Background: A Fuzzy Cubic Set (FCS) is composed of a Fuzzy Set (FS) (certain fuzzy numbers) and an Interval-Valued Fuzzy Set (IVFS) (uncertain fuzzy numbers) to describe the hybrid information of both. To enhance the credibility of both, they should be closely related to the measures/degrees of credibility owing to the vagueness and uncertainty of humans’ cognitions regarding the real world.Objective: This paper presents the notions of a Fuzzy Cubic Credibility Set (FCCS) and a Fuzzy Cubic Credibility Number (FCCN) as the new generalization of the FCS notion to enhance the credibility level of FCS by means of the credibility degrees of both FS and IVFS. Next, we define operations of FCCNs, an expected value of FCCN, and the FCCN Weighted Arithmetic Averaging (FCCNWAA) and FCCN Weighted Geometric Averaging (FCCNWGA) operators for Decision Making (DM) strategy. Methods: A DM strategy using the FCCNWAA or FCCNWGA operator is proposed to solve multicriteria DM problems in the environment of FCCNs. Then, the proposed DM strategy is applied to a DM example of slope design schemes for an open-pit mine in the environment of FCCNs to reflect the feasibility of the proposed DM strategy. Result: By comparison with the fuzzy cubic DM strategy, the DM results with and without the degrees of credibility, can impact on the ranking of alternatives in the DM example to reflect the effectiveness of the proposed DM strategy. Conclusion: However, the highlighting advantage of this study is that the proposed DM strategy not only indicates the degrees of credibility regarding the assessed values of FCNs in the DM process but also enhances the DM reliability in the environment of FCCNs. Hence, the proposed DM strategy is superior to the fuzzy cubic DM strategy in the environment of FCCNs.
Keywords: Fuzzy credibility cubic set, Fuzzy credibility cubic number, Expected value, Fuzzy credibility cubic number weighted arithmetic averaging (FCCNWAA) operator, Fuzzy credibility cubic number weighted geometric averaging (FCCNWGA) operator, Decision-making strategy, Slope design scheme.