2 Fuzzy sets theory and fuzzy TOPSIS method To deal with vagueness of human thought, ZADEH [17] first introduced the fuzzy set theory, which was oriented to the rationality of uncertainty due to imprecision or vagueness。 A major contribution of the fuzzy set theory is its capability of representing vague data。 The theory also allows mathematical operators and programming to apply the fuzzy domain。 A fuzzy set is a class of objects with a continuum of grades of membership。 This set is characterized by a membership (characteristic) function, which assigns to each object a grade of membership ranging between zero and one。 A tilde “~” will be placed above a symbol if the symbol represents a fuzzy set。 Triangular fuzzy numbers are expressed as indicate the smallest possible value, the most promising value, and the largest possible value that describe a fuzzy event, respectively。 A triangular fuzzy number (TFN), n~, is shown in Fig。 1 [18]。 In this work, the importance weights of various criteria and ratings of qualitative criteria are considered as linguistic variables。 Linguistic assessments are appropriate for the subjective judgment of decision-makers, so that we use triangular fuzzy numbers to capture the vagueness of the linguistic assessments for importance weight of each criterion and rating。 Fuzzy linguistic variables are very low (VL), low (L), middle low (ML), middle (M), middle high (MH), high (H) and very high (VH), where VL=(0,0,1), L=(0, 1, 3), ML=(1, 3, 5), M=(3, 5, 7), MH=(5, 7, 9), H=(7, 9, 10) and VH=(9, 10, 10) [17]。 The FTOPSIS procedure involves carrying out following steps [16, 13, 19]。 Step 1: Form a committee of decision-makers and then identify the evaluation criteria。 The decision makers use the linguistic weighting variables to assess the importance of the criteria。 Step 2: Choose the appropriate linguistic variables for the importance weight of the criteria and the linguistic ratings for alternatives with respect to criteria。 Step 3: Aggregate the weight of criteria to get the aggregated fuzzy weight (j~) of criterion Cj。 And pool the decision makers’ opinions to get the aggregated fuzzy rating (x) of alternative A under criterion CStep 4: Establish decision matrix。 In a decision committee that has K decision makers, fuzzy rating of each decision maker D can be represented as triangular fuzzy number The aggregated fuzzy rating can be defined asStep 5: Establish a normalized matrix R To avoid the complicated normalization formula used in classical TOPSIS, the linear scale transformation can be used to transform the various criteria scales into a comparable scale。 Therefore, it is possible to obtain the normalized fuzzy decision matrix denoted by Where B and C are the set of benefit criteria and cost criteria, respectively。 Step 6: Criteria weighted matrix。 It cannot be assumed that each evaluation criterion is of equal importance because the evaluation criteria have various meanings。Step 7: Construct the normalized weighted fuzzy decision matrix。 Considering the different importance of each criterion, the weighted normalized fuzzy-decision matrix is formed as follows。 Step 8: Calculate the separation measure from the ideal solutions (FPIS) and the negative ideal solutions (FNIS)。 According to the weighted normalized fuzzy- decision matrix, normalized positive triangular fuzzy numbers can also approximate the elements Then, the fuzzy positive ideal solution (FPIS, A Step 9: Calculate the distance of each alternative from FPIS and FNIS。 Step 10: Calculate the closeness coefficient of each alternative。 A closeness coefficient is defined to determine the order of all possible alternatives。 The closeness coefficient represents the distances to the fuzzy positive ideal solution and fuzzy negative ideal solution simultaneously。 The closeness coefficient of 模糊TOPSIS方法对初级破碎机英文文献和中文翻译(2):http://www.youerw.com/fanyi/lunwen_92562.html