Notes on Dependent Attributes in TOPSIS

AbstractTOPSIS is a multicriteria decision making technique based on the minimization of geometric distances that allows the ordering of compared alternatives in accordance with their distances from the ideal and anti-ideal solutions. The technique, that usually measures distances in the Euclidean norm, implicitly supposes that the contemplated attributes are independent. However, as this rarely occurs in practice, it is necessary to adapt the technique to the new situation. Using the Mahalanobis distance to incorporate the correlations among the attributes, this paper proposes a TOPSIS extension that captures the dependencies among them, but, in contrast to the Euclidean distance, does not require the normalization of the data. Results obtained by the new proposal have been compared by means of the three Minkowski norms most commonly employed for the calculation of distance: (i) the Manhattan distance (p=1); (ii) the Euclidean distance (p=2); and (iii) the Tchebycheff distance (p=∞). Furthermore, simulation techniques are used to analyse the connection between the TOPSIS results traditionally obtained with the Euclidean distance and those obtained with the Mahalanobis distance

Construction of Vehicle Theft Index by Using TOPSIS Method with Entropy Based Criteria Weights

Property theft especially vehicle theft is a major contribution of entire crime. Estimating the level of crime by depending solely on the total of vehicle theft cases recorded is insufficient in order to observe the direction of the problem itself. The aim of this paper is to construct a vehicle theft index based on multi-criteria decision method to analyse vehicle theft pattern in particular and property theft in general for 82 areas in peninsular Malaysia. As vehicle theft is the major part of property crime, it is influenced by other criteria such as unemployment, level of education, immigrant and drug which should be considered in the vehicle theft index construction. Hence, this study takes into account the diversity of intrinsic of information in the criteria by measuring the entropy or the degree of diverseness of the data as proxies of the relative importance of the criteria. Then a Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS) was used to construct the vehicle theft index of 82 areas in peninsular Malaysia. The finding shows the top three areas in descending order are Kuala Lumpur, Petaling and Johor Bahru. The vehicle theft index constructed in this study can illustrate the actual direction of theft problem in Malaysia and the index construction process can be applied in other countries as well

A new synthesis procedure for TOPSIS based on AHP

Vega et al. [1] analyzed the influence of the attributes’ dependence when ranking a set of alternatives in a multicriteria decision making problem with TOPSIS. They also proposed the use of the Mahalanobis distance to incorporate the correlations among the attributes in TOPSIS. Even in those situations for which dependence among attributes is very slight, the results obtained for the Mahalanobis distance are significantly different from those obtained with the Euclidean distance, traditionally used in TOPSIS, and also from results obtained using any other distance of the Minkowsky family. This raises serious doubts regarding the selection of the distance that should be employed in each case. To deal with the problem of the attributes’ dependence and the question of the selection of the most appropriate distance measure, this paper proposes to use a new method for synthesizing the distances to the ideal and the anti-ideal in TOPSIS. The new procedure is based on the Analytic Hierarchy Process and is able to capture the relative importance of both distances in the context given by the measure that is considered; it also provides rankings, which are closer to the distances employed in TOPSIS, regardless of the dependence among the attributes. The new technique has been applied to the illustrative example employed in Vega et al. [1]

An out-of-sample framework for TOPSIS-based classifiers with application in bankruptcy prediction

This work was conducted while Prof. Pérez-Gladish was a visitant researcher at the Business School of The University of Edinburgh. She would like to thank the Spanish Ministry of Education Culture and Sport for its financial support within the framework of its International Mobility Program for Senior Researchers “Salvador de Madariaga” (Reference PRX16-0169).Since the publication of the seminal paper by Hwang and Yoon (1981) proposing Technique for Order Performance by the Similarity to Ideal Solution (TOPSIS), a substantial number of papers used this technique in a variety of applications requiring a ranking of alternatives. Very few papers use TOPSIS as a classifier (e.g. Wu and Olson, 2006; Abd-El Fattah et al., 2013) and report a good performance as in-sample classifiers. However, in practice, its use in predicting discrete variables such as risk class belonging is limited by the lack of an out-of-sample evaluation framework. In this paper, we fill this gap by proposing an integrated in-sample and out-of-sample framework for TOPSIS classifiers and test its performance on a UK dataset of bankrupt and non-bankrupt firms listed on the London Stock Exchange (LSE) during 2010–2014. Empirical results show an outstanding predictive performance both in-sample and out-of-sample and thus opens a new avenue for research and applications in risk modelling and analysis using TOPSIS as a non-parametric classifier and makes it a real contender in industry applications in banking and investment. In addition, the proposed framework is robust to a variety of implementation decisions.PostprintPeer reviewe

Flow shop scheduling decisions through Techniques for Order Preference by Similarity to an Ideal Solution (TOPSIS)

