Analytic Hierarchy Process (AHP) is a broadly applied multi-criteria decision-making method to determine the weights of criteria and priorities of alternatives in a structured manner based on pairwise comparison. As subjective judgments during comparison might be imprecise, fuzzy sets have been combined with AHP. This is referred to as fuzzy AHP or FAHP. An increasing amount of papers are published which describe different ways to derive the weights/priorities from a fuzzy comparison matrix, but seldomly set out the relative benefits of each approach so that the choice of the approach seems arbitrary. A review of various fuzzy AHP techniques is required to guide both academic and industrial experts to choose suitable techniques for a specific practical context. This paper reviews the literature published since 2008 where fuzzy AHP is applied to decision-making problems in industry, particularly the various selection problems. The techniques are categorised by the four aspects of developing a fuzzy AHP model: (i) representation of the relative importance for pairwise comparison, (ii) aggregation of fuzzy sets for group decisions and weights/priorities, (iii) defuzzification of a fuzzy set to a crisp value for final comparison, and (iv) consistency measurement of the judgements. These techniques are discussed in terms of their underlying principles, origins, strengths and weakness. Summary tables and specification charts are provided to guide the selection of suitable techniques. Tips for building a fuzzy AHP model are also included and six open questions are posed for future work.

A review of fuzzy AHP methods for decision-making with subjective judgements

A bibliometric based survey on AHP and TOPSIS methods has been conducted.Scopus database was employed to retrieve the required data for this analysis.Assessment of quantitative and qualitative bibliometric indicators was obtainable.Efficacy of these methods promotes the development of related research.More scientific research interests will be devoted to these methods in the future. In recent years, the employment of multiple criteria decision analysis (MCDA) techniques in solving complex real-world problems has increased exponentially. The willingness to build advanced decision models, with higher capabilities to support decision making in a wide range of applications, promotes the integration of MCDA techniques with efficient systems such as intelligence and expert systems, geographic information systems, etc. Amongst the most applied MCDA techniques are Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS). The development of a comprehensive perspective on research activities associated with the applications of these methods provides insights into the contributions of countries, institutes, authors and journals towards the advancements of these methods. Furthermore, it helps in identifying the status and trends of research. This in turn will help researchers in shaping up and improving future research activities and investments. To meet these aims, a bibliometric analysis based on data harvested from Scopus database was carried out to identify a set of bibliometric performance indicators (i.e. quantitative indicators such as productivity, and qualitative indicators such as citations and Hirsch index (h-index)). Additionally, bibliometric visualization maps were employed to identify the hot spots of research. The total research output was 10,188 documents for AHP and 2412 documents for TOPSIS. China took a leading position in AHP research (3513 documents; 34.5%). It was also the leading country in TOPSIS research (846 documents; 35.1%). The most collaborated country in AHP research was the United States, while in case of TOPSIS it was China. The United States had gained the highest h-index (78) in AHP research, while in TOPSIS it was Taiwan with h-index of 46. Expert Systems with Applications journal was the most productive journal in AHP (204; 2.0%) and TOPSIS research (125; 5.2%), simultaneously. University of Tehran, Iran and Islamic Azad University, Iran were the most productive institutions in AHP (173; 1.7%) and TOPSIS (115; 4.8%) research, simultaneously. The major hot topics that utilized AHP and will continue to be active include different applications of geographic information systems, risk modeling and supply chain management. While for TOPSIS, they are supply chain management and sustainability research. Overall, this analysis has shown increasing recognition of powerful of MCDA techniques to support strategic decisions. The efficacy of these methods in the previous context promotes their progress and advancements.

https://scholar.ptuk.edu.ps/bitstream/123456789/349/1/TOPSIS.pdf

A bibliometric-based survey on AHP and TOPSIS techniques

Fuzzy AHP-TOPSIS approaches to prioritizing solutions for reverse logistics barriers

