University of Sistan and Baluchestan Iranian Journal of Fuzzy Systems 1735-0654 20 1 2023 02 01 Quintuple intuitionistic fuzzy implications reasoning algorithms and application 153 170 7352 10.22111/ijfs.2023.7352 EN Z. S. Liu Key Laboratory of Oceanographic Big Data Mining and Application of Zhejiang Province, Zhoushan, 316022, China X. Li School of Information and Engineering, Zhejiang Ocean University, Zhoushan, 316000, China Journal Article 2023 01 15 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<br />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.<br />Finally, an application example for medical diagnosis is implemented to illustrate our proposed approaches. https://ijfs.usb.ac.ir/article_7352_b5ff1fab5a1f65f978d1416c52077a0b.pdf