Interval-valued Atanassov intuitionistic t-norms and t-conorms endowed with the usual or admissible orders. (English) Zbl 1524.03043
Summary: The interval-valued fuzzy sets and Atanassov intuitionistic fuzzy sets can be extended to a more general framework to simultaneously deal with uncertainty in both membership and non-membership values. This fact leads to the concept of interval-valued Atanassov intuitionistic fuzzy sets (IVAIFS), as given by K. Atanassov and G. Gargov [Fuzzy Sets Syst. 31, No. 3, 343–349 (1989; Zbl 0674.03017)]. In this paper, we focus on the study of interval-valued Atanassov intuitionistic t-norms and t-conorms, studying important properties and characterizations of some of their sub-classes. In addition, we do not only consider just the usual order on IVAIFS, but also admissible orders. Finally, we establish the basis for the use of this study in the approximate reasoning context.
MSC:
| 03E72 | Theory of fuzzy sets, etc. |
Keywords:
interval-valued Atanassov intuitionist fuzzy sets; admissible linear orders; t-norms; t-conorms; composition of fuzzy relations; approximate reasoningCitations:
Zbl 0674.03017References:
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