Journal
AXIOMS
Volume 11, Issue 11, Pages -Publisher
MDPI
DOI: 10.3390/axioms11110593
Keywords
fuzzy logic; information fusion; pseudo overlap function; pseudo t-norm; fuzzy implication
Categories
Funding
- National Natural Science Foundation of China [12271319]
- Major Program of the National Social Science Foundation of China [20ZD047]
- AEI [PID2019-108392GB-I00]
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This paper introduces the concepts of pseudo overlap functions and pseudo grouping functions, which expand the original notions of overlap and grouping functions. By removing the commutativity of the original functions, the pseudo functions show greater flexibility and practicality, allowing for more in-depth research and applications in various fields.
Overlap and grouping functions are important aggregation operators, especially in information fusion, classification and decision-making problems. However, when we do more in-depth application research (for example, non-commutative fuzzy reasoning, complex multi-attribute decision making and image processing), we find overlap functions as well as grouping functions are required to be commutative (or symmetric), which limit their wide applications. For the above reasons, this paper expands the original notions of overlap functions and grouping functions, and the new concepts of pseudo overlap functions and pseudo grouping functions are proposed on the basis of removing the commutativity of the original functions. Some examples and construction methods of pseudo overlap functions and pseudo grouping functions are presented, and the residuated implication (co-implication) operators derived from them are investigated. Not only that, some applications of pseudo overlap (grouping) functions in multi-attribute (group) decision-making, fuzzy mathematical morphology and image processing are discussed. Experimental results show that, in many application fields, pseudo overlap functions and pseudo grouping functions have greater flexibility and practicability.
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