The capability of complex fuzzy sets plays a valuable role in resolving many real-life problems. In this paper, we present the compositions of complex fuzzy relations by using the idea of implication operators and max-product compositions of complex fuzzy relations and illustrate these compositions with concrete examples. The converse of these newly invented triangular compositions in terms of compositions of the converse relations is also defined. We also study the interactions with the union and intersection. The main goal of this article is to present a new technique to enhance medical diagnostic models that can assist in improving the features of healthcare systems. We utilize these compositions to diagnose diseases in patients on the basis of the intensity of symptoms.

Fuzzy implication operators are vital in the modeling of uncertain reasoning, particularly in approximate reasoning and fuzzy inference systems. The objective of this survey is to provide a structured and comprehensive overview of fuzzy implication, intuitionistic fuzzy implication, and hesitant fuzzy implication. We examine their properties, representations, and characterizations. We discuss a number of findings about fuzzy negations, fuzzy implications, intuitionistic fuzzy implication, and hesitant fuzzy implications, including their characterizations with respect to the identity principle and ordering property, which lead to fundamental results.

The capability of the complex fuzzy sets plays a valuable role to resolve many real life problems. In this paper, we present the compositions of complex fuzzy relations by using the idea of implication operators and max-product compositions of complex fuzzy relations and illustrate these compositions with concrete examples. The converse of these newly invented triangular compositions in terms of compositions of the converse relations are also defined. We also study the interactions with union and intersection. The main goal of this article to present a new technique to enhance medical diagnostic model that can assist to increase the features of healthcare systems. We utilize these compositions to determine the diseases of patients on the basis of intensity of symptoms.