Bulanık kümelerde optimizasyon problemi ve çözüm yöntemleri

dc.contributor.advisor Eksin, İbrahim
dc.contributor.author Çakmakçı, Altuğ
dc.contributor.authorID 39317
dc.contributor.department Kontrol ve Otomasyon Mühendisliği tr_TR
dc.date.accessioned 2023-03-16T05:59:25Z
dc.date.available 2023-03-16T05:59:25Z
dc.date.issued 1993
dc.description Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1993 tr_TR
dc.description.abstract Bu çalışma bulanık kümelerde optimizasyon probleminin çözümü üzerine yapılmıştır. Optimizasyon problemi, bulanık küme teorisinin yapısı gereği kolaylık la çözül ememektedir. Bu çözümü elde etmek amacıyla ilk olarak bula nık küme teorisinin genel tanımlan incelenmiştir. En basit yapılı bulanık kontrolörün tanıtımından sonra, problemin çözümünde temel oluşturan bulanık ilişki denk lemlerinin çözümleri incelenmiştir. Çalışma boyunca üç ayrı bulanık kontrolör yapısı göz önüne alınmıştır. Bunlardan ilki kendini düzenleyen kontrolördür. ikincisi ise optimizasyon problemi için elde edilen ilk çözüm yöntemidir. Son olarak ise ilk ikisine oranla daha başarılı sonuç veren alternatif çözüm yöntemi tanıtılmıştır. tr_TR
dc.description.abstract This work is on the solution of the optimiza tion problem on fuzzy systems. To reach a Plausible solution a wide study was done on the fuzzy set theory. Some basic notations are necessary to go with the study. Also the solution lies on the basis of solutions to fuzzy relational equations. A fuzzy set A defined in universe of discourse X is expressed by its membership function. A s *?*[(), 1] where A(x) expresses the extent which x fulfills the category specified by A. Any fuzzy set can be represented by the sum of its elements. Therefore A(x) can be shown as, ?/. A(x) or A = SrAL*>. With A and B, two fuzzy sets defined in X, the following can be defined A(x) - 1 - A(x) (AlİB) (x) = max(A(x),B(x) ) (Afifi) (x) - min(A(x), B(x) ) men t s such that By a t - norm we mean afunction of two argu- t : [0,1] x [0,1]-[0,1] a) For x£y,w*z,xtw £ ytz b) It is commutative. c) It is associative. d) It satisfies x t 0 = 0 and x t 1 = x VIII By an s - norm, we mean a function of two arguments t : [0,1] X [0,1]-[0,1] such that a) for x*y,w£z,xsw*ysz b) it is commutative. c) it is associative. d) it satisfies xs0 = x;xs1 = 1. By a fuzzy relation R, defined in the carte sian product X x Y, we mean a mapping R : *xY- [0,1] (2.10) Thus, to each pair of elements (x,y) a number, which expresses the strength of ties, is assigned. For a given R and X couple Y is gathered by their composition. Most frequently used compositions are i ) sup - t ; r(y) = (x°r) (y) = supr [X(x) tR(x,y)] ii ) inf - s ; Y(y) = (XOR) (y) = infr [X(x) sR(x,y)] If the sup-t composition, Y = X. R and its dual y «x o R is given two main problems can be taken into considera tion; i) determine R for given X, Y ii) determine X for given R, Y IX X can be accepted as the input of a system, while Y is the output and R is the characteristic of it. The following theorems with the following definitions give the solutions to above questions. AtpB » 8Upzc(A t C £ B) and ApB - infıc(A s c * B) Theorem 1. : (1) If XeF(X) and Y?F(Y) fulfil Y = X. R the greatest fuzzy relation satisfying the formula can be given by if = X Q Y (2) If RSF(XxY) and YeF(Y) satisfy Y = X. R the maximum input can be given by the equation £ <* R t, t ? (0.11 2. Interactions of control rules There is interaction between control rules if the following holds 3. Consistency of control rules. The points given above are for the simple fuzzy controller. Moreover, a different approach to fuzzy controller is reached by fuzzy modelling. Let X, U, Y be state, control and output spaces respectively. Therefore, a system of order p can be modelled by Yk+p " Xk*p * & Here, R : U x X x X (p times) x X - [0,1] and S : X x Y - [0,13 XI For the problem given here, the system is said to be strictly known. Therefore R and S is clear for the problem. The performance index is given by the above equation J - 2?.i B Yi en_US
dc.description.degree Yüksek Lisans tr_TR
dc.identifier.uri http://hdl.handle.net/11527/23493
dc.language.iso tr
dc.publisher Fen Bilimleri Enstitüsü tr_TR
dc.rights Kurumsal arşive yüklenen tüm eserler telif hakkı ile korunmaktadır. Bunlar, bu kaynak üzerinden herhangi bir amaçla görüntülenebilir, ancak yazılı izin alınmadan herhangi bir biçimde yeniden oluşturulması veya dağıtılması yasaklanmıştır. tr_TR
dc.rights All works uploaded to the institutional repository are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. en_US
dc.subject Bulanık kümeler tr_TR
dc.subject Optimizasyon tr_TR
dc.subject Fuzzy sets en_US
dc.subject Optimization en_US
dc.title Bulanık kümelerde optimizasyon problemi ve çözüm yöntemleri tr_TR
dc.title.alternative Optimization problem and solution methods in fuzzy sets en_US
dc.type Tez tr_TR
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