Abstract
This paper presents axiomatic as well as constructive definitions of intuitionistic fuzzy bi-implicators based on intuitionistic fuzzy t-norms and their intuitionistic fuzzy residual implicators. The inter-relationship among different proposed classes is presented along with a detailed study of the properties of one of these intuitionistic fuzzy bi-implicators called the intuitionistic fuzzy beta-bi-operator constructed using Lukasiewicz intuitionistic fuzzy t-norm and its R-implicator.
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