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The main objective of the study is to review different types of multi-criteria decision-making (MCDM) problems that are analysed by using the fuzzy TOPSIS method and its different variants. An effort has been made to review different studies in which either the TOPSIS method is used or its extensions have been developed to analyse any real-life MCDM problem. A total of 184 research papers were carefully selected and reviewed from 83 reputed journals published by Elsevier, Springer, Wiley, Taylor and Francis, and others from 1981 to the first quarter of 2023. These papers are selected on the basis of different kinds of applications in the fields of mathematics, engineering, science, environment, technology, management, business, etc. The selected papers are further categorised based on the application areas, publication year, contributions of the countries, authors, journals, and type of research. This study will give an idea of different types of TOPSIS methods, their extensions, and applications, along with recent trends in diverse research fields. Based on the findings, it is observed that in recent years, the number of papers in which TOPSIS and its extensions have been used has increased exponentially.

The type of criterion weight can be distinguished according to different decision methods. Subjective weights are given by decision makers based on their knowledge, experience, expertise, and other factors. Objective weights are obtained through multi-step calculations of the evaluation matrix constructed from the actual information about the evaluation criteria of the alternatives. A single consideration of these two types of weights often results in biased results. In addition, in order to build an effective supply chain source, buyers must find suitable quality products and/or service providers in the process of supplier selection. Based on the above reasons, it is difficult to accurately select the appropriate alternative. The main contribution of this paper is to combine entropy weight, analytic hierarchy process (AHP) weight, and the technique for order preference by similarity to an ideal solution (TOPSIS) method into a suitable multi-criteria decision making (MCDM) solution. The TOPSIS method is extended with entropy-AHP weights, and entropy-AHP weights are used instead of subjective weights. A novel decision-making model of TOPSIS integrated entropy-AHP weights is proposed to select the appropriate supplier. Finally, we take the selection of building material suppliers as an example and use sensitivity analysis to show that the combination of the TOPSIS method based on entropy-AHP weights can effectively select the appropriate supplier.

The technique for order preference by similarity to ideal solution (TOPSIS) is a widely used ranking method which provides a composite index representing the relative proximity of each decision alternative to an ideal solution. The relative proximity index construction relays on the use of a single criterion aggregation approach. Its output, regardless the certainty or uncertainty nature of the problem’s data, is usually a real number. In TOPSIS classical approach alternatives are ordered based on these numbers. The closer the number to 1, the higher the position of the alternative in the ranking. However, although the relative proximity index can be highly sensible to the weighting scheme, as far as the authors of this work know, the relative proximity index has never been treated as a function. In this work, a new TOPSIS approach is proposed in which weights are not fixed in an exact way a priori. On the contrary, they are handled as decision variables in a set of optimization problems where the objective is to maximize the relative proximity of each alternative to the ideal solution. The only possible a priori information about the weights is that related to the existence of upper and lower bounds in their values. This information is incorporated into the optimization problems as constraints. The result is a new relative proximity index which is a function depending on the values of the weights. This feature of the proposed method could be useful in some decision situations in which the determination of subjective precise weights from decision makers could be problematic.

Taking the Guojiawan coal mine in the Shenfu Mining Area as a case study, five evaluation factors (aquifer thickness, brittle–plastic rock thickness ratio, core recovery rate, number of sandstone–mudstone interbeds, and fractal dimension of the faults) were selected as indicators to evaluate the water richness of the sandstone aquifer in the roof strata of the main coal seam. Accordingly, the weights of the water richness evaluation indicators, derived using the criteria importance through intercriteria correlation (CRITIC) evaluation method, were integrated with the computational procedures of the technique for order of preference by similarity to ideal solution (TOPSIS) evaluation method. The indicator weights and evaluation approaches were combined through different fusion strategies. Finally, based on the water richness zoning results for the study area, the advantages and disadvantages of the two fusion approaches, C-TOPSIS-a and C-TOPSIS-b, were compared. Comprehensive analysis was conducted to evaluate the rationality of the water richness zoning. The C-TOPSIS-b evaluation method achieved the optimal evaluation outcome. The water richness was classified into five grades: weak, relatively weak, moderate, relatively strong, and strong. Among these, the regions with weak to relatively weak, moderate, and strong to relatively strong water richness are primarily in the northern, central, southern, and southwestern parts, respectively.

