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quintuple implication principle on interval-valued intuitionistic fuzzy sets

SOFT COMPUTING 2020年第16期24卷 12091-12109页

作者： Jin, Jianhua Ye, Mingfei Pedrycz, Witold Southwest Petr Univ Coll Sci Chengdu 610500 Peoples R China Univ Alberta Dept Elect & Comp Engn Edmonton AB T6G 1H9 Canada

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.

关键词： Fuzzy modus ponens Fuzzy modus tollens Interval-valued intuitionistic fuzzy sets quintuple implication principle Triple implication principle

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The quintuple implication principle of fuzzy reasoning based on interval-valued S-implication

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JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING 2018年 100卷 185-194页

作者： Li, Dechao Qin, Sijian Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316000 Peoples R China Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Peoples R China

Interval-valued fuzzy reasoning is an important issue in approximate reasoning and decision making under fuzzy and uncertainty. To improve the quality of interval-valued fuzzy reasoning, this paper proposes the quintuple implication principle (QIP) of fuzzy reasoning based on interval-valued S-implication in order to solve interval-valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT). We first present the QIP solutions of IFMP and IFMT for interval-valued S-implications, then discuss the reductivity and continuity of fuzzy reasoning with QIP method for interval-valued S implications. Finally, we also provide several examples to illustrate and substantiate our theoretical developments. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Interval-valued fuzzy implication Interval-valued S-implication Interval-valued fuzzy reasoning quintuple implication principle

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The quintuple implication principle of fuzzy reasoning

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INFORMATION SCIENCES 2015年 297卷 202-215页

作者： Zhou, Baokui Xu, Genqi Li, Sanjiang Tianjin Univ Dept Math Tianjin 300072 Peoples R China Univ Technol Sydney Ctr Quantum Computat & Intelligent Syst QCIS Broadway NSW 2007 Australia

Fuzzy Modus Ponens (FMP) and Fuzzy Modus Tollens (FMT) are two fundamental patterns of approximate reasoning. Suppose A and B are fuzzy predicates and "IF A THEN B" is a fuzzy rule. Approximate reasoning often requires to derive an approximation B* of B from a given approximation A* of A, or vice versa. To solve these problems, Zadeh introduces the well-known Compositional Rule of Inference (CRI), which models fuzzy rule by implication and computes B* (A*, resp.) by composing A* (B*, resp.) with A -> B. Wang argues that the use of the compositional operation is logically not sufficiently justified and proposes the Triple implication principle (TIP) instead. Both CRI and TIP do not explicitly use the closeness of A and A* (or that of B and B*) in the process of calculating the consequence, which makes the thus computed approximation sometimes useless or misleading. In this paper, we propose the quintuple implication principle (QIP) for fuzzy reasoning, which characterizes the approximation B* of B (A* of A, resp.) as the formula which is best supported by A -> B, A* -> A and A* (A -> B, B -> B* and B*, resp.). Based upon Monoidal t-norm Logic (MTL), this paper applies QIP to solve FMP and FMT for four important implications. Most importantly, we show that QIP, when using Godel implication, computes exactly the same approximation as Mamdani-type fuzzy inference does. This is surprising as Mamdani interprets fuzzy rules in terms of the minimum operation, while CRI, TIP and QIP all interpret fuzzy rules in terms of implication. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Fuzzy reasoning Compositional rules of inference Triple implication principle Mamdani-type fuzzy inference Monoidal t-norm Logic quintuple implication principle

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Interval-valued pointwise sustaining degree fuzzy reasoning methods based on the left-continuous t-representable t-norms

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022年第6期42卷 5013-5029页

作者： Luo, Minxia Xu, Donghui China Jiliang Univ Dept Informat & Comp Sci Hangzhou 310018 Peoples R China

In this paper, the concept of alpha(x, y)-interval-valued pointwise sustaining degree based on the left-continuous trepresentable t-norms is put forward. And then, as a general extension based on the interval-valued pointwise sustaining degree, the interval-valued alpha(x, y)-full implication triple I method model, the interval-valued alpha(x, y)-quintuple implication principle models and the interval-valued alpha(x, y)-similarity measure method models are given. Moreover, the interval-valued R-type alpha(x, y)-fuzzy reasoning solutions with triple I method, quintuple implication principle and similarity measure method are given. Some existing results are special cases of the main conclusions in this paper.

关键词： Interval-valued pointwise staining degree left-continuous t-representable t-norms Triple I method quintuple implication principle similarity measure method

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Performance analysis of fuzzy systems based on quintuple implications method

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2018年 96卷 20-35页

作者： Li, Dechao Qin, Sijia Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316022 Peoples R China Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Peoples R China

To improve the quality of approximate reasoning in fuzzy system, quintuple implication principle (QIP) to resolve fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT) problems has been proposed by Zhou et al. [32]. The same approximation as Mamdani-type fuzzy inference can be reached by fuzzy reasoning with QIP method for Godel implication. It therefore is essential to establish some fundamental properties of fuzzy inference system with QIP method. This paper mainly investigates the robustness and universal approximation capability of fuzzy inference system with QIP method. Firstly, we present the QIP solutions of FMP and FMT for R-, S-, QL-, f- and g-implications. And then the robustness of fuzzy inference system with QIP method is discussed. Finally, we study the universal approximation properties of multiple-input and single-output (MISO) fuzzy systems with QIP method for R-, S- and QL-implications. These results reveal that the OIP method possesses better performance in fuzzy rule-based system. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Fuzzy reasoning Fuzzy implication quintuple implication principle Robustness Universal approximator

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Interval-valued fuzzy inference based on aggregation functions

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INTERNATIONAL JOURNAL OF APPROXIMATE REASONING 2019年 113卷 74-90页

作者： Li, Dechao Zhu, Min Zhejiang Ocean Univ Sch Math Phys & Informat Sci Zhoushan 316000 Peoples R China Key Lab Oceanog Big Data Min & Applicat Zhejiang Zhoushan 316022 Peoples R China

Generalized modus ponens (GMP) and generalized modus tollens (GMT), as two basic patterns of approximate reasoning, aim to acquire some reasonable imprecise conclusions from a collection of imprecise premises using some inference rules. To solve the GMP and GMT problems under interval-valued fuzzy setting, an interval-valued A-compositional rule of inference (ACRI) method and quintuple implication principle (QIP) method with interval valued implication generated by A under any partial order are presented in this paper, where A is an interval-valued aggregation function. In order to develop these methods, we firstly discuss interval-valued negation generated by an interval-valued aggregation function with any partial order. Some properties of interval-valued implications generated by interval-valued aggregation functions with an arbitrary order are then analyzed. We further investigate the ACRI method and quintuple implication principle (QIP) method with interval-valued implication generated by interval-valued aggregations to solve the interval valued fuzzy modus ponens (IFMP) and interval-valued fuzzy modus tollens (IFMT). Finally, two examples are implemented to illustrate our proposed approaches using some special interval-valued aggregation functions. (C) 2019 Elsevier Inc. All rights reserved.

关键词： Interval-valued aggregation Interval-valued negation Interval-valued implication Compositional rule of inference quintuple implication principle

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Semi-overlap functions and novel fuzzy reasoning algorithms with applications

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INFORMATION SCIENCES 2022年 614卷 104-122页

作者： Zhang, Xiaohong Wang, Mei Bedregal, Benjamin Li, Mengyuan Liang, Rong Shaanxi Univ Sci & Technol Sch Math & Data Sci Xian 710021 Shaanxi Peoples R China Shaanxi Univ Sci & Technol Sch Elect & Control Engn Xian 710021 Shaanxi Peoples R China Univ Fed Rio Grande do Norte Dept Informat & Matemat Aplicada Campus Univ S-N BR-59072970 Natal Brazil

In order to get a more general result related on fuzzy implications that induced by aggre-gation functions, we relax the definition of general overlap functions, more precisely, removing its right-continuous, and introduce a new kind of aggregation function, which called semi-overlap function. Subsequently, we explore some of their related algebraic properties and its corresponding residual implications. Moreover, serval scholars have pro-vided kinds of methods for fuzzy modus ponens (FMP, for short) problems, such as Zadeh's compositional rule of inference (CRI, for short), Wang's triple I method (TIM, for short) and quintuple implication principle (QIP, for short). Compared with CRI and TIM, QIP has some advantages in solving FMP problems. Based on the above theory foundation of semi -overlap functions and their residual implications, we further consider the QIP for FMP problems. Finally, we propose a new classification algorithm that based on semi-overlap functions and QIP, which called SO5I-FRC algorithm. Through the comparative tests, the average accuracy of SO5I-FRC algorithm is higher than FARC-HD algorithm. The experi-mental results indicate that semi-overlap functions and QIP have certain advantages and a wide range of applications in classification problems.(c) 2022 Elsevier Inc. All rights reserved.

关键词： Overlap function Semi-overlap function Fuzzy reasoning quintuple implication principle Classification algorithm

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