A Method of Generating Fuzzy Implications with Specific Properties

In this paper we introduce a new method of generating fuzzy implications via known fuzzy implications. We focus on the case of generating fuzzy implications via a fuzzy connective and at least one known fuzzy implication. We present some basic desirable properties of fuzzy implications that are invariant via this method. Furthermore, we suggest some ways of preservation or violation of these properties, based in this method. We show how we can generate not greater or not weaker fuzzy implications with specific properties. Finally, two subclasses of any fuzzy implication arise, the so called T and S subclasses.

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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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A new class of fuzzy implications. Axioms of fuzzy implication revisited

Fuzzy Sets and Systems ◽

10.1016/s0165-0114(97)00066-3 ◽

1998 ◽

Vol 100 (1-3) ◽

pp. 267-272 ◽

Cited By ~ 45

Author(s):

I. Burhan Türkşen ◽

Vladik Kreinovich ◽

Ronald R. Yager

Keyword(s):

New Class ◽

Fuzzy Implications ◽

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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Generating Fuzzy Implications by Ordinal Sums

Tatra Mountains Mathematical Publications ◽

10.1515/tmmp-2016-0018 ◽

2016 ◽

Vol 66 (1) ◽

pp. 39-50 ◽

Cited By ~ 3

Author(s):

Paweł Drygaś ◽

Anna Król

Keyword(s):

Fuzzy Implications ◽

Fuzzy Implication

Abstract This paper deals with ordinal sums of fuzzy implications. Some of the known constructions are recalled and new ways of generating fuzzy implications from given ones are proposed. Sufficient properties of fuzzy implications as summands for obtaining a fuzzy implication as a result are presented.

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(T,N) and Residual Fuzzy Co-Implication in Dual Heyting Algebra with Applications

10.20944/preprints201608.0027.v1 ◽

2016 ◽

Cited By ~ 1

Author(s):

Iqbal H. Jebril

Keyword(s):

Heyting Algebra ◽

Fuzzy Implications ◽

Fuzzy Implication ◽

New Concepts

Recently, many authors have been interested to introduce fuzzy implications over t-norms and t-conorms. In this paper, we introduce (S,N) and residuum fuzzy implication for Dubois t-norm and Hamacher's t-norm. Also, new concepts so-called (T,N) and residual fuzzy co-implication in dual Heyting Algebra are investigated. Some examples as well as application are discussed as well.

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Modifications of Łukasiewicz’s intuitionistic fuzzy implication

Notes on Intuitionistic Fuzzy Sets ◽

10.7546/nifs.2021.27.3.32-39 ◽

2021 ◽

Vol 27 (3) ◽

pp. 32-39

Author(s):

Alžbeta Michalíková ◽

◽

Eulalia Szmidt ◽

Peter Vassilev ◽

◽

...

Keyword(s):

Basic Properties ◽

Fuzzy Implications ◽

Intuitionistic Fuzzy ◽

Fuzzy Implication

In [6], G. Klir and B. Yuan named after J. Łukasiewicz the implication p \rightarrow q = min(1, p+q). In a series of papers, 198 different intuitionistic fuzzy implications have been introduced, and their basic properties have been studied. Here we introduce six new implications which are modifications of Łukasiewicz’s intuitionistic fuzzy implication, and we describe and prove some of their properties.

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LEVELS OF SIGNIFICANCE FOR FUZZY IMPLICATION

International Journal of Uncertainty Fuzziness and Knowledge-Based Systems ◽

10.1142/s021848859400002x ◽

1994 ◽

Vol 02 (01) ◽

pp. 1-10

Author(s):

WYLLIS BANDLER ◽

SUSAN I. HRUSKA

Keyword(s):

Upper Bounds ◽

Lower And Upper Bounds ◽

Hasse Diagrams ◽

Fuzzy Implications ◽

Fuzzy Implication ◽

Intended Use

Fuzzy implication operators have been proposed as a tool for measuring the strength of connections between recorded concepts. Hasse diagrams are used to graphically illustrate the sometimes complicated relationships between such concepts. Establishing measures of significance for fuzzy implications is the focus of this paper. Lower and upper bounds for mean implication using the Kleene-Dienes operator are established. Examples of the intended use of these measures are given.

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Parametric Fuzzy Implications Produced via Fuzzy Negations with a Case Study in Environmental Variables

Symmetry ◽

10.3390/sym13030509 ◽

2021 ◽

Vol 13 (3) ◽

pp. 509

Author(s):

Stefanos Makariadis ◽

Georgios Souliotis ◽

Basil Papadopoulos

Keyword(s):

Environmental Variables ◽

Real Data ◽

Matlab Code ◽

Fuzzy Implications ◽

Fuzzy Implication ◽

Final Goal ◽

Best Value ◽

Temperature And Humidity ◽

Real Temperature

In this paper, we present a new Fuzzy Implication Generator via Fuzzy Negations which was generated via conical sections, in combination with the well-known Fuzzy Conjunction. The new Fuzzy Implication Generator takes its final forms after being configured by the fuzzy strong negations and combined with the most well-known fuzzy conjunctions TM, TP, TLK, TD, and TnM. The final implications that emerge, given that they are configured with the appropriate code, select the best value of the parameter and the best combination of the fuzzy conjunctions. This choice is made after comparing them with the Empiristic implication, which was created with the help of real temperature and humidity data from the Hellenic Meteorological Service. The use of the Empiristic implication is based on real data, and it also reduces the volume of the data without canceling them. Finally, the MATLAB code, which was used in the programming part of the paper, uses the new Fuzzy Implication Generator and approaches the Empiristic implication satisfactorily which is our final goal.

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A Normative Approach to Fuzzy Logic Reasoning Using Residual Implications

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2009.p0262 ◽

2009 ◽

Vol 13 (3) ◽

pp. 262-267 ◽

Cited By ~ 2

Author(s):

Yahachiro Tsukamoto ◽

Keyword(s):

Fuzzy Logic ◽

Fuzzy Reasoning ◽

Modus Ponens ◽

Normative Approach ◽

Fuzzy Implications ◽

Fuzzy Implication ◽

Normative Criteria ◽

Logic Reasoning

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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