The bilateral fuzzy soft set and its application in multi-criteria multi-person decision making under conflict information

Fuzzy soft set is a general mathematical tool to deal with uncertain and fuzziness information. But inadequacy lies in which cannot express various uncertainty in a more natural and accurate manner, due to the reason of adopting the fuzzy membership which restricts to [0, 1]. As a result, it merely concerns non-negative fuzzy belongingness of elements, so as to be incapable of capturing the conflict information that supporting, neutral and opposing scenarios regarding belongingness of elements in a set to taken into account. To overcome the limitation, this paper extends fuzzy soft set to bilateral fuzzy soft set (BFSS), which considers both non-negative and negative sides for fuzzy membership and normalizes the range to [−1, 1]. Then defines some basic operations on BFSS, as well as a detail study of relevant properties. In order to eliminate redundant parameters and draw the essential part of BFSS, the parameters reduction on BFSS is also investigated, and the significance of parameters is introduced accordingly. On this basis, an assessment approach for multi-criteria multi-person decision making under conflict information, together with the algorithm for implementation is presented. Finally, a typical numerical example regarding voting demonstrates the validity and feasibility of the proposed method.