Multi-Criteria Decision Aid (MCDA) or Multi-Criteria Decision Making (MCDM) methods have received much attention from researchers and practitioners in evaluating, assessing and ranking alternatives across diverse industries. Among numerous MCDA/MCDM methods developed to solve real-world decision problems, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) continues to work satisfactorily across different application areas. In this paper, we conduct a state-of-the-art literature survey to taxonomize the research on TOPSIS applications and methodologies. The classification scheme for this review contains 266 scholarly papers from 103 journals since the year 2000, separated into nine application areas: (1) Supply Chain Management and Logistics, (2) Design, Engineering and Manufacturing Systems, (3) Business and Marketing Management, (4) Health, Safety and Environment Management, (5) Human Resources Management, (6) Energy Management, (7) Chemical Engineering, (8) Water Resources Management and (9) Other topics. Scholarly papers in the TOPSIS discipline are further interpreted based on (1) publication year, (2) publication journal, (3) authors' nationality and (4) other methods combined or compared with TOPSIS. We end our review paper with recommendations for future research in TOPSIS decision-making that is both forward-looking and practically oriented. This paper provides useful insights into the TOPSIS method and suggests a framework for future attempts in this area for academic researchers and practitioners.

Review: A state-of the-art survey of TOPSIS applications

In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

Multiple criteria decision making

In this paper the authors review the developments of the analytic hierarchy process (AHP) since its inception. The focus of this paper is a neutral review on the methodological developments rather than reporting its applications that have appeared since its introduction. In particular, we discuss problem modelling, pair-wise comparisons, judgement scales, derivation methods, consistency indices, incomplete matrix, synthesis of the weights, sensitivity analysis and group decisions. All have been important areas of research in AHP.

https://pure.port.ac.uk/ws/files/94447/AHP_review_Preprint.pdf

Review of the main developments in the analytic hierarchy process

Multiple criteria decision-making (MCDM) is considered as a complex decision-making (DM) tool involving both quantitative and qualitative factors. In recent years, several MCDM techniques and approaches have been suggested to choosing the optimal probable options. The purpose of this article is to systematically review the applications and methodologies of the MCDM techniques and approaches. This study reviewed a total of 393 articles published from 2000 to 2014 in more than 120 peer reviewed journals (extracted from Web of Science). According to experts’ opinion, these articles were grouped into 15 fields. Furthermore, these articles were categorised based on authors, publication date, name of journals, methods, tools, and type of research (MCDM utilising research, MCDM developing research, and MCDM proposing research). The results of this study indicated that in 2013 scholars have published articles more than in other years. In addition, the analytic hierarchy process (AHP) method in the individual tool...

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Multiple criteria decision-making techniques and their applications – a review of the literature from 2000 to 2014

This article describes the original Analytic Hierarchy Process (AHP) as it is implemented in the software package Expert Choice. We demonstrate its application through a practical example. In particular, we discuss problem modelling, pairwise comparisons, judgement scales, derivation methods, consistency indices, synthesis of the weights and sensitivity analysis. Finally, the limitations of the original AHP along with the new proposed development are explained.

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Analytic Hierarchy Process and Expert Choice: Benefits and limitations

In this paper, we present a statistical criterion for accepting/rejecting the pairwise reciprocal comparison matrices in the analytic hierarchy process. We have studied the consistency in random matrices of different sizes. We do not agree with the traditional criterion of accepting matrices due to their inflexibility and because it is too restrictive when the size of the matrix increases. Our system is capable of adapting the acceptance requirements to different scopes and consistency necessities. The advantages of our consistency system are the introduction of adaptability in the acceptance criterion and the simplicity of the index we have used, the eigenvalue (λmax) and the simplicity of the criterion.

Consistency in the analytic hierarchy process: a new approach

On rank reversal and TOPSIS method

The requirements to satisfy the energy needs of today without compromising those of future generations have forced humans to adopt rules that permit a better use of the available resources, of which the sun is an inexhaustible energy source. Amongst the energy sources that offer the possibility of exploiting the resources offered by the Earth, solar energy has acquired great strength. Photovoltaic energy has presented a major evolution and it is forecasted as being an important contributor to power generation and an alternative to other non-renewable energy sources. The high cost of solar electricity is today the main reason why electricity from photovoltaic systems has not been introduced in a more widespread way. In this context, the aim of this paper is the study and analysis of the decision criteria to be used when searching for the best photovoltaic cell, studying both the criteria that exert most influence or their manufacture (defined by quantitative and qualitative values) and the alternatives which will be the decision problem to be solved; each alternative will correspond to one type of photovoltaic cell. Thus, relevant information has been provided by three experts and the TOPSIS method has been used to aggregate all the information combined with the use of fuzzy sets which will model the use of linguistic labels in the process.

Evaluation of photovoltaic cells in a multi-criteria decision making process

This paper develops an evaluation approach based on the Technique for Order Performance by Similarity to Ideal Solution (TOPSIS). When the input for a decision process is linguistic, it can be understood that the output should also be linguistic. For that reason, in this paper we propose a modification of the TOPSIS algorithm which develops the above idea and which can also be used as a linguistic classifier. In this new development, modifications to the classic algorithm have been considered which enable linguistic outputs and which can be checked through the inclusion of an applied example to demonstrate the goodness of the new model proposed.

The LTOPSIS: An alternative to TOPSIS decision-making approach for linguistic variables

Different methods have been proposed for ranking fuzzy numbers. These include methods based on distances, centroid point, coefficient of variation, and weighted mean value. However, there is still no method that can always give a satisfactory result to every situation; some are counterintuitive and not discriminating. This paper presents an approach for ranking fuzzy numbers with integral value that is an extension of the index of Liou and Wang. This method, that is independent of the type of membership function used, can rank more than two fuzzy numbers simultaneously. This ranking method use an index of optimism to reflect the decision maker's optimistic attitude, but rather it also contains an index of modality that represents the neutrality of the decision maker. The approach is illustrated with numerical examples.

M. Teresa Lamata

Papers

Consistency in the analytic hierarchy process: a new approach

On rank reversal and TOPSIS method

Evaluation of photovoltaic cells in a multi-criteria decision making process

The LTOPSIS: An alternative to TOPSIS decision-making approach for linguistic variables

A modification of the index of liou and wang for ranking fuzzy number