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.