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İmalat sanayiinin performansını değerlendirmede bulanık küme ve yaklaşık çıkarsama yaklaşımı

Başlık çevirisi mevcut değil.

  1. Tez No: 55849
  2. Yazar: ADEM GÜLEÇ
  3. Danışmanlar: Y.DOÇ.DR. CENGİZ GÜNGÖR
  4. Tez Türü: Yüksek Lisans
  5. Konular: Endüstri ve Endüstri Mühendisliği, Industrial and Industrial Engineering
  6. Anahtar Kelimeler: Belirtilmemiş.
  7. Yıl: 1996
  8. Dil: Türkçe
  9. Üniversite: İstanbul Teknik Üniversitesi
  10. Enstitü: Fen Bilimleri Enstitüsü
  11. Ana Bilim Dalı: Belirtilmemiş.
  12. Bilim Dalı: Belirtilmemiş.
  13. Sayfa Sayısı: 64

Özet

ÖZET Bu çalışmada Türk İmalat Sanayiinin performansını tanıma ve karar verme için insan düşüncesini karekterize eden bulanık ifadelerle bir değerlendirme modeli kurulmuştur. Bu değerlendirme modeli, bulanık yapay karar ve bulanık çok-kriterli kararla temsil edilen iki aşamada gerçekleştirilmiştir ve imalat sanayiindeki sektörlerin performansını kantitatif bir değerlendirme yapmak için kullanılmıştır. Bu çalışmada daha fazla bilgi kaybını önlemek için D = (Min;=1 _j dj(m, /)) bulanık operatörü D- (ll=1^y(^, 0) olarak değiştirilmiştir ve bulanık çok-kriterli karar modelinin daha doğru ve güvenilir bir sonuç verdiği görülmüştür. Bu değerlendirmeyi yapmak için önce bulanık kümeler, bulanık küme karakteristikleri, bulanık mantık, yaklaşık çıkarsama ve bulanık şartlı (eğer... o halde...) önermeler üzerinde durulmuştur. Daha sonra değerlendirme modeli kurulmuş ve yapılan anket sonucunda elde edilen veriler kullanılarak bu modelin uygulanması yapılmıştır. Bu uygulama neticesinde sektörlerin performansı iyiden kötüye doğru sıralanmıştır. VIII

Özet (Çeviri)

