Advances in Neural Networks – ISNN 2009: 6th International by Jiacai Fu, Thi Tra Giang Dang, Minh Nhut Nguyen, Daming Shi

By Jiacai Fu, Thi Tra Giang Dang, Minh Nhut Nguyen, Daming Shi (auth.), Wen Yu, Haibo He, Nian Zhang (eds.)

The 3 quantity set LNCS 5551/5552/5553 constitutes the refereed complaints of the sixth foreign Symposium on Neural Networks, ISNN 2009, held in Wuhan, China in could 2009.

The 409 revised papers offered have been rigorously reviewed and chosen from a complete of 1.235 submissions. The papers are prepared in 20 topical sections on theoretical research, balance, time-delay neural networks, computing device studying, neural modeling, choice making platforms, fuzzy platforms and fuzzy neural networks, aid vector machines and kernel tools, genetic algorithms, clustering and class, trend attractiveness, clever regulate, optimization, robotics, picture processing, sign processing, biomedical purposes, fault prognosis, telecommunication, sensor community and transportation platforms, in addition to applications.

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Additional resources for Advances in Neural Networks – ISNN 2009: 6th International Symposium on Neural Networks, ISNN 2009 Wuhan, China, May 26-29, 2009 Proceedings, Part II

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In Section 2, we give an expectation-reduction method for T2 fuzzy variables. In Section 3, we propose a DEA model with T2 fuzzy inputs and outputs and discuss its properties in some special cases. Section 4 provides a numerical example to illustrate the efficiency of the proposed DEA model. In Section 5 we draw our conclusions. 2 Reduction of T2 Fuzzy Variables T2 fuzziness allows us to handle linguistic uncertainties as well as numerical uncertainties. But it is very complex due to fuzzy membership functions.

Thus, to make the computation more convenience, we propose a new reduction method for T2 fuzzy variable in this section. The proposed method is very easy to implement and also may be very useful in building the programming with T2 fuzzy coefficients. ˜ Let (Γ, A, Pos) be a fuzzy possibility space [12], and ξ a T2 fuzzy variable with the second possibility distribution function μ ˜ξ (x). , the possibility of T2 fuzzy variable ξ taking on value x is a regular fuzzy variable (RFV). To reduce ξ, we consider to represent the second possibility by Modeling Fuzzy DEA with Type-2 Fuzzy Variable Coefficients 27 a crisp number.

Then with the expectation-reduction method, we obtain the reduction of ξ, denoted by y˜, as a fuzzy variable with the following possibility distribution μy˜(x) = = x−r1 r2 −r1 + θ2 −θ1 4 1 min{ rx−r , r2 −x }, if x ∈ [r1 , r2 ] 2 −r1 r2 −r1 r3 −x + θ2 −θ1 min{ r3 −x , x−r2 }, if x ∈ [r2 , r3 ] ⎧ r3 −r2 θ2 −θ1 4 x−r1 r3 −r2 r3 −r2 2 (1 + 4 ) r2 −r1 , if x ∈ [r1 , r1 +r ⎪ 2 ] ⎪ ⎪ ⎪ ⎪ ⎨ 4−(θ2 −θ1 ) x − 4r1 −(θ2 −θ1 )r2 , if x ∈ [ r1 +r2 , r2 ] 4(r2 −r1 ) 4(r2 −r1 ) 2 −4+(θ2 −θ1 ) 4r3 −(θ2 −θ1 )r2 ⎪ 3 ⎪ , if x ∈ [r2 , r2 +r ⎪ 4(r3 −r2 ) x + 4(r3 −r2 ) 2 ] ⎪ ⎪ ⎩ r3 −x 1 3 (1 + θ2 −θ if x ∈ [ r2 +r 4 ) r3 −r2 , 2 , r3 ] which is plotted in Fig.

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