Formalization of Fuzzy Control in Possibility Theory via Rule Extraction

Mei, Wei

doi:10.1109/access.2019.2928137

“…Defuzzification is the last stage of this method where a precise quantitative value from the truncated output MF is determined [27]. Center of gravity is the most popular and efficient defuzzification method [20].…”

Section: Tablementioning

confidence: 99%

Fuzzy Logic Expert System for Health Condition Assessment of Power Transformers

Manoj¹,

Ranga²

2022

Fuzzy Systems - Theory and Applications

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In the present chapter, a new fuzzy logic (FL) model is proposed to evaluate the overall health index (OHI) of power transformers. The most significant attributes such as dissolved gases, acidity, 2-furfuraldehyde, water content, breakdown voltage and dissipation factor that influence the health condition of transformers solid and liquid insulations are considered. These attributes are further divided into three different sets. Based on these sets, three different sub fuzzy models i.e. F1, F2 and F3 are designed in order to reduce the possible combinations of fuzzy rules. It results in reducing the complexity issues of the proposed OHI model. In addition, consideration of all significant testing parameters makes the model more reliable and accurate. Further, the proposed fuzzy model helps in initiating appropriate and early action on faulty conditions of the transformers. Conventional fuzzy logic models generally utilize large number of inputs and more number of rules in a single fuzzy model. It makes the models complex and inaccurate. Such shortcomings of existing conventional models are successfully overcame by the present proposed model. Furthermore, the results obtained from the proposed model are compared with the results obtained from expert model proposed by Abu-Elanien et al. This comparison ensures the reliability of the proposed method. Also, it is envisioned that the proposed model can be easily implemented by both the experienced and the inexperienced utility managers.

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“…Proof: We can verify by ( 20) that joint distribution 𝑝(𝑥 𝑖 𝑦 𝑗 ) do not satisfy (5). (20) where the expression to the right of the second equal-sign comes from the substitute of 𝑝(𝑥 𝑖 ) and 𝑝(𝑦 𝑗 |𝑥 𝑖 ) by 𝜋(𝑥 𝑖 ) and 𝜋(𝑦 𝑗 |𝑥 𝑖 ) using (5).…”

Section: Information Preservation In 2-ary Distribution Of Parallel Probability/ Possibility Systemsmentioning

confidence: 99%

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

Mei¹,

Gan²,

Xu³

et al. 2022

Preprint

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Information-preservation is recognized as the only principle for probability-possibility transformation in this work and the normalized transformation is the right method. This is based on the viewpoint that the reason we can transfer probability and possibility is that we believe the uncertainty being handled can be information-equivalently described by both probability and possibility. That viewpoint is endorsed by the random-fuzzy dual interpretation of unknown uncertainty, which says that unknown uncertainty being estimated could be interpreted as either randomness or fuzziness, depending on the available prior information and the perspective of cognition and modeling. Information of uncertain variable is defined in this work as its distribution. The suggested information-preservation principle is different from Klir’s principle, which is in fact an entropy-preservation principle. Then we investigated the problem of information preservation and propagation in parallel probability-possibility systems. By parallel, we mean the two uncertainty systems have the same priori information. After uncertainty propagation the two parallel systems will generally bifurcate, which means information preservation only holds locally between the two parallel systems. This observation accords with our intuition since probability and possibility use different normalizations as well as different disjunctive operators, which makes them two different uncertainty systems appropriate for randomness and fuzziness, respectively.

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“…In contrast, possibility is marked by the key axiom of "maxitivity" [1,2,6], which says that the possibility of two disjunctive non-exclusive fuzzy concepts is equal to the maximum of the two constituent possibilities. Possibility theory could be regarded as the foundation for fuzzy sets, since membership function of fuzzy sets could be recognized as likelihood function of possibility [16], and composition of fuzzy relations is equivalent to composition of conditional possibilities [5].…”

Section: Fuzziness Is the Classification Uncertainty Of The Both-and Outcome Of A Cognition Experiment Characterized By The Lack Of Clearmentioning

confidence: 99%

“…Therefore, the person is voted to be strong with possibility of 1, and to be between with possibility of 0.3. And these possibilities can be transformed into probabilities by using (5) or the method shown in Table 1. As we can see in Table 2, among 100 people, 80 people vote strong, and 20 people vote between and no one votes thin.…”

Section: A Transformation Example With Dual Interpretation Of Unknown Uncertaintymentioning

confidence: 99%

See 1 more Smart Citation

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

Mei¹,

Gan²,

Xu³

et al. 2021

Preprint

Self Cite

1

0

View full text Add to dashboard Cite

Information-preservation is recognized as the only principle for probability-possibility transformation in this work and the normalized transformation is the right method. This is based on the viewpoint that the reason we can transfer probability and possibility is that we believe the uncertainty being handled can be information-equivalently described by both probability and possibility. That viewpoint is endorsed by the random-fuzzy dual interpretation of unknown uncertainty, which says that unknown uncertainty being estimated could be interpreted as either randomness or fuzziness, depending on the available prior information and the perspective of cognition and modeling. Information of uncertain variable is defined in this work as its distribution. The suggested information-preservation principle is different from Klir’s principle, which is in fact an entropy-preservation principle. Then we investigated the problem of information preservation and propagation in parallel probability-possibility systems. By parallel, we mean the two uncertainty systems have the same priori information. After uncertainty propagation the two parallel systems will generally bifurcate, which means information preservation only holds locally between the two parallel systems. This observation accords with our intuition since probability and possibility use different normalizations as well as different disjunctive operators, which makes them two different uncertainty systems appropriate for randomness and fuzziness, respectively.

show abstract

Formalization of Fuzzy Control in Possibility Theory via Rule Extraction

Cited by 18 publications

References 38 publications

Fuzzy Logic Expert System for Health Condition Assessment of Power Transformers

Fuzzy Logic Expert System for Health Condition Assessment of Power Transformers

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

Probability-Possibility Transformation under Perspective of Random-fuzzy Dual Interpretation of Unknown Uncertainty

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