A method for stochastic multiple attribute decision making based on concepts of ideal and anti-ideal points

Fan, Zhi‐Ping; Xiao, Zhao; Liu, Yang; Zhang, Yao

doi:10.1016/j.amc.2013.05.039

Cited by 27 publications

(14 citation statements)

References 28 publications

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“…Following Wei et al [13], we consider an investment company that intends to invest money in a panel of five possible alternatives: (1) 1 A is a car company; (2) 2 A is a food company; (3) 3 A is a computer company; (4) 4 A is an arms company; and (5) 5 A is a TV company. DM summarizes the investment information in four criteria: (1) 1 G stands for the risk analysis; (2) 2 G denotes the growth analysis; (3) 3 G indicates the sociopolitical impact analysis; and (4) 4 G represents the environmental impact analysis.…”

Section: Numerical Examplementioning

confidence: 99%

“…Multi-criteria decision-making (MCDM) is an important component of modern decision-making science, and has been extensively used in economics, management, engineering, military, and society, among others [1][2][3][4][5]. Due to the complexity and uncertainty of the decision-making environment, many researchers have focused on the intuitionistic fuzzy set (IFS) [6], which is substantially useful in dealing with vagueness.…”

Section: Introductionmentioning

confidence: 99%

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A New Prospect Projection Multi-Criteria Decision-Making Method for Interval-Valued Intuitionistic Fuzzy Numbers

Gao

Liu

2016

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Abstract:To depict the influence of decision makers' risk psychology on the interval-valued intuitionistic fuzzy multi-criteria decision-making process, this paper proposes a new method based on prospect theory. Considering the risk attitude of the decision maker, we transform interval-valued intuitionistic fuzzy numbers into real numbers via a prospect value function and consequently derive the prospect decision matrices. Regarding the criteria weights that are incompletely known or completely unknown, a new nonlinear optimization model is developed to determine the criteria weights by considering the subjective and objective factors. Furthermore, we calculate the prospect projection of each alternative for the ideal solution and rank all the alternatives according to the prospect projection values. Finally, an example is provided to illustrate the application of the developed approach.

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Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A New Prospect Projection Multi-Criteria Decision-Making Method for Interval-Valued Intuitionistic Fuzzy Numbers

Gao

Liu

2016

Information

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“…Scholars have conducted a great deal of research on the development of TOPSIS for solving various MADM problems in recent years. Fan et al [11] proposed a new method for dealing with stochastic MADM problems based on the ideal and anti-ideal cumulative distribution functions. Kaveh et al [12] transformed the multi-objective decision making (MODM) problem into a bi-objective one based on TOPSIS, and proposed an integrated multi-objective framework to solve MODM problems including both tangible and intangible factors based on the extended efficient epsilon-constraint method.…”

Section: Introductionmentioning

confidence: 99%

Structural Optimization of a High-Speed Press Considering Multi-Source Uncertainties Based on a New Heterogeneous TOPSIS

et al. 2018

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Abstract:In order to achieve high punching precision, good operational reliability and low manufacturing cost, the structural optimization of a high-speed press in the presence of a set of available alternatives comprises a heterogeneous multiple-attribute decision-making (HMADM) problem involving deviation, fixation, cost and benefit attributes that can be described in various mathematical forms due to the existence of multi-source uncertainties. Such a HMADM problem cannot be easily resolved by existing methods. To overcome this difficulty, a new heterogeneous technique for order preference by similarity to an ideal solution (HTOPSIS) is proposed. A new approach to normalization of heterogeneous attributes is proposed by integrating the possibility degree method, relative preference relation and the attribute transformation technique. Expressions for determining positive and negative ideal solutions corresponding to heterogeneous attributes are also developed. Finally, alternative structural configurations are ranked according to their relative closeness coefficients, and the optimal structural configuration can be determined. The validity and effectiveness of the proposed HTOPSIS are demonstrated by a numerical example. The proposed HTOPSIS can also be applied to structural optimization of other complex equipment, because there is no prerequisite of independency among various attributes for its application.

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“…Fuzzy positive-ideal and negative-ideal solution solutions were defined to implement TOPSIS. Fan et al [14] proposed a new method to solve stochastic MCDM problem, in which the consequences of alternatives associated with criteria were denoted by random variables with cumulative distribution functions. By means of TOPSIS, the ideal and anti-ideal points of the stochastic MCDM problem were determined as cumulative distribution function vectors.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Programming Model to Determine Objective Weights for the Interval Extension of TOPSIS

Shen

Lai

2018

Mathematical Problems in Engineering

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Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method has been extended in previous literature to consider the situation with interval input data. However, the weights associated with criteria are still subjectively assigned by decision makers. This paper develops a mathematical programming model to determine objective weights for the implementation of interval extension of TOPSIS. Our method not only takes into account the optimization of interval-valued Multiple Criteria Decision Making (MCDM) problems, but also determines the weights only based upon the data set itself. An illustrative example is performed to compare our results with that of existing literature.

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A method for stochastic multiple attribute decision making based on concepts of ideal and anti-ideal points

Cited by 27 publications

References 28 publications

A New Prospect Projection Multi-Criteria Decision-Making Method for Interval-Valued Intuitionistic Fuzzy Numbers

A New Prospect Projection Multi-Criteria Decision-Making Method for Interval-Valued Intuitionistic Fuzzy Numbers

Structural Optimization of a High-Speed Press Considering Multi-Source Uncertainties Based on a New Heterogeneous TOPSIS

A Mathematical Programming Model to Determine Objective Weights for the Interval Extension of TOPSIS

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