دانلود رایگان مقاله لاتین بهینه سازی در برنامه ریزی موجودی با انتخاب عرضه کننده از سایت الزویر
عنوان فارسی مقاله:
بهینه سازی چند هدفه در برنامه ریزی موجودی با انتخاب تامین کننده
عنوان انگلیسی مقاله:
Multi-objective Optimisation in Inventory Planning with Supplier Selection
سال انتشار : 2017
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بخشی از مقاله انگلیسی:
2. Background
This section introduces the background for the techniques used as a part of the proposed approach and provides an overview of related studies in the scientific literature. 2.1. Type-2 Fuzzy Logic In many problems, knowledge comprises of objective knowledge which is the formal description of the problem, i.e., mathematical model and subjective knowledge which encapsulates the linguistic information. Generally in mathematical models, subjective knowledge is overlooked (Ross, 2004). However, Zadeh (1965) overcame this issue by introducing fuzzy sets. Mendel & John (2002) provided the following list of situations where T1FS could be insufficient for capturing the uncertainty in the problems: 1. Meaning of a word often relates to perception and so it could vary from one person to another with the perception. 2. Further uncertainty may arise if a group of experts do not agree on the definition of the consequents of a fuzzy system. 3. The input activating a T1FL system may be noisy, and therefore imprecise. 4. The data used for parameter tuning of a T1FL system could be noisy. Nevertheless, the 3 dimensional fuzzy sets generated using Type-2 Fuzzy Sets (T2FS)s are extremely complicated, hence it can not be easily understood and applied. Because of this complexity, many T2FSs applications have been modelled using Interval Type-2 Fuzzy Logic Systems (Greenfield et al., 2012). The difference between T2FSs and IT2FSs is that for IT2FS, the membership function is an interval. This allows us to cope with uncertainty associated with the membership grades. We use IT2FS to depict the ambiguity inherent in the supplier selection problem. 2.1.1. Basic Concepts of IT2FS In this section, we provide the fundamentals of IT2FS as explained in Mendel et al. (2006). 6 ACCEPTED MANUSCRIPT ACCEPTED MANUSCRIPT Definition 2.1. (Mendel et al., 2006) In the universe of discourse X, a Type-2 Fuzzy Set A˜ can be assigned by a Type-2 membership function µA˜ indicated as: A˜ = ((x, u), µA˜(x, u))| ∀x ∈ X, ∀u ∈ Jx ⊆ [0, 1] (1) where x ∈ X and u ∈ Jx ⊆ [0, 1] in which 0 ≤ µA˜(x, u) ≤ 1. The primary membership function is depicted as Jx ⊆ [0, 1]. It is also demonstrated as: A˜ = Z x∈X Z u∈Jx µA˜(x, u)/(x, u) Jx ⊆ [0, 1] (2) where R Rdenotes a union over all admissible x and u. Definition 2.2. (Mendel et al., 2006) A˜ is defined as a Type-2 Fuzzy Set in the universe of discourse X expressed by the Type-2 membership function µA˜. When all µA˜(x, u) = 1 for ∀x ∈ X and u ∈ Jx ⊆ [0, 1], A˜ is termed an Interval Type-2 Fuzzy Set depicted as: A˜ = Z x∈X Z u∈Jx 1/(x, u) Jx ⊆ [0, 1] (3) where Jx ⊆ [0, 1], i.e. Definition 2.3. (Mendel et al., 2006) The IT2FS can be considered as a particular case of type 2 fuzzy set, where the upper and lower membership functions are both Type-1 membership functions, respectively. As an example, a trapezoidal IT2FS A˜ i for all x ∈ X represented by; A˜ i = (A˜U i , A˜L i ) = ((a u i1 , au i2 , au i3 , au i4 ; h1(A˜U i ), h2(A˜U i )), (a l i1 , al i2 , al i3 , al i4 ; h1(A˜L i ), h2(A˜L i )) (4) where hj (A˜U i ) and hj (A˜L i ) for 1 ≤ j ≤ 2 depict membership values of the corresponding elements a u i(j+1) and a l i(j+1), respectively (Hu et al., 2013). The height of each constituent membership function is not explicitly defined as it is assumed to be equal to 1.
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