Q-Rung Orthopair Fuzzy Integrals in the Frame of Continuous Archimedean T-Norms and T-Conorms and Their Application
Autor: | Ronald R. Yager, Zhenghai Ai, Zeshui Xu, Jianmei Ye |
---|---|
Rok vydání: | 2021 |
Předmět: |
Pure mathematics
Class (set theory) Basis (linear algebra) Generalization Applied Mathematics Multiple integral Fuzzy set 02 engineering and technology Fuzzy logic Computational Theory and Mathematics Artificial Intelligence Control and Systems Engineering Ordered pair 0202 electrical engineering electronic engineering information engineering Fuzzy number 020201 artificial intelligence & image processing Mathematics |
Zdroj: | IEEE Transactions on Fuzzy Systems. 29:996-1007 |
ISSN: | 1941-0034 1063-6706 |
DOI: | 10.1109/tfuzz.2020.2965887 |
Popis: | Yager's q -rung orthopair fuzzy set is a generalization of fuzzy sets, whose prominent feature is that the q th power sum of the membership and the nonmembership degrees is equal to or less than one, and we call its core, an ordered pair, q -rung orthopair fuzzy number ( q -ROFN). More recently, the scholars have constructed the q -rung orthopair fuzzy calculus ( q -ROFC), which can effectively deal with continuous q -rung orthopair fuzzy information. Nevertheless, the q -ROFC is only based on the basic operational laws of the q -ROFNs, in fuzzy theory, Archimedean t-norms and t-conorms (ATTs) are a significant class of continuous triangular norms and conorms, which are the generalizations of the intersection and union related to fuzzy sets. Thus, in order to extend the q -ROFC to a wider area, in this article, we systematically discuss the q -rung orthopair fuzzy double integrals ( q -ROFDIs) in the frame of ATTs. First, we construct the q -ROFDI in the frame of Archimedean t-conorms in detail, and then provide its concrete value. In addition, we reveal the relationships with respect to two types of q -rung orthopair fuzzy spaces. Based on which, we can easily obtain another types of q -ROFDI. After that, we investigate their fundamental properties in detail so as to comprehend these kinds of q -ROFDIs in-depth. Finally, we point out the essences of these kinds of q -ROFDIs, on the basis of which we provide a practical application to show their effectiveness and elasticity via comparing with the existing methods. |
Databáze: | OpenAIRE |
Externí odkaz: |