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Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems

Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems,10.1016/j.amc.2003.12.087,Applied Mathematics and Computation,Mahm

Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems   (Citations: 55)
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In this paper, we focus on multi-objective large-scale nonlinear programming (MOLSNLP) problems with block angular structure. We extend technique for order preference by similarity ideal solution (TOPSIS) approach to solve (MOLSNLP) problems. Compromise (TOPSIS) control minimizes the measure of distance, providing that the closest solution should have the shortest distance from the positive ideal solution (PIS) as well as the longest distance from the negative ideal solution (NIS). As the measure of “closeness” LP-metric is used. Thus, we reduce a q-dimensional objective space to a two-dimensional space by a first-order compromise procedure. The concept of membership function of fuzzy set theory is used to represent the satisfaction level for both criteria. Also, we get a single objective large-scale nonlinear programming (LSNLP) problem using the max–min operator for the second-order compromise operation. Finally, a numerical illustrative example is given to clarify the main results developed in the paper.
Journal: Applied Mathematics and Computation - AMC , vol. 162, no. 1, pp. 243-256, 2005
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    • ...Technique for ordered preference by similarity to ideal solution (TOPSIS) is a popular method and has been widely used in the literature [1]‐[9]...
    • ...Each fuzzy set is specified by a membership function, which assigns to each element in the universe of discourse a value within the unit interval [0, 1]. The assigned value is called degree (or grade) of membership, which specifies the extent to which a given element belongs to the fuzzy set or is related to a concept...
    • ...A fuzzy number is a convex fuzzy set, characterized by a given interval of real numbers, each with a grade of membership within [0, 1]. Its membership function is piecewise continuous and satisfies the following properties...
    • ...Hence, the bigger fi, is the better the alternative Ai. However, since fi values are the centroid of the fuzzy numbers ˜ ξi, it may occur that its values are diverse throughout a large range over real line R .I t may seem more convenient to map these values into [0, 1] .T he seclusion factor, which is denoted by si, is accordingly proposed and defined as...

    Abdollah Hadi-Venchehet al. Seclusion-Factor Method to Solve Fuzzy-Multiple Criteria Decision-Maki...

    • ...Recently, Abo-sinna and Amer [37] solved multi-objective nonlinear programming problems by using TOPSIS approach...

    Gui-Wu Wei. Extension of TOPSIS method for 2-tuple linguistic multiple attribute g...

    • ...The underlying logic of TOPSIS emphasises the fact that the chosen alternative should not only have the shortest distance from the positive ideal solution (PIS), but also the farthest distance from the negative ideal solution (NIS) (Abo-Sinna and Amer 2005)...

    Liang-Hsuan Chenet al. An integrated fuzzy approach for the selection of outsourcing manufact...

    • ...Abosinna and Amer [4] extended TOPSIS approach to solve multi-objective large-scale nonlinear programming problems...
    • ...Section 4 introduces the hierarchy of criteria and execution flow chart...
    • ...(4) Determine the ideal�ƒ V �≈ and negative-ideal solution...
    • ...According to previously definition of the classification criteria, the actual data has been corresponded to the 1-9 scale with similar criteria for weight, after the processing,, the weight matrix will be converted into AHP model, which has been showed in the table 4...
    • ...6KDQGRQJ +XQDQ -LDQJ[L 4. Line chart of two results...

    Yu Shiet al. FMCDM: A fuzzy multi-criteria decision-making hybrid approach to evalu...

    • ...There are many examples of applications of fuzzy TOPSIS in the literature (for instance: the evaluation of service quality (Tsuar, Chang, & Yen, 2002); inter company comparison (Deng, Yeh, & Willis, 2000); the applications in aggregate production planning (Wang & Liang, 2004) and large scale nonlinear programming (Abo-Sina & Amer, 2005))...

    Mahmoud Saremiet al. TQM consultant selection in SMEs with TOPSIS under fuzzy environment

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