Uncertain multi-attributes decision making method based on interval number with probability distribution weighted operators and stochastic dominance degree

In real world decision making problems, real numbers, random numbers, and interval numbers are often used simultaneously to express the attribute values of alternatives. To solve these uncertain multi-attribute decision making problems, we propose a definition of interval number with probability distribution (INPD). This definition gives a uniform form for real numbers, interval numbers, and random numbers. Under certain conditions, an INPD can degrade to one of the three number forms. We then propose three weighted operators that aggregate opinions expressed by INPD. Furthermore, we propose a new stochastic dominance degree (SDD) definition based on the idea of almost stochastic dominance to rank two INPD. The new definition overcomes defects in traditional stochastic dominance methods. It takes all stakeholders' preferences into account and can measure both standard and almost SDDs. For real numbers and interval numbers, results derived from SDD are consistent with traditional methods. On this basis, a method using INPD weighted operators and SDD is proposed to solve uncertain multi-attribute decision making problems. Finally, three numerical examples are given to illustrate the applicability and effectiveness of the proposed method.