[EN] The flow-shop scheduling problem (FSP) has been widely studied in the literature and having a very active research area. Over the last few decades, a number of heuristic/meta-heuristic solution techniques have been developed. Some of these techniques offer excellent effectiveness and efficiency at the expense of substantial implementation efforts and being extremely complicated. This paper brings out the application of a Multi-Criteria Decision Making (MCDM) method known as techniques for order preference by similarity to an ideal solution (TOPSIS) using different weighting schemes in flow-shop environment. The objective function is identification of a job sequence which in turn would have minimum makespan (total job completion time). The application of the proposed method to flow shop scheduling is presented and explained with a numerical example. The results of the proposed TOPSIS based technique of FSP are also compared on the basis of some benchmark problems and found compatible with the results obtained from other standard procedures.Gupta, A.; Kumar, S. (2016). Flow shop scheduling decisions through Techniques for Order Preference by Similarity to an Ideal Solution (TOPSIS). International Journal of Production Management and Engineering. 4(2):43-52. doi:10.4995/ijpme.2016.4102.SWORD43524

Gender influence, social responsibility and governance in performance

Purpose – This paper aims to analyze the influence of gender diversity on the relationship between corporate social responsibility (CSR), corporate governance (CG) and economic and financial performance of Brazilian publicly traded companies. Design/methodology/approach – The sample comprises 68 non-financial public companies comprising the IBX100 index of BM&FBOVESPA. For that, it was used panel data modeling, correlation and ranking by TOPSIS method. Findings – The results suggest a significant relationship between CG and economic–financial performance when mediated by gender diversity. This relationship was not observed between CSR and economic–financial performance. Thus, it can be concluded that in a diversified board of directors, in terms of gender, better monitoring of managers can occur because of the increase in their independence in decisions, as well as performance increase. These results diverge from the literature on the influence of women’s participation in corporate boards in CSR. It is assumed that this result is because of the fact that the participation of women is recent in Brazil. Research limitations/implications – The main limitations are the number of companies analyzed, the choice of ISE index to verify the CSR variable and the metric used to verify the CG mechanisms. Originality/value – In general, this research contributes to the literature of the area, especially in Brazil, in confirming that the mediating variable gender diversity makes the relationship between CG and performance more significant

A new synthesis procedure for TOPSIS based on AHP

Vega et al. [1] analyzed the influence of the attributes’ dependence when ranking a set of alternatives in a multicriteria decision making problem with TOPSIS. They also proposed the use of the Mahalanobis distance to incorporate the correlations among the attributes in TOPSIS. Even in those situations for which dependence among attributes is very slight, the results obtained for the Mahalanobis distance are significantly different from those obtained with the Euclidean distance, traditionally used in TOPSIS, and also from results obtained using any other distance of the Minkowsky family. This raises serious doubts regarding the selection of the distance that should be employed in each case. To deal with the problem of the attributes’ dependence and the question of the selection of the most appropriate distance measure, this paper proposes to use a new method for synthesizing the distances to the ideal and the anti-ideal in TOPSIS. The new procedure is based on the Analytic Hierarchy Process and is able to capture the relative importance of both distances in the context given by the measure that is considered; it also provides rankings, which are closer to the distances employed in TOPSIS, regardless of the dependence among the attributes. The new technique has been applied to the illustrative example employed in Vega et al. [1]

Pembinaan indeks jenayah curi kenderaan dengan pendekatan berbilang kriterium dalam persekitaran kabur

An index is a measure of the performance of a situation that displays the value of the final score resulting from a combination of several criteria values mathematically. The existing index of vehicle theft is built on the assumption that all criteria are equally important and based on numerical data only without considering ambiguity aspect, particularly the causes of the crime. Moreover, there was no decision-makers involvement to assess the level of contribution of criminal criteria based on their knowledge and experience. Therefore, this study developed an improved InJeCK by considering the fuzziness. InJeCK also involves decision-makers in determining the degree of importance of vehicle theft crime criteria, in addition to numerical data analysis obtained from related agencies. The subjective weights in this study utilized Z-numbers through the level of contribution of the criteria evaluated in the representation of two triangular fuzzy numbers. Objective weights used the degree of uncertainty through entropy measurements. These two weights were aggregated to form an aggregated weight that balances the weaknesses of both subjective and objective weights. Next, InJeCK was computed based on the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) to rank 82 areas in Peninsular Malaysia. InJeCK values were visualized using color maps to be more informative. The results show that the criteria of car theft, higher education and unemployment are the three most influential criteria in vehicle theft crime based on the aggregated weights. The InJeCK values show that Kuala Lumpur is the riskiest area for vehicle theft cases. This study has contributed to the field of multi-criteria decision-making by considering fuzzy environment in the development of vehicle theft crime index. Besides, the findings of the study can also assist those involved in curbing vehicle theft in particular and property crime in general