A Cognitive Information-Based Decision-Making Algorithm Using Interval-Valued q-Rung Picture Fuzzy Numbers and Heronian Mean Operators

The complexity of the socioeconomic environment means that it is challenging to make decisions that rely on cognitive information. Decision makers normally cannot obