Investigation of the Turkish university rankings using InterCriteria Analysis

: In the current investigation Turkish university rankings are analyzed. The dataset for overall ranking of universities for 2021-2022 is used. The information is downloaded from the University Ranking by Academic Performance website. Dependencies and independencies between Turkish universities are analyzed. The relationship between university rankings indicators are investigated.


Introduction to InterCriteria Analysis
InterCriteria Analysis is a decision making method based on the two fundamental concepts: intuitionistic fuzzy sets [2,5] and index matrices [1]. Intuitionistic fuzzy set are introduced in 198 1983 by Krassimir Atanassov as an extension of fuzzy sets. The intuitionistic fuzzy pairs are calculated on the base of the comparison of different values for criteria and objects. Index matrices are used as a tool for representing the values and degrees of dependencies and independencies between the criteria and objects. ICA determines the correlations by pairwise comparison to achieve possible relationships between different objects or criteria [3,6]. Different extensions of ICA are developed in the years [4,7,8,13]. ICA is successfully applied to analyze different correlations and opposite behaviors between the objects/criteria of the datasets in the area of genetic algorithms, medicine, crude oils, university rankings of different countries and etc., [9,12].

InterCriteria Analysis applied to Turkish university rankings
The dataset for Turkish university ranking for 2021-2022 is downloaded from the University Ranking by Academic Performance website. The methodology of indicators selection is described in the Methodology section of the website. The input dataset contains information for 179 Turkish universities estimated by 5 indicators: paper score, total citation score, total scientific document score, number of graduated doctoral students and scientist/student score. The universities are numbered from C001 to C179 [14].

Application of ICA to Turkish University Rankings for identification the relationships between the indicators
Firstly, ICA is applied to investigate the relationships between the indicators. The analysis is performed using IcrAData software [11]. The investigation is a continuation of the applications of the ICA for years 2019-2020 and 2020-2021 [10]. The result of ICA application for 2021-2022 are presented in Table 1. Description of the pairs of indicators is presented in Table 2. ICA determines 3 pairs of indicators in positive consonance, 3 pairs of indicators in weak dissonance and 4 pairs of indicators in strong dissonance. The pairs of indicators in the area of dissonance are independent. The pairs of indicators in positive consonance have weak dependencies.
The received results are presented in the intuitionistic fuzzy triangle ( Figure 1). They are compared with the results from previous investigation, published in [10]. The behavior of the indicators is constant in time with small exceptions. The pairs of indicators "Total scientific document score -Number of graduated doctoral students" varies from 1 year in weak dissonance to 3 years in weak positive consonance. Thereafter, despite of the indicators in the area of positive consonance, the selected indicators of Turkish university rankings are correct. They are constant in time. The weak variation is observed only in single event. The indicators that are in dissonance field are constant in time. Paper score -Total citation score, Paper score -Total scientific document score, Total citation score -Total scientific document score

Application of ICA to Turkish university rankings for identification the relationships between the universities
The ICA is applied to identify the relationships between the 179 universities. The distribution of the pairs of the universities according to their dependencies or independencies is written in Table 3. The universities in strong negative consonance have different functioning. These universities work differently to achieve their goals. The universities have opposite characteristics in their educational procedures. The universities in strong negative consonance have strong opposite relations between them.
Obviously, the received pairs of universities in strong positive consonance have strong dependencies each other. These universities have very close relationships. The pairs of universities in weak positive consonance and positive consonance have weak similarities. These universities have similar functionalities with small differences. The pairs of universities in 206 dissonance, weak dissonance and strong dissonance are independent. These universities have not relationships. The pairs of universities strong negative consonance have strong opposite behavior. The pairs of universities in weak negative consonance and negative consonance have opposite properties. The results are presented into the intuitionistic fuzzy triangle (Figure 2).

Conclusion
In the presented investigation the Turkish University Rankings are analyzed. ICA analysis is applied to the datasets for the year 2021-2022. The correlations between the pairs of indicators and pairs of universities are determined. The universities are segmented in different areas of similarities and differences. The pairs of indicators are mainly independent excluding 3 pairs of indicators in positive consonance. The received outcomes present good choice for the most indicators. The university segmentation according their similarities is made. In the future research work the tendency of university distribution in the time will be observed.