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Keywords
(8)
Decision Making
Fuzzy Set Theory
Large Scale
Large Scale System
Membership Function
Nonlinear Programming
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(2)
Intercompany comparison using modified TOPSIS with objective weights
Extensions of the TOPSIS for group decisionmaking under fuzzy environment
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Extensions of TOPSIS for multiobjective largescale nonlinear programming problems
Extensions of TOPSIS for multiobjective largescale nonlinear programming problems,10.1016/j.amc.2003.12.087,Applied Mathematics and Computation,Mahm
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Extensions of TOPSIS for multiobjective largescale nonlinear programming problems
(
Citations: 55
)
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Mahmoud A. Abosinna
,
Azza H. Amer
In this paper, we focus on multiobjective largescale
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” LPmetric is used. Thus, we reduce a qdimensional objective space to a twodimensional space by a firstorder 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 largescale
nonlinear programming
(LSNLP) problem using the max–min operator for the secondorder 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. 243256, 2005
DOI:
10.1016/j.amc.2003.12.087
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Citation Context
(19)
...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 HadiVencheh
,
et al.
SeclusionFactor Method to Solve FuzzyMultiple Criteria DecisionMaki...
...Recently, Abosinna and Amer [
37
] solved multiobjective nonlinear programming problems by using TOPSIS approach...
GuiWu Wei
.
Extension of TOPSIS method for 2tuple 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) (AboSinna and Amer
2005
)...
LiangHsuan Chen
,
et al.
An integrated fuzzy approach for the selection of outsourcing manufact...
...Abosinna and Amer [
4
] extended TOPSIS approach to solve multiobjective largescale nonlinear programming problems...
...Section
4
introduces the hierarchy of criteria and execution flow chart...
...(
4
) Determine the ideal�ƒ V �≈ and negativeideal solution...
...According to previously definition of the classification criteria, the actual data has been corresponded to the 19 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 Shi
,
et al.
FMCDM: A fuzzy multicriteria decisionmaking 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 (
AboSina & Amer, 2005
))...
Mahmoud Saremi
,
et al.
TQM consultant selection in SMEs with TOPSIS under fuzzy environment
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