Weighted aggregation operators of fuzzy credibility numbers and their decision-making approach for slope design schemes

In fuzzy decision-making problems, existing fuzzy decision-making methods only indicate fuzzy assessment values but lack the degrees/levels of credibility regarding the fuzzy assessment values in alternatives over attributes due to the vagueness and uncertainty of human cognitions/judgments for complicated decision-making problems. Therefore, the credibility degree of the fuzzy assessment value shows its importance and necessity in the fuzzy decision-making problem. To enhance the credibility degrees/levels of fuzzy assessment values, the fuzzy assessment values should be closely related to their credibility measures, which make the assessment information more abundant and more credible. Hence, this study proposes the concept of a fuzzy credibility number (FCN) as a new extension of the fuzzy concept, where both a fuzzy value and a credibility degree are expressed by a pair of fuzzy values. Then, we present operations of FCNs, a score function of FCN, a FCN weighted arithmetic averaging (FCNWAA) operator, and a FCN weighted geometric averaging (FCNWGA) operator. Next, a multi-attribute decision-making (MADM) approach using the FCNWAA or FCNWGA operator is established to deal with MADM problems in the setting of FCNs. Eventually, the established MADM approach is used for a decision-making example on selecting a suitable slope design scheme for an open pit mine in the setting of FCNs to reflect the usability and effectiveness of the established decision-making approach. Compared with the classical fuzzy MADM approach, the established MADM approach makes the assessment information more abundant and more credible, then the sensitivity analysis indicates the importance and efficiency of credibility measures in the ranking order of alternatives, which reflect main advantages of the established MADM approach in the environment of FCNs. However, this study reflects the novelty and new contribution of the proposed information expression and aggregation operations and decision-making method in fuzzy decision theory and methods.

Automated summary

This study introduces a new fuzzy decision-making method by proposing the concept of fuzzy credibility number (FCN) to enhance the credibility levels of fuzzy assessment values, making the assessment information more abundant and credible. By establishing a multi-attribute decision-making (MADM) approach using FCNs, it is applied to a decision-making example on selecting a suitable slope design scheme, reflecting the usability and effectiveness of the method.