A Mixed Model for Pairwise Comparisons and Its Applications

Abstract

The method of Pairwise Comparisons was first described by Ramon Llull in the end of XIII century. At present, this method is identified with controversial Saaty’s Analytic

Hierarchy Process that was first proposed in 1977. The Analytic Hierarchy Process is a formal method to derive ranking orders from pairwise comparisons and it is used around the world in a wide variety of decision making, in fields such as education, industry, and government. However many researchers consider it as a flawed procedures that might produce arbitrary rankings.

In the last two decades alternative models, also based on pairwise comparisons paradigm, that appear to work better in many cases and have better theoretical fundamentals. One of them is ‘qualitative pairwise comparisons based ranking’, the other one is a quantitative pairwise comparisons ranking but based on the concept of ‘distance-based consistency’, refined and used relatively often in last decade.

In this thesis we will substantially refine ‘mixed model’, and then apply this model for several ‘real world’ cases. The ‘mixed model’ is a systematic composition of quantitative model and qualitative model. In this thesis we clarify and provide some formal foundations for scales and assignment of numerical values for qualitative factors and based on these we provide a formal process to be followed.

Seven applications in such fields as software evaluation, software quality in use, quality in use in video games, software reuse, smart grid analysis, healthcare quality and quality analysis of medical devices are provided and analysed. They show the mixed method to be useful and appreciated by users.