Over the past few years, urban waterlogging disasters have caused serious losses to the national economy of China; therefore, creating technology for assessing waterlogging risk levels has become an important goal. Based on 25 post-screened evaluation indexes regarding the construction of waterlogging facilities, social and economic developments, and investments in scientific and technological innovation, the capacity of 31 provinces to prevent and mitigate waterlogging was comprehensively evaluated. The scores of six principal component factors were calculated by using the entropy weight TOPSIS method, and the coupled entropy weight TOPSIS–principal component analysis evaluation model was established. Moreover, in accordance with the evaluation results, measures for waterlogging prevention and disaster reduction are proposed. The results show that Beijing, Shanghai and Tianjin are the top three provinces regarding the capacity to control floods and mitigate disasters; this agrees well with the actual flood drainage standards and disaster losses of all provinces.

Risk decision matrix has widely been favoured by the researchers in the area of construction safety risk assessment. Although it provides the construction safety professionals with the final illustration of the risks magnitude, it suffers from major shortcomings, including inability to considering the importance of probability and severity, impaired analysis resulting from the use of raw numbers for ratings, and the limited range of classifications for assessing the risks. All these shortages give an impaired insight to the concerned parties, deteriorating the involved workers’ safety. As such, this paper aims to develop a novel Risk Assessment Model (RAM) through the integration of the Fuzzy Best Worst Method (FBWM) with the Interval-Valued Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (IVFTOPSIS). Based on the application of RAM to a real-life case study, it was observed that the developed RAM contributes to the body of construction safety risk assessment in five unique ways: (1) computing the importance of the two risk parameters (i.e. probability and severity) using fuzzy-reference-based comparisons, (2) obviating the needs for having statistical data, (3) prioritizing the identified risks using the combination of interval-valued triangular fuzzy numbers with TOPSIS, (4) providing the safety analysts with wider ranges of classifications for conducting risk assessment, and (5) providing the safety professionals with appropriate evaluation strategies for controlling the analysed risks. The developed model in the study can be applied to any projects, giving a conclusive plan to the concerned safety professionals for adopting the further prudent mitigation measurements.

Existing decision-making methods cannot work under the probabilistic uncertain linguistic environment where the decision makers give different uncertain linguistic terms as their assessments and the weights of assessments are different. In this paper, a novel concept called probabilistic uncertain linguistic term set is proposed, which is composed of some possible uncertain linguistic terms associated with the corresponding probabilities. Then, the normalization process, comparison method, basic operations, and aggregation operators are studied for probabilistic uncertain linguistic term sets. After that, an extended technique for order preference by similarity to an ideal solution method and an aggregation-based method are developed to rank the alternatives and then select the best one for multi-attribute group decision-making with probabilistic uncertain linguistic information. Finally, a practical case concerning the selection of Cloud storage services is shown to illustrate the applicability of probabilistic uncertain linguistic term sets.

In this paper, we propose Fermatean fuzzy sets. We compare Fermatean fuzzy sets with Pythagorean fuzzy sets and intuitionistic fuzzy sets. We focus on complement operator of Fermatean fuzzy sets. We find out the fundamental set of operations for the Fermatean fuzzy sets. We define score function and accuracy function for ranking of Fermatean fuzzy sets. In addition, we also study Euclidean distance between two Fermatean fuzzy sets. Later, we establish a Fermatean fuzzy TOPSIS method to fix multiple criteria decision-making problem. Ultimately, an interpretative example is stated in details to justify the elaborated method and to illustrate its viability and usefulness.

Multi-criteria group decision-making is a process in which decision makers assess the performance of alternatives on the basis of conflicting criteria to opt the most worthy alternative as solution. TOPSIS and ELECTRE are effective and commonly used methods to solve multiple criteria decision-making problems. The aim of this study is to propose two new models, namely, complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method and complex Pythagorean fuzzy ELECTRE I (CPF-ELECTRE I) method, to tackle multiple criteria group decision-making problems comprising complex Pythagorean fuzzy data. In these methods, we compare complex Pythagorean fuzzy numbers on the basis of their score functions. We use revised closeness index for the ranking of alternatives in CPF-TOPSIS method. {In complex Pythagorean fuzzy concordance and discordance sets, we compare the alternatives on being superior and inferior to other alternatives on the basis of score degree, accuracy degree and indeterminacy. In CPF-ELECTRE I method, we use outranking decision graph to obtain the best alternative.} We illustrate the structure of both methods with the help of flow charts. To verify the accuracy of {proposed methods}, we present an explanatory example for selection of best interior designer for a hotel renovation. {We authenticate the proposed techniques by providing a brief comparative analysis of these methods with existing methods}.