Extension of TOPSIS for decision-making problems with interval data: Interval efficiency

Jahanshahloo, G. R.; Lotfı, Farhad Hosseinzadeh; Davoodi, Alireza

doi:10.1016/j.mcm.2008.07.009

Cited by 173 publications

(80 citation statements)

References 13 publications

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“…Specifying an interval for an attribute in decision matrix indicates that it can take any value within the interval. The interval numbers do not indicate how probable it is to the value to be in the interval, nor do it indicate which of the many values in the interval is the most likely to occur (Jahanshahloo et al, 2009). Thus, when determining the exact values of the attributes is difficult or impossible, it is more appropriate to consider them as interval numbers.…”

Section: Interval Vikor Methodsmentioning

confidence: 99%

A comparative analysis of VIKOR method and its variants

Chatterjee¹,

Chakraborty²

2016

10.5267/j.dsl

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The VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje which means multicriteria optimization and compromise solution, in Serbian) method has already become a quite popular multi-criteria decision making tool for its computational simplicity and solution accuracy. This method focuses on selecting and ranking from a set of feasible alternatives, and determines compromise solution for a problem with conflicting criteria to help the decision maker in reaching a final course of action. It determines the compromise ranking list based on the particular measure of closeness to the ideal solution. Depending upon the type of decision problem and necessity of the decision maker, apart from VIKOR method, different variants of it, like comprehensive VIKOR, fuzzy VIKOR, regret theory-based VIKOR, modified VIKOR and interval VIKOR methods have also been subsequently developed. In this paper, the ranking performance of original VIKOR method and its five variants is analyzed based on two demonstrative examples. It is observed that interval VIKOR method performs unsatisfactorily and when the information in a decision problem is imprecise, fuzzy VIKOR method should always be preferred. But, for any decision problem, original VIKOR is the best method for solution without unnecessarily complicating the related mathematical computations.

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Section: Interval Vikor Methodsmentioning

confidence: 99%

A comparative analysis of VIKOR method and its variants

Chatterjee¹,

Chakraborty²

2016

10.5267/j.dsl

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“…The main steps to calculate the interval extension of TOPSIS could be summarized as follows [6,7]: (i) Normalizing the interval decision matrix using the following vector transformations to reduce the effect of data magnitude:…”

Section: Interval Extension Of Topsismentioning

confidence: 99%

“…Specifically, there exist a large spectrum of papers that involve the extension of TOPSIS with interval parameters. Jahanshahloo et al [6,7] extended the TOPSIS method to solve MCDM problems with interval data and determined the most preferable alternative with both crisp numbers and interval scores. Tsaur [8] took into account decision makers' risk attitude towards the interval criteria values and developed a new TOPSIS method to normalize the collected data and rank the alternatives.…”

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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“…To illustrate how to use proposed approach, this study selects a small example using data given by Jahanshahloo et al (2009) we examine the proposed model for six cities in Iran to find the best place for creating a date factory. These cities must be evaluated based on four criteria, two of them are cost oriented (C 1 , C 2 ) and the others are benefit oriented (C 3 , C 4 ).…”

Section: Empirical Examplementioning

confidence: 99%

A novel method to extend SAW for decision-making problems with interval data

Alireza¹,

Izadikhah²

2014

10.5267/j.dsl

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Decision making problem is the process of finding the best option out of all feasible alternatives. There are some methods for solving Multiple Criteria Decision-Making problems and Simple Additive Weighting (SAW) is one of the most popular ones. In this paper, among multi-criteria models in making complex decisions and multiple attribute models for the most preferable choice, SAW technique is extended using interval numbers. For this purpose, we first propose a method for extending Entropy method for dealing with interval data, and then the extended SAW method with interval data is proposed by using the interval weights derived by the proposed interval Entropy method. The extended SAW method is an algorithm to determine the most preferable choice out of all possible choices, when the input data are stated in interval.

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Extension of TOPSIS for decision-making problems with interval data: Interval efficiency

Cited by 173 publications

References 13 publications

A comparative analysis of VIKOR method and its variants

A comparative analysis of VIKOR method and its variants

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

A novel method to extend SAW for decision-making problems with interval data

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