A set of axioms for defuzzification strategies towards a theory of rational defuzzification operators

Runkler, Thomas A.; Glesner, Manfred

doi:10.1109/fuzzy.1993.327350

Cited by 94 publications

(38 citation statements)

References 4 publications

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“…Furthermore, different criteria for ''good'' operators have been considered in these areas. For more details, we refer reader to [7,12,14,[22][23][24].…”

Section: Weighted Trapezoidal Approximation Of a Fuzzy Numbermentioning

confidence: 99%

Weighted trapezoidal approximation-preserving cores of a fuzzy number

Abbasbandy

Hajjari

2010

Computers & Mathematics with Applications

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a b s t r a c tRecently, various researchers have proved that approximations of fuzzy numbers may fail to be fuzzy numbers. In this contribution, we suggest a new weighted trapezoidal approximation of an arbitrary fuzzy number, which preserves its cores. We prove that the weighted trapezoidal approximation-preserving core is always a fuzzy number. We then discuss properties of the approximation strategy including translation invariance, scale invariance identity and continuity. The advantage is that the method presented here is simpler than other methods computationally.

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“…Furthermore, different criteria for ''good'' operators have been considered in these areas. For more details, we refer reader to [7,12,14,[22][23][24].…”

Section: Weighted Trapezoidal Approximation Of a Fuzzy Numbermentioning

confidence: 99%

Weighted trapezoidal approximation-preserving cores of a fuzzy number

Abbasbandy

Hajjari

2010

Computers & Mathematics with Applications

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“…A nice description of these defuzzification criteria can be found in W. Van Leeckwijck and E. Kerre [148,149]. Some defuzzification criteria historically go back to the ideas T. Runkler proposed in [128]. Other interesting remarks about criteria that influence the choice of a defuzzification operator are given in Section 3.6 of [24].…”

Section: Criteriamentioning

confidence: 97%

An Overview of Fuzzy Control Theory

Peeters

2008

Foundations of Generic Optimization

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This chapter may serve as an introductory article, and is meant to give an overview of the mathematical methods applied in fuzzy control techniques, such as fuzzification, aggregation and defuzzification. We will also discuss the advantages and disadvantages of the several techniques, with respect to the achievability of their goals, and we will give a brief overview of "hybrid techniques", techniques that involves fuzzy control as well as other artificial intelligent computing methods, such as neural networks and genetic algorithms.

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“…Considering the type of system, one can distinguish a fuzzy inference system, for which such property as processing power, is less important than for a diffuse control system, for which the processing power is an important parameter. The study [35,37] introduced criteria of defuzzification operators for classic fuzzy numbers, on the basis of which individual defuzzification methods were assessed. The main conclusion is that there is no all-purpose defuzzification method.…”

Section: Definitionmentioning

confidence: 99%

Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes

Czerniak

Dobrosielski

Filipowicz

2017

Theory and Applications of Ordered Fuzzy Numbers

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This chapter concerns an issue of comparing fuzzy numbers. The relationship of similarity is probably the most widely used and most difficult to determine the measure of compliance precisely. Analysis of the similarity between two objects is an essential tool in biology, taxonomy, and psychology, and is the basis for reasoning by analogy. This chapter describes methods for determining the similarity used in fuzzy logic. Many of them were dedicated only to triangular or trapezoidal fuzzy numbers. This was a computing inconvenience and raised the question about the axiological basis for such comparisons. The authors have proposed two new approaches to comparing fuzzy numbers using one of the known fuzzy number extensions that are Ordered Fuzzy Numbers (OFNs). This has allowed us to simplify operations and eliminate said dualism. Two order-sensitive defuzzification methods are presented in the chapter. For OFN numbers with positive order (compliant with the direction of the OX axis increase) the results of defuzzifications are results for numbers of different notations, for example, L-R, whereas for numbers with negative orders, the defuzzification result changes. An important part of the chapter is a catalogue of the shapes of numbers in OFN notation. This is probably the first summary of basic shapes of those numbers with the results of defuzzifications using several methods.

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A set of axioms for defuzzification strategies towards a theory of rational defuzzification operators

Cited by 94 publications

References 4 publications

Weighted trapezoidal approximation-preserving cores of a fuzzy number

Weighted trapezoidal approximation-preserving cores of a fuzzy number

An Overview of Fuzzy Control Theory

Comparing Fuzzy Numbers Using Defuzzificators on OFN Shapes

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