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Soft Computing

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28.01.2020 | Methodologies and Application

Quintuple Implication Principle on interval-valued intuitionistic fuzzy sets

verfasst von: Jianhua Jin, Mingfei Ye, Witold Pedrycz

Erschienen in: Soft Computing | Ausgabe 16/2020

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Abstract

This paper mainly aims to introduce Quintuple Implication Principle (QIP) on interval-valued intuitionistic fuzzy sets (IVIFSs). Firstly, some algebraic properties of a class of interval-valued intuitionistic triangular norms are discussed in detail. In particular, a unified expression of residual interval-valued intuitionistic fuzzy implications generated by left-continuous triangular norms is presented. Secondly, Triple Implication Principles (TIPs) of both interval-valued intuitionistic fuzzy modus ponens (IVIFMP) and fuzzy modus tollens (IVIFMT) based on residual interval-valued intuitionistic fuzzy implications are analyzed. It is shown that the TIP solution of IVIFMP is recoverable, and the TIP solution of IVIFMT is only weakly local recoverable. Moreover, it sees by an illustrated example that the TIP method sometimes makes the computed solutions for IVIFMP and IVIFMT meaningless or misleading. To avoid the above shortcoming and enhance the recovery property of TIP solution of IVIFMT, QIP and \(\alpha \)-QIP for IVIFMP and IVIFMT are investigated and the corresponding expressions of solutions of them are also given, respectively. In addition, the QIP methods for IVIFMP and IVIFMT are recoverable and sound. Finally, QIP solutions of IVIFMP for multiple fuzzy rules are provided. An application example for medical diagnosis is given to illustrate the feasibility and effectiveness of the QIP of IVIFMP.

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Titel: Quintuple Implication Principle on interval-valued intuitionistic fuzzy sets
verfasst von: Jianhua Jin
Mingfei Ye
Witold Pedrycz
Publikationsdatum: 28.01.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 16/2020
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-019-04649-1

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