Bipolar aggregation method for fuzzy nominal classification using Weighted Cardinal Fuzzy Measure (WCFM)

The issue of designing a procedure to assign objects (candidates, projects, decisions, options, etc.) characterized by multiple attributes or criteria to predefined classes characterized by fuzzyly defined multiple features, conditions or constraints, is considered in this paper. Such assignment problems are known in the literature as nominal or non ordered classification problems as opposed to ordinal classification in which case classes are ordered according to some desires of decision maker(s). Because of the importance of these problems in many domains such as social, economics, medical, engineering, mangement etc., there is a need to design sound and appropriate evaluation algorithms and methods to deal with them. In this paper we will consider an approach based on an evaluation strategy that consists in aggregating separately elements that act in the same sens (either contributing to the exlusion of a class from assignment or its consideration for inclusion given an object) that we refer to as bipolar analysis. Then, relying on the fact that elements to aggregate have synergetic relationships (they are complementary), we propose to use Choquet integral as the appropriate aggregation operator with a proposed fuzzy measure or capacity known as weighted cardinal fuzzy measure (WCFM) which tractability permits to overcome dificulties that dissuade the use of Choquet integral in practices. Furthermore, bipolar property results in evaluation by two degrees: classifiability measure that measures to what extent an object can be considered for inclusion in a class and rejectability measure, a degree that measures the extent to which one must avoid including an object to a class rendering final choice flexible as many classes may be qualified for inclusion of an object. Application of this approach to a real world problem in the domain of banking has shown a real potentiality.