Intuitionistic fuzzy bipolar approach for flexible querying in e-commerce applications

Several e-commerce applications ask customers to leave comments about the purchased products and to rate them positively or negatively as an opportunity to obtain valuable feedback on them. These information could be seen as user's preferences in a process of flexible query evaluation, which is capable to distinguish amongst the product items those that are the most suitable or most preferred to a given buyer. In this paper, we model product items (or alternatives) attached with positive and negative ratings as intuitionistic fuzzy sets [1], such that positive and negative ratings correspond to membership and nonmembership degrees respectively. Then, we show that available heterogeneous bipolar approaches developed in the field of flexible querying are not adequate in our case, and we introduce two new operators to rank intuitionistic alternatives, namely, Intuitionistic minimum, denoted by Imin, and Intuitionistic maximum, denoted by Imax. Finally, we show that each of these operators forms a linear order and both can represent a couple of extended intuitionistic t-norm and t-conorm that can be used as a basis of an intuitionistic bipolar fuzzy querying approach.