Experimental analysis of score functions in multi-criteria decision-making with intuitionistic fuzzy sets

The purpose of this article is to examine individual differences of various score functions in multiple criteria decision analysis based on intuitionistic fuzzy sets (IFSs). A review of the literature indicates that score functions have been widely used in multi-criteria evaluations from a variety of research fields. There exist several types of score functions to identify the mixed result of positive and negative parts in a bi-dimensional framework of IFSs. However, very few studies have conducted a comparative analysis of different score functions. Considering various perspectives of score functions, this study developed an integrated programming model to cope with the problems of incompletely known membership grades and positivity and negativity biases by utilizing both deviation variables and weighted score functions. An experimental analysis was conducted to examine the relationship between the results yielded from different score functions with discussions on average Spearman correlation coefficients and contradiction rates. Additional discussions are made to clarify the relative differences in the ranking orders obtained from different combinations of numbers of alternatives and criteria and for different importance conditions.