Logic

Fuzzy Logic and Applications: 8th International Workshop, by Enric Trillas (auth.), Vito Di Gesù, Sankar Kumar Pal,

By Enric Trillas (auth.), Vito Di Gesù, Sankar Kumar Pal, Alfredo Petrosino (eds.)

This quantity constitutes the refereed complaints of the eighth overseas Workshop on Fuzzy good judgment and functions held in Palermo, Italy in June 2009.

The papers are geared up in topical sections on fuzzy set concept, intuitionistic fuzzy units, fuzzy category and clustering, fuzzy picture processing and research, and fuzzy systems.

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Extra resources for Fuzzy Logic and Applications: 8th International Workshop, WILF 2009 Palermo, Italy, June 9-12, 2009 Proceedings

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Arithmetic and logical operations on RL-numbers are straightforward and unique extensions of the operations on crisp numbers, verifying the following: • They verify all the usual properties of crisp arithmetic and logical operations. • The imprecision does not necessarily increase through operations, and can even diminish. The maximum imprecision is related to the number of restriction levels employed. 3 Evaluation of Quantified Sentences We shall consider the evaluation of quantified sentences of type II because of lack of space, and since type I sentences are a particular case of type II sentences, under the following assumptions: – Q is a fuzzy quantifier – A,D are imprecise properties defined on a finite, crisp set X by RLrepresentations (ΛA , ρA ) and (ΛD , ρD ), respectively.

G. triangular. This assumption, combined with assumptions 1, 2 and 3 leads to the conclusion that ξt have independent L-R possibility distributions of the same membership function shape with expected value equal zero and a variance σ 2 . Knowing the realisations ut of the fuzzy random component, we can determine the estimators of the mean value and the variance of the model error: respectively T T 2 t=1 ut t=1 ut , T −k−1 . Further, making use of (7) - (8) or (9) - (10) or (12) depending T on the form of the probabilistic distribution of the random component, we can determine the parameters of the fuzzy variable if it is a symmetric triangular fuzzy variable ξ = (mξ , αξ , αξ ).

G. [9], [10], [11]. We are proposing an approach analogous to the classical regression concept, taking as input for the fuzzy econometric model the observations of the variables, both the independent and the dependent ones. We give an example of the application of the proposed method in the energy load forecasting. 2 Classical Regression Model In the classical econometric approach the input data for the regression equation construction are observations (yt , xt1 , . . , xtk ), t = 1, . . , T .

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