Unity and diversity of fuzziness-from a probability viewpoint

Laviolette, Michael; Seaman, John W.

doi:10.1109/91.273123

Cited by 28 publications

(9 citation statements)

References 11 publications

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“…This frustration is evident in an engineering text when the authors complain: "We require proof-mathematical proof-that probability is deficient for the representation of uncertainty. Multicultural polemics such as Kosko's are not persuasive" [47].…”

Section: Actions and Reasonsmentioning

confidence: 99%

Good Engineers

Monk¹

1997

European Journal of Engineering Education

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Section: Actions and Reasonsmentioning

confidence: 99%

Good Engineers

Monk¹

1997

European Journal of Engineering Education

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“…In the conventional FIS, whose MFs are conventional Fuzzy sets, cannot able to model and minimize the effects of rule uncertainties [2]. Therefore, to overcome the shortcomings of conventional FIS, a new concept of probabilistic fuzzy inference system (PFIS) is introduced by integrating fuzzy theory and probability theory, which has been discussed in [3][4][5][6][7][8][9], but these works presented only the relationship of randomness and fuzziness, and not applied to process control engineering applications. In this PFIS, the MFs of the antecedent and consequent are probabilistic fuzzy sets (PFS), whose membership grades for each element of this set is a fuzzy number in (0, 1), hence useful for incorporating uncertainties [10].…”

Section: Introductionmentioning

confidence: 99%

A Probabilistic Fuzzy Inference System for Modeling and Control of Nonlinear Process

Sozhamadevi

Sathiyamoorthy²

2015

Arab J Sci Eng

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A new class of fuzzy inference system is introduced, a probabilistic fuzzy inference system, for the modeling and control problems, one that model and minimize the effects of uncertainties, i.e., existing randomness in many real-world systems. The fusion of two different concepts, degree of truth and probability of truth in a distinctive framework leads to this new concept. This combination is carried out both in fuzzy sets and fuzzy rules, which gives rise to probabilistic fuzzy sets and probabilistic fuzzy rules. Consuming these probabilistic elements, a distinctive probabilistic fuzzy inference system is developed as a fuzzy probabilistic model, which improves the stochastic modeling capability. This probabilistic fuzzy inference system involves fuzzification, inference and output processing. The output processing includes order reduction and defuzzification. This integrated approach accounts for all of the uncertainty like rule uncertainties and measurement uncertainties present in the systems and has led to the design which performs optimally after training. A probabilistic fuzzy inference system is applied for modeling and control of a continuous stirred tank reactor process, which exhibits dynamic nonlinearity and demonstrated its improved performance over the conventional fuzzy inference system. Electronic supplementary materialThe online version of this article (

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“…As probabilistic methods and fuzzy techniques are good of processing stochastic and nonstochastic uncertainties respectively [10], [11], it is a valuable job to endow the FLS with probabilistic features. The integration of probability theory and fuzzy logic has been studied [6], [12], [13], however, these research works only discussed the relationship of randomness and fuzziness, and Manuscript received August 12, 2004 could not be applied to engineering applications directly.…”

Section: Introductionmentioning

confidence: 99%

A probabilistic fuzzy logic system for modeling and control

Zhi

2005

IEEE Trans. Fuzzy Syst.

166

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In this paper, a probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. Similar to the ordinary fuzzy logic system (FLS), the PFLS consists of the fuzzification, inference engine and defuzzification operation to process the fuzzy information. Different to the FLS, it uses the probabilistic modeling method to improve the stochastic modeling capability. By using a three-dimensional membership function (MF), the PFLS is able to handle the effect of random noise and stochastic uncertainties existing in the process. A unique defuzzification method is proposed to simplify the complex operation. Finally, the proposed PFLS is applied to a function approximation problem and a robotic system. It shows a better performance than an ordinary FLS in stochastic circumstance.Index Terms-Probabilistic fuzzy logic system (PFLS), probabilistic fuzzy set, robotic control, stochastic modeling.

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Unity and diversity of fuzziness-from a probability viewpoint

Cited by 28 publications

References 11 publications

Good Engineers

Good Engineers

A Probabilistic Fuzzy Inference System for Modeling and Control of Nonlinear Process

A probabilistic fuzzy logic system for modeling and control

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