SUMMARY AN APPROACH OF FUZZY SET AND APPROXIMATE REASONING IN EVALUATION OF MANUFACTURING INDUSTRY PERFORMANCE With the intention of reflecting the fuzzy characteristic of a person's brain for recognition and judgment in the Turkish Manufacturing Industry, a double model based on fuzzy synthetic decision and multicriterian decision is presented in this work. The model has been used successfully to make a quantitative evaluation of the manufacturing sectors. Some basic notations, fuzzy set operations, fuzzy relations, cc-level-sets and fuzzy propositions that are used in this study will be discussed briefly. In classical sets, or crisp sets, the transition between membership and non- membership in a given set for an element in the universe is abrupt and well-defined. For an element in a universe which contains fuzzy sets this transition can be gradual. This transition among various degrees of membership can be thought of as conforming to the fact that the boundaries of the fuzzy sets are vague and ambiguous. Hence, membership of an element from the universe in this set is measured by a function which attempts to describe vagueness and ambiguity. A fuzzy set then is a containing elements which have varying degrees of membership in the set. This idea is contrasted with classical, or crisp, sets because members of a crisp set would not be members unless their membership was full or complete in that set (i.e., their membership is assigned a value of 1). Elements in a fuzzy set, because their membership can be a value other than complete, can also be members of other fuzzy sets on the same universe. Elements of a fuzzy set are mapped to a universe of“membership values”using a function-theoretic form. This function maps elements of a fuzzy set A to a real numbered value on the interval 0 to 1. If an element in the universe, say u, is a member of fuzzy set A then this mapping is given as, ^(M)e[0, 1] A = (u, fiA(u)\ u nA{u)< nu{u) Vu nPW = ooDeMorgan's laws for classical sets also hold for fuzzy sets, as denoted by the expressions below, (XnB) = JuB (AuB) = Âr^B All other operations on classical sets, as enumerated before, also hold for fuzzy sets, except for the excluded middle laws. These two laws do not hold for fuzzy sets because of the fact that since fuzzy sets can overlap, a set and its complement can also overlap. The excluded middle laws, extended for fuzzy sets, are expressed by, AuA~*U Ar\A~± v) = max( Mr(«, v)> Ms (“> v» Intersection: Mr^ (u> v) = min( Mr (», v), Ms (», v)) Complement: ^(«,v) = l-^(«.v) Containment : R c s => Mr (», ”) < fts (u, v) XIThe operations that do not hold for fuzzy relations, as is the case for fuzzy sets in general, are the Excluded Middle laws. Since a fuzzy relation R is also a fuzzy set, there is overlap between a relation and its complement, and RvR*E RnR*0 As seen, the Excluded Middle laws for relations do not result in the null relation, 0, or the complete relation, E. Because fuzzy relations in general are fuzzy sets, can define the Cartesian product between fuzzy sets. Let A be a fuzzy set on universe U and B be a fuzzy set on universe V; then the Cartesian product between fuzzy sets A and B will result in a fuzzy relation R^ or AxB = R c UxV with membership function, HR{u,v) = nAxB{u,v) = min(juA(u), [iB(v)) Fuzzy composition can be defined just as it is for crisp (binary) relations. Suppose R is a fuzzy relation on the Cartesian space UxV, S is a fuzzy relation on VxW, and T is a fuzzy relation on UxW; then the fiizzy max-min composition is defined as: LetT=R°S Hr(u,w)= vUr(u,v)a{İS{v,w)) veV and the fuzzy max-product composition is defined as, fJLp (u,w) = v ( nR («, v). fis (v, w)) veK It should be pointed out that neither crisp nor fuzzy compositions have inverses in general; that is R»S*S°R This result is general for any matrix operation, fuzzy or otherwise, which must satisfy consistency between the cardinal counts of elements in respective universes. Even for the case of square matrices, the composition inverse is not guaranteed. xnLevel-Sets of a Fuzzy Set For a fuzzy set A, Aa &{»\Ma (“)>«}; « e [0,l) As A{u\fiA(u)>a); a e (O, l] are called the weak a-cut and strong a-cut, respectively. The term a-cut is a general term that includes both strong and weak types. The weak a-cut is also called the a level-set. The difference between strong and weak is the presence or absence of the equal sign. If the membership function is continuous, the «distinction between strong and weak is not necessary due to the logical development inherent in the a-cut. Calculations with weak a-cuts are easier to deal with. Fuzzy Propositions Here we will sum up a few of the basic aspects of the fuzzy propositions used in fuzzy logic. Fuzzy propositions are propositions that include fuzzy predications like ”it will probably rain tomorrow“ and ”u is a small number.“ Generally, they are written uisA A is a. fuzzy predicate and is called the fuzzy variable. Fuzzy variables are also called linguistic variables and are expressed in terms of fuzzy sets. Without delving into fuzzy logic here, we will discuss the expression of modifications in fuzzy propositions and composite fuzzy propositions. When the predicate of ”u is a small number“ is modified to give the form ”u is a very small number,“ we can think in terms of the membership function for the fuzzy set that represents the linguistic variable. This is a proposition modification problem. Words like ”extremely“ and ”very,“ which change the predicate in this way, are called modifiers, and are indicated by the symbol m. If u is A is modified with m, we use the expression uismA The negation of A, ”not“, can also be thought of as a modifier. To find the fuzzy sets mA from fuzzy set A we do as follows: xmvery A = A' more or less A = AV2 not A = \-A The membership functions of the right-hand terms are JUAm(u) = (MAİu)) 1/2 respectively. The method for representing mA needs to express the meaning of m well, so there is no generalized form. Next we should discuss composite propositions that are the tying-together of two different propositions, as in ”v is a small number, or u is a large number“ and ”« is small, and is an average-sized number.“ What connects the propositions is a logical conjunction, and representative examples are ”and“ and ”or.“ If two propositions are connected we get something like what follows: u is A or u is B = u is A^jB uisA and u isB = u is Ar\B If we take ”u is not very large, it's an average sized number“ as an example, we can use the expression ”w is (1 - large2)oabout average.“ However, composite propositions like ”tall“ (his height), and ”heavy“ are not expressed in this way, because the subject is different in each of the two propositions. In this case the expressions are: m is C and v is D = (w, v) is C x D u is C or v is D = (u, v) is C x Vkj UxD C x D is the direct product of C and D; U is the support set of C, and V is the support set of D. This kind of tying-together of two propositions with different subjects (dimensions) is formally expressed by using a fuzzy subsets are what are called fuzzy relations as decried in the next paragraph. XIVA typical combination of fuzzy propositions is ”if u is C, v is D.“ The logic symbol for ”if' is an arrow ->, and it is called an implication. This proposition can be seen as a two-dimensional composition, and if we write u is C -> v is D = (u, v) is C -> D C -> D is the fuzzy subset UxV, and its membership function is expressed by Mc^d(u>v) = 0 - Mc(u) + ^z>(v)) a L Aside from“and”and“or”there are many ways to express“->,”and then- applications are divided according to the situation. In this study a new approach is presented to evaluated the Turkish Manufacturing Industry. This approach is a double model of fuzzy synthetic decision and fuzzy multicriteria decision. The advantage is that both methods can show off their strong points and avoid their weak points. The amount of calculation of the fuzzy synthetic decision is small and it is simple. It can be used in lower level decision but the weights are distributed among the factors only one time. So it has its limitation. Fuzzy multicriteria decision is more flexible and adaptable, especially to the higher level decision. Thus, if we use them together, it is more in accordance with the thinking process of a human being to make a decision on a complex issue. Besides a double model, we can builds a multiple model, so as to meet the needs of the decision and recognition of complex systems. Any question about the study have an answer in the text. XV

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