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Cubic picture fuzzy set (CPFS) is the hybrid version of the interval-valued picture fuzzy set (IPVFS) and the picture fuzzy set (PFS) simultaneously. Clearly, the CPFS contains significantly more information than the general IVPFS and PFS in order to address the vulnerability of decision-making problems. Lamentably, the aggregation operators have not been researched so far on the basis of CPFS. In the techniques of group decision-making, aggregation operators are an important mathematical method to resolve ambiguity in decision-making problems. The present paper proposes few novel geometric mean aggregation operators, in particular, cubic picture fuzzy geometric and cubic picture fuzzy geometric star aggregation operators between cubic picture fuzzy numbers to aggregate the different predispositions of the decision maker. Then, based on the proposed operators in the cubic picture fuzzy environment, we developed a decision-making method and illustrated a numerical example. Finally, in order to demonstrate the supremacy of the proposed technique, classify its comparison with the existing approach. The results showed that the established decision-making technique was superior, accurate and effective.

In this paper, we define linguistic hesitant fuzzy sets. We introduce cubic linguistic fuzzy sets and their operational laws. We propose a cubic linguistic hesitant fuzzy sets and their operational laws. We describe aggregation operators for cubic linguistic hesitant fuzzy sets which extended the generalized cubic linguistic hesitant fuzzy averaging (geometric) operator, generalized cubic linguistic hesitant fuzzy weighted averaging (GLCHFWA) operator, generalized cubic linguistic hesitant fuzzy weighted geometric (GCHFWG) operator, generalized cubic linguistic hesitant fuzzy ordered weighted average (GCLHFOWA) operator, generalized cubic linguistic hesitant fuzzy ordered weighted geometric (GCLHFOWG) operator, generalized cubic linguistic hesitant fuzzy hybrid averaging (GCLHFHA) operator and generalized cubic linguistic hesitant fuzzy hybrid geometric (GCLHFHG) operator. Moreover, we relate these aggregation operators to develop an approach to multiple-attribute group decision-making with cubic linguistic-hesitant fuzzy information. Finally, the overall ranking of an alternative is obtained. This example is presented to illustrate the feasibility and effectiveness of the proposed approach.

The information aggregation of cubic fuzzy numbers and picture fuzzy numbers have played an important role in decision making. This paper introduces a novel approach to address the problem of testing facility of COVID-19 under picture cubic fuzzy environment. As the picture cubic fuzzy set is a generalized fuzzy structure to handle more uncertainty and ambiguity in decision making problems We discuss its various properties. Based on geometric aggregation operators and Hamacher operations, we introduce some Hamacher geometric aggregation operators under picture cubic fuzzy information. Namely, picture cubic fuzzy Hamacher weighted geometric aggregation operator, picture cubic fuzzy Hamacher hybrid geometric operator, picture cubic fuzzy Hamacher order weighted geometric aggregation operator. Discuss some properties of the defined operators. To verify the importance of the proposed operators, develop multicriteria group decision making (MCGDM) algorithm under picture cubic fuzzy environment and apply this strategy for the selection of an authentic laboratory for COVID-19 test. Further to validate the supremacy of our proposed operators, we present a comparative analysis with pre-existing aggregation operators. Results show that the proposed technique is more effective and suitable for MCGDM problems.