A bipolar approach for intuitionistic fuzzy alternative ranking

Ranking intuitionistic fuzzy alternatives has been widely studied by Szmidt and Kacprzyk in many work. The lake of a linear order amongst elements of intuitionistic fuzzy alternative sets, as stated in [1], oriented the researches to the definition of aggregation methods measuring the distance of each alternative to the best element of an intuitionistic fuzzy set. However, in some real applications such as raking possible items or alternatives according to positive and negative ratings, expressing respectively the satisfaction and dissatisfaction of some buyers in e-commerce applications, the distance may deliver some counter-intuitive results from the user´s standpoint. Therefore, by considering intuitionistic fuzzy alternatives as particular fuzzy bipolar sets, we introduce in this paper an intuitionistic bipolar approach for alternative ranking, based on (i) two intuitionistic preference relations, namely intuitionistic more preferred than or equal to (denoted by equation) and intuitionistic less preferred than or equal to (denoted by equation), each of which is a linear order, which can be used to rank bipolar alternatives attached with both degrees of acceptance (membership) and rejection (non-membership), and on (ii) two algebraic operators called Intuitionistic minimum, denoted by Imin, and Intuitionistic maximum, denoted by Imax, to compute respectively the intersection and the union of intuitionistic fuzzy bipolar alternative sets.