Fuzzy complex numbers and their application for classifiers performance evaluation

There are a variety of measures to describe classification performance with respect to different criteria and they are often represented by numerical values. Psychologists have commented that human beings can only reasonably manage to process seven or-so items of information at any one time. Hence, selecting the best classifier amongst a number of alternatives whose performances are represented by similar numerical values is a difficult problem faced by end users. To alleviate such difficulty, this paper presents a new method of linguistic evaluation of classifiers performance. In particular, an innovative notion of fuzzy complex numbers (FCNs) is developed in an effort to represent and aggregate different evaluation measures conjunctively without necessarily integrating them. Such an approach well maintains the underlying semantics of different evaluation measures, thereby ensuring that the resulting ranking scores are readily interpretable and the inference easily explainable. The utility and applicability of this research are illustrated by means of an experiment which evaluates the performance of 16 classifiers using different benchmark datasets. The effectiveness of the proposed approach is compared to conventional statistical approach. Experimental results show that the FCN-based performance evaluation provides an intuitively reliable and consistent means in assisting end users to make informed choices of available classifiers.