Quintuple intuitionistic fuzzy implications reasoning algorithms and application

Atanassov's intuitionistic fuzzy sets have succussed in the application of decision making, data mining, artificial intelligence, image processing, and so on. In these applications, intuitionistic fuzzy reasoning plays a crucial role. To improve the quality of intuitionistic fuzzy reasoning, this paper presents a quintuple intuitionistic fuzzy implication principle (QIIP) to resolve intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) problems. The QIIP algorithms of IFMP and IFMT problems for intuitionistic R-implication, S-implication, and several fuzzy implications are represented. Moreover, we investigate the recovery property and continuity of QIIP algorithms for IFMP and IFMT. Finally, an application example for medical diagnosis is implemented to illustrate our proposed approaches.