In recent years, with the development of the internet, there has been an increase in interest in the internet thanks to other technological developments. In the face of increased user demand, educational institution websites have to maintain high quality of service for a sustainable success. The authors present the possibility degree based TOPSIS method with IT2F numbers as an extension of TOPSIS method to evaluate the educational institution websites. In contrast to precise numbers in TOPSIS method, the merit of fuzzy TOPSIS method is to handle the fuzzy numbers to evaluate the alternatives. Type-1 fuzzy numbers consider crisp membership degrees to express fuzzy numbers but IT2F numbers handle more uncertainties than type-1 fuzzy numbers. The subjective judgments of the decision makers are aggregated by using the IT2F number operations to determine the weights of these criteria. IT2TrF numbers-based TOPSIS phase is employed to rank alternatives based on criteria so that assessment process is completed. The proposed method is applied to evaluate the educational institution websites.
TopIntroduction
Information storage is one of the basic attributes of corporation performance. Internet, which is indispensable for our daily activities, ensures storing large datasets. Internet affects marketing methods as handling relationships between consumers and corporations. Websites of big corporations present interactive experience to the consumers to help deciding between buying alternatives. Similarly, educational institutions must develop their websites to increase the content and quality of information for users. The future and current students can reach the desired information more easily. The quality of the institution websites also help to the institution’s own teaching personel looking for specific information related to the teaching process and scientific research (Pamučar et al., 2018).
Pamučar et al. (2018) considered the integration of interval rough AHP and interval rough MABAC methods for evaluating university web pages. Akıncılar and Dağdeviren (2014) presented the combination of AHP and PROMETHEE methods for evaluating hotel websites. Tzeng et al. (2005) handled fuzzy based Choquet integral model for evaluating enterprise intranet web sites. Stanujkic et al. (2015) used the intuitionistic fuzzy set for measuring website quality. Roy et al. (2017) presented AHP approach to consider the quality of academic websites. Hsu and Shih (2016) considered ANP, Kano model, DEMATEL and VIKOR methods the e-service quality of house rental websites. Bilsel et al. (2006) presented AHP and fuzzy PROMETHEE methods for measuring performance of hospital websites. Yu et al. (2011) utilized AHP and fuzzy TOPSIS methods for e-commerce websites. Lee and Kozar (2006) investigated the effect of website quality on e-business success by using AHP approach. Büyüközkan and Ruan (2007) employed fuzzy AHP and fuzzy TOPSIS methods for evaluating the quality of government websites. Dominic et al. (2013) considered to determine the best university website by using fuzzy AHP and linear weightage model.
We present the possibility degree based TOPSIS method with IT2F numbers as an extension of TOPSIS method. In contrast to precise numbers in TOPSIS method, the merit of fuzzy TOPSIS method is to handle the fuzzy numbers to evaluate the alternatives. Type-1 fuzzy numbers consider crisp membership degrees to express fuzzy numbers but IT2F numbers handle more uncertainties than type-1 fuzzy numbers. IT2F numbers ensure us with additional information to describe the fuzziness and the uncertainty of the real-life world. This study aims to extend the TOPSIS method by utilizing interval type-2 trapezoidal fuzzy (IT2TrF) numbers in order to model more uncertainties of the subjective judgments in complex problems. The aim of this study is to introduce a novel IT2F TOPSIS method based on possibility mean value and possibility degree. This study uses the approximate positive and negative ideal solutions with IT2TrF numbers to evaluate the alternatives. This study presents the possibility mean value and possibility degree measures instead of distance measures in current TOPSIS to define a comparative index. The closeness coefficient based on the possibility degree of each alternative is calculated according to the approximate positive and negative ideal solutions. This study also uses the IT2F number operations to aggregate the subjective judgments of the decision makers about the relative importance of criteria and criteria based alternative evaluations. The subjective judgments of the decision makers are aggregated by using the IT2F number operations to determine the weights of the criteria. These weights with IT2TrF numbers are used into IT2TrF numbers based TOPSIS phase to rank the alternatives. The proposed method is applied to evaluate the university websites.
TopPreliminaries
If a IT2FS 
and 
show the upper membership function and the lower membership function, respectively. These upper and lower membership functions are type-1 membership functions.