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Ranking Intuitionistic Fuzzy Sets (IFS) using distance-based methods involves calculating the distance between an IFS and a reference point which represents either maximum (positive ideal solution) or minimum (negative ideal solution) value. These methods assume that similarity of an IFSs to the reference point increases as its distance from it decreases. While it is a common practice to use nonlinear distance functions for ranking IFSs, this paper proves that no nonlinear IF distance function can be robust. In this study, the shortcomings of the conventional procedure are demonstrated by providing a mathematical proof and an alternative ranking method based on the hypervolume metric is proposed. In addition, the suggested ranking approach is extended as a new multi-criteria decision making method called Hypervolume-based Evaluation and Ranking Technique (HEART). HEART is applied for multi-criteria assessment of Turkey's energy alternatives. Results are compared with three distance based multi-criteria decision making methods: TOPSIS, VIKOR, and CODAS. • The study uncovers the critical shortcomings of distance-based methods in ranking Intuitionistic Fuzzy Sets (IFS). • An alternative ranking method to distance based approaches, based on the hypervolume metric is proposed. • The hypervolume based ranking approach is extended for use in multi-criteria decision making problems. [ABSTRACT FROM AUTHOR]

Likened to the economic calamity of World War Two, the COVID-19 pandemic has sparked fears of a deep economic crisis, killed more than six million people worldwide and had a ripple effect on all aspects of life. MCDM (multi-criteria decision making) methods have become increasingly popular in modeling COVID-19 problems owing to the multi-dimensionality of this crisis and the complexity of health and socio-economic systems. This paper is aimed to review 72 papers published in 37 leading peer-reviewed journals indexed in Web of Science that used MCDM methods in different areas of COVID-19 pandemic. In this paper, data retrieval follows the PRISMA protocol for systematic literature reviews. 35 countries have contributed to this multidisciplinary research and India is identified as the leading country in this field followed by Turkey and China. Also 36 articles, namely 50% of papers are presented in the form of international cooperation. " Applied Soft Computing " is the journal with the highest number of articles whereas "Journal of infection and public health" and " Operations Management Research " are ranked in the second place. The results indicate that AHP (including fuzzy AHP) is the most popular MCDM method applied in 37.5% of papers followed by TOPSIS and VIKOR. This review reveals that the use of MCDM methods is one of the most attractive research areas in the field of COVID-19. As a result, one of the main purposes of this work is to identify diverse applications of MCDM methods in the COVID-19 pandemic. Most studies i.e. 69% (49 papers) of the papers combined various fuzzy sets with MCDM methods to overcome the problem of uncertainty and ambiguity while analyzing information. Nevertheless, the main drawback of those papers has been the lack of theoretical justifications. In fact, fuzzy MCDM methods impose heavy computational load and there is no general consensus on the clear advantage of fuzzy methods over crisp methods in terms of the solution quality. We hope the researchers who applied fuzzy MCDM methods to COVID-19-related research understand the theoretical basis of MCDM methods and the serious challenges associated with basic operations of fuzzy numbers to avoid potential disadvantages. This paper contributes to the body of knowledge via suggesting a deep vision to critique the fuzzy MCDM methods from mathematical perspective. • We provide a literature review on peer-reviewed journal articles with high impact factor related to the application of MCDM methods in COVID-19 era. • A total of 72 articles are collected from 37 leading journals and categorized into 52 types of application. • We highlight some claims on fuzzy arithmetic which are at use in the fuzzy literature but having little theoretical support. [ABSTRACT FROM AUTHOR]

Combinative Distance based ASsesment (CODAS) method aims to perform multi-criteria selection process according to the largest Euclidean and Taxicab distance with respect to negative ideal solutions. Recently, several CODAS methods have been applied to multi-criteria decision making problems with interval valued intuitionistic fuzzy sets. This paper demonstrates the weaknesses of using Euclidean and Taxicab distance on interval valued intuitionistic fuzzy sets and provides alternative strategies to model the vagueness and uncertainty in decision maker evaluations more effectively. The contribution of this paper is twofold. First, a new selection metric is defined in order to eliminate the disadvantages of using Euclidean and Taxicab distance in interval valued intuitionistic fuzzy CODAS. Second, a new fuzzy aggregation operator is proposed for aggregating decision maker evaluations by using fuzzy weights rather than using crisp weights. To show the effectiveness of the modified CODAS method, an application is given for multi-criteria selection of renewable energy alternatives in Turkey and the results are compared with two other interval valued intuitionistic fuzzy CODAS methods in the literature. • This paper criticizes the existing IVIF-CODAS methods in the literature. • The drawbacks of using Euclidean and Hamming distance are highlighted. • A new distance metric and fuzzy aggregation operator for IVIF CODAS is proposed. • The proposed IVIF-CODAS method does not have any user-defined parameters. • Results show the difference between existing and proposed IVIF CODAS methods. [ABSTRACT FROM AUTHOR]