Basic uncertain information soft set and its application to multi-criteria group decision making

Abstract

The purpose of this paper is to develop a novel type of soft set called basic uncertain information soft set (BUISS), which combines the notion of basic uncertain information and soft set theory. Since basic uncertain information can measure the quality of datum by using the degree of certainty, the developed BUISS provides a novel extension of soft set. In this paper, set operations and comparison law of basic uncertain information are also developed. Then, operations on BUISSs include set operations, ’AND’ operation and ’OR’ operation are defined. Besides, the Jaccard similarity between two BUISSs is introduced. The properties of the operations and similarity measure are studied. Theoretically, a multi-criteria group decision making (MAGDM) problem under basic uncertain information environment is analysed by using BUISSs. Two decision algorithms based on level BUISS and the aggregation of ϵ-approximate elements are proposed. Finally, an assessment of natural gas security in China is investigated to illustrate the feasibility and validity of the developed decision approaches.