A Review on Ranking of Z-numbers

There are numerous studies about Z-numbers since its inception in 2011. Because Z-number concept reflects human ability to make rational decisions, Z-number based multi-criteria decision making problems are one of these studies. When the problem is translated from linguistic information into Z-number domain, the important question occurs that which Z-number should be selected. To answer this question, several ranking methods have been proposed. To compare the performances of these methods, benchmark set of fuzzy Z-numbers has been created in time. There are relatively new methods that their performances are not examined yet on this benchmark problem. In this paper, we worked on these studies which are relative entropy based Z-number ranking method and a method for ranking discrete Z-numbers. The authors tried to examine their performances on the benchmark problem and compared the results with the other ranking algorithms. The results are consistent with the literature, mostly. The advantages and the drawbacks of the methods are presented which can be useful for the researchers who are interested in this area

The implementation of z-numbers in fuzzy clustering algorithm for wellness of chronic kidney disease patients

By gleaning insights from the data, fuzzy clustering capable to learn from data, identify patterns and make decision with minimum human intervention. However, it cannot simply study in detail regarding the quality of data, particularly knowledge of human being. Since the data are collected through decision-makers, the quality and human knowledge of the particular data are crucial factors to be considered. Compared to classical fuzzy numbers, z-numbers has ability to describe the human knowledge because it has both restraint and reliability part in its definition. Consequently, the implementation of z-numbers in fuzzy clustering algorithm is taken into consideration, where it has more authority to describe the knowledge of human being and extensively used in uncertain information development. Thus, there are two objectives of this paper; (i) to propose a reliable fuzzy clustering algorithm using z-numbers and; (ii) to cluster the Chronic Kidney Disease (CKD) patients based on the selected indicators to identify which cluster the patients belongs to (Cluster 0, Cluster 1, Cluster 2, Cluster 3 or Cluster 4) based on the membership functions defined. A case study of the CKD patients with the selected indicators is considered to demonstrate the capability of z-numbers to handle the knowledge of human being and uncertain information and also will present the idea in developing a robust and reliable fuzzy clustering algorithm particularly in dealing with knowledge of human being using z-numbers

Synergic ranking of fuzzy Z-numbers based on vectorial distance and spread for application in decision-making

Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values

Synergic ranking of fuzzy Z-numbers based on vectorial distance and spread for application in decision-making

Decision science has a wide range of applications in daily life. Decision information is usually incomplete and partially reliable. In the fuzzy set theory, Z-numbers are introduced to handle this situation because they contain the restriction and reliability components, which complement the impaired information. The ranking of Z-numbers is a challenging task since they are composed of pairs of fuzzy numbers. In this research, the vectorial distance and spread of Z-numbers were proposed synergically, in which the vectorial distance measures how much the fuzzy numbers are apart from the origin, which was set as a relative point, and their spreads over a horizontal axis. Furthermore, a ranking method based on the convex compound was proposed to combine the restriction and reliability components of Z-numbers. The proposed ranking method was validated using several empirical examples and a comparative analysis was conducted. The application of the proposed ranking method in decision-making was illustrated via the development of the Analytic Hierarchy Process-Weighted Aggregated Sum Product Assessment (AHP-WASPAS) model to solve the prioritization of public services for the implementation of Industry 4.0 tools. Sensitivity analysis was also conducted to evaluate the performance of the proposed model and the results showed that the proposed model has improved its consistency from 66.67% of the existing model to 83.33%. This research leads to a future direction of the application of ranking based on the vectorial distance and spread in multi-criteria decision-making methods, which use Z-numbers as linguistic values