Fuzzy Rule Based Modeling as a Universal Approximation Tool

Kreinovich, Vladik; Mouzouris, G.C.; Nguyen, Hung T.

doi:10.1007/978-1-4615-5505-6_5

Cited by 55 publications

(37 citation statements)

References 94 publications

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“…. , x n ) and for every ε > 0, there exists a set of rules for which the corresponding input-output function is ε-close to f ; see, e.g., [1,8,9,11,12,16,18,19,22,23,25] and references therein.…”

Section: Universal Approximation Resultsmentioning

confidence: 99%

Fuzzy without Fuzzy: Why Fuzzy-Related Aggregation Techniques Are Often Better Even in Situations without True Fuzziness

Nguyen

Kreinovich

Modave

et al. 2009

Foundations of Computational Intelligence Volume 2

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Summary. Fuzzy techniques have been originally invented as a methodology that transforms the knowledge of experts formulated in terms of natural language into a precise computer-implementable form. There are many successful applications of this methodology to situations in which expert knowledge exist, the most well known is an application to fuzzy control.In some cases, fuzzy methodology is applied even when no expert knowledge exists: instead of trying to approximate the unknown control function by splines, polynomials, or by any other traditional approximation technique, researchers try to approximate it by guessing and tuning the expert rules. Surprisingly, this approximation often works fine, especially in such application areas as control and multi-criteria decision making.In this paper, we give a mathematical explanation for this phenomenon.

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Section: Universal Approximation Resultsmentioning

confidence: 99%

Fuzzy without Fuzzy: Why Fuzzy-Related Aggregation Techniques Are Often Better Even in Situations without True Fuzziness

Nguyen

Kreinovich

Modave

et al. 2009

Foundations of Computational Intelligence Volume 2

Self Cite

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“…This universality property is well known and actively used, e.g., in digital design: when we design, e.g., a wending machine, then to implement a general logical condition in terms of "and", "or", and "not"-gates, we first represent this condition in Conjunctive Normal Form (CNF) or in a Disjunctive Normal Form (DNF). These forms correspond exactly to our formulas (1) and (4) (equivalent to (2), and the possibility to transform each logical condition into one of these forms is our universality property. Comment.…”

Section: Introductionmentioning

confidence: 77%

“…Both approaches have a universality property. Both Mamdani's and logical approaches to fuzzy control have a universality (universal approximation) property [2], [3], [6] meaning that an arbitrary control strategy can be, with arbitrary accuracy, approximated by controls generated by this approach.…”

Section: Introductionmentioning

confidence: 99%

Mamdani approach to fuzzy control, logical approach, what else?

Bravo

Nava

2011

2011 Annual Meeting of the North American Fuzzy Information Processing Society

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Abstract-In fuzzy control, two approaches are mainly used: Mamdani's approach, in which we represent the knowledge base as a disjunction of statements Ai(x) & Bi(u) corresponding to individual rules, and logical approach, in which the knowledge based is represented as a conjunction of the rules themselves Ai(x) → Bi(u). Both approaches are known not to be perfect, so a natural question arises: what other approaches are possible? In this paper, we describe all possible approaches; alternative approaches use an "exclusive or" operation and correspond, e.g., to the fuzzy transform idea.

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“…However, since we are interested in generating a crisp value for the automatical controller, we must transform the fuzzy membership function µ(u) into a single value u c . This transformation from fuzzy to crisp is called defuzzification; see, e.g., a survey [6].…”

Section: Applications Of Fuzzy Sets: In Briefmentioning

confidence: 99%