Normalization in TOPSIS-based approaches with data of different nature: application to the ranking of mathematical videos

YouTube is the largest Internet video-sharing site in the world and in the last years it has become an important learning resource making educational contents accessible for hundreds of millions of people around the world, from developed and developing countries, allowing students to watch contents on demand. The utility of the performance assessment and ranking of educational videos available in You Tube goes beyond the simple control of the correctness and precision of the instructional contents. It requires considering other important didactical features as waste of time in the exposition, empathy with the user and the degree of adaptation of the contents to the educational context. In this paper a ranking method for instructional videos will be proposed, taking into account decision criteria of different nature: precise and imprecise and a reference solution (ideal solution). The decision matrix describing the assessment of videos with respect to each criterion will be formed by data of diverse nature: real numbers, intervals on the real line and/or linguistic or sets of categorical variables. Classical normalization procedures do not always take into account situations where the different nature of the data of the decision matrix could make the ranking of the alternatives quite unstable. A new normalization method will be proposed allowing us to mitigate this problem. Through this normalization procedure, the nature of the transformed normalized data will reflect the similarity of each alternative with the reference solution becoming thus, the decision matrix of homogeneous nature.