & Technology, Xi’an 710021, China
Mei Wang: School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China
Xiaohong Zhang: School of Electrical and Control Engineering, Shaanxi University of Science & Technology, Xi’an 710021, China

Mathematics, 2024, vol. 12, issue 22, 1-25

Abstract: 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.

Keywords: fuzzy logic; information fusion; overlap function; fuzzy multi-attribute group decision-making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/22/3569/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/22/3569/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:22:p:3569-:d:1521776

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().