A Normative Approach to Fuzzy Logic Reasoning Using Residual Implications

Logical problems with fuzzy implications have been investigated minutely (Baczynski and Jayaram [1]). Considering some of the normative criteria to be met bygeneralized modus ponens, we have formulated a method of fuzzy reasoning based on residual implication. Among these criteria, the specificity possessed by the conclusion deduced bygeneralized modus ponensshould not be stronger than that of the consequent in the fuzzy implication.

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On the Ordering Property and Law of Importation in Fuzzy Logic

International Journal of Artificial Life Research ◽

10.4018/jalr.2010070102 ◽

2010 ◽

Vol 1 (3) ◽

pp. 17-30

Author(s):

Huiwen Deng ◽

Huan Jiang

Keyword(s):

Fuzzy Logic ◽

Sufficient Conditions ◽

Necessary And Sufficient Conditions ◽

Sufficient Condition ◽

Fuzzy Implications ◽

Fuzzy Implication ◽

The Law ◽

Necessary And Sufficient ◽

Triple I Method

In this paper, the authors investigate the ordering property (OP), , together with the general form of the law of importation(LI), i.e., , whereis a t-norm andis a fuzzy implication for the four main classes of fuzzy implications. The authors give necessary and sufficient conditions under which both (OP) and (LI) holds for S-, R-implications and some specific families of QL-, D-implications. Following this, the paper proposes the sufficient condition under which the equivalence between CRI and triple I method for FMP can be established. Moreover, this conclusion can be viewed as a unified triple I method, a generalized form of the known results proposed by Wang and Pei.

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Pythagorean fuzzy full implication multiple I method and corresponding applications

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210527 ◽

2021 ◽

pp. 1-15

Author(s):

TaiBen Nan ◽

Haidong Zhang ◽

Yanping He

Keyword(s):

Decision Making ◽

Modus Ponens ◽

Pythagorean Fuzzy Set ◽

Implication Operator ◽

Continuity Properties ◽

Fuzzy Implication ◽

Decision Making Problem ◽

Fuzzy Implication Operator ◽

Degree Of Similarity ◽

Fuzzy Modus Ponens

The overwhelming majority of existing decision-making methods combined with the Pythagorean fuzzy set (PFS) are based on aggregation operators, and their logical foundation is imperfect. Therefore, we attempt to establish two decision-making methods based on the Pythagorean fuzzy multiple I method. This paper is devoted to the discussion of the full implication multiple I method based on the PFS. We first propose the concepts of Pythagorean t-norm, Pythagorean t-conorm, residual Pythagorean fuzzy implication operator (RPFIO), Pythagorean fuzzy biresiduum, and the degree of similarity between PFSs based on the Pythagorean fuzzy biresiduum. In addition, the full implication multiple I method for Pythagorean fuzzy modus ponens (PFMP) is established, and the reversibility and continuity properties of the full implication multiple I method of PFMP are analyzed. Finally, a practical problem is discussed to demonstrate the effectiveness of the Pythagorean fuzzy full implication multiple I method in a decision-making problem. The advantages of the new method over existing methods are also explained. Overall, the proposed methods are based on logical reasoning, so they can more accurately and completely express decision information.

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Application of interpolation-based fuzzy logic reasoning in behaviour-based control structures

2004 IEEE International Conference on Fuzzy Systems (IEEE Cat. No.04CH37542) ◽

10.1109/fuzzy.2004.1375404 ◽

2005 ◽

Cited By ~ 7

Author(s):

S. Kovacs ◽

L.T. Koczy

Keyword(s):

Fuzzy Logic ◽

Control Structures ◽

Logic Reasoning

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A method of constructing fuzzy implications from the FIφ-construction

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-202385 ◽

2021 ◽

pp. 1-14

Author(s):

Yifan Zhao ◽

Kai Li

Keyword(s):

Specific Property ◽

New Method ◽

Aggregation Function ◽

Fuzzy Implications ◽

Construction Methods ◽

Fuzzy Implication ◽

New Construction

In the recent years, several new construction methods of fuzzy implications have been proposed. However, these construction methods actually care about that the new implication could preserve more properties. In this paper, we introduce a new method for constructing fuzzy implications based on an aggregation function with F (1, 0) =1, a fuzzy implication I and a non-decreasing function φ, called FIφ-construction. Specifically, some logical properties of fuzzy implications preserved by this construction are studied. Moreover, it is studied how to use the FIφ-construction to produce a new implication satisfying a specific property. Furthermore, we produce two new subclasses of fuzzy implications such as UIφ-implications and GpIφ-implications by this method and discuss some additional properties. Finally, we provide a way to generate fuzzy subsethood measures by means of FIφ-implications.

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CONTRAPOSITIVE SYMMETRY OF DISTRIBUTIVE FUZZY IMPLICATIONS

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s0218488502001880 ◽

2002 ◽

Vol 10 (supp01) ◽

pp. 135-147 ◽

Cited By ~ 19

Author(s):

MICHAŁ BACZYŃSKI

Keyword(s):

Functional Equation ◽

Functional Equations ◽

Strong Negation ◽

Fuzzy Implications ◽

Fuzzy Implication

Recently, we have examined the solutions of the system of the functional equations I(x, T(y, z)) = T(I(x, y), I(x, z)), I(x, I(y, z)) = I(T(x, y), z), where T : [0, 1]2 → [0, 1] is a strict t-norm and I : [0, 1]2 → [0, 1] is a non-continuous fuzzy implication. In this paper we continue these investigations for contrapositive implications, i.e. functions which satisfy the functional equation I(x, y) = I(N(y), N(x)), with a strong negation N : [0, 1] → [0, 1]. We show also the bounds for two classes of fuzzy implications which are connected with our investigations.

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