In this paper, the frequently used normalization methods for the entropy method (EM) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) when these two methods are used in combination with each other are summarized. Taking information entropy (IE) as an indicator to measure the diversity of attribute data (DAD), the effects of normalization on the entropy-based TOPSIS method are analyzed. It is found that normalization can affect the decision result by affecting the DAD, while the DAD affects the contribution of attributes to the distance of each alternative from the ideal solution and the negative ideal solution, manifested in that the higher the DAD is, the bigger the contribution of the attribute will be. It is proved that vector normalization (VN) and sum normalization (SN) will not change the DAD, whereas min-max normalization (MMN) not only will change the DAD, but also may cause the appearance of numerous zero values, finally resulting in the fact that the calculated results of IE cannot represent the diversity of raw data. Therefore, normalization is not suggested for the EM, and VN is suggested for TOPSIS method. Some discussions on the combinability between the EM and TOPSIS method are also given as well as the applicability of different normalization methods in TOPSIS method.

Effects of normalization on the entropy-based TOPSIS method

Application of SAW, TOPSIS and fuzzy TOPSIS models in cultivation priority planning for maize, rapeseed and soybean crops

A multi-criteria decision analysis method for water loss management is proposed.The method integrates AHP and TOPSIS methods under fuzzy environment.It is applied to a real water distribution system in a developing country.The prevalent strategies were highly connected to the local conditions. Facing water scarcity conditions water utilities cannot longer tolerate inefficiencies in their water systems. To guarantee sustainable water management one central task is reducing water losses from the supply systems. There are numerous challenges in managing water losses, manifested in a variety of options, their complexities, multiple evaluation criteria, inherent uncertainties and the conflicting objectives and interests of different stakeholders. This study demonstrates the effectiveness of multi criteria decision analysis (MCDA) approaches for decision support in this complex topic. The study covers identifying the key options among a set of options that have been proposed within a framework of strategies to reduce water losses in water distribution systems of developing countries. The proposed methodology was initiated by developing a hierarchical structure of the decision problem that consists of four levels: Overall objective, main criteria, evaluation criteria and options. Different stakeholders were engaged in the process of structuring and evaluating the decision problem. An integrated methodology that combines fuzzy set theory with Analytic Hierarchy Process (AHP) and Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods was then employed. This methodology has the potential to transform qualitative data into equivalent quantitative measures. Fuzzy AHP was used to create weights for main and evaluation criteria, while Fuzzy TOPSIS was used to aid the ranking of options in terms of their potential to meet the overall objective based on the evaluations and preferences of decision makers. The results showed that pressure management and control strategy was the most prevalent one, followed by employing advanced techniques and establishment of district metered areas. Their dominance was highly connected to the local and boundary conditions of the case study. The sensitivity analysis results showed that strongest and weakest options were less sensitive to changes in weights of evaluation criteria, which could be attributed to the strong consensus in strengthening the best option and neglecting the worst option. This study emphasized the successful application of MCDA in dealing with complicated issues in the context of water loss management. It is anticipated that, the integration of this developed framework in the planning policies of water utilities in developing countries can help in conducting better control over water losses.

A framework for water loss management in developing countries under fuzzy environment

Increasing water demands, in parallel with water scarcity, force water utilities in developing countries to follow complex operation techniques for the distribution of the available amounts of water. The reduction of water losses from water supply systems can help fill the gap between supply and demand. This strategy is characterized by the variety of options and the identification of the most appropriate option is a demanding process. An integrated multi- criteria decision making framework, precisely analytic hierarchy process (AHP) is applied to prioritize water loss reduction options for a typical intermittent water supply network in Palestine. The AHP was applied to structure the decision problem into a hierarchy framework, and four groups of decision makers were engaged to evaluate the elements. The results show that the strategic plan which comprises controlling and managing operational pressure was the best option. The selection of this option was highly connected to the conditions of the case study and to well-known advantages of this strategy to reduce losses. It is anticipated that the developed methodology will help water utilities to identify integrated water loss management plans which will guide utility managers to conduct better control for water losses.

Subhi Samhan

Papers

A framework for water loss management in developing countries under fuzzy environment

Utilizing analytic hierarchy process (AHP) for decision making in water loss management of intermittent water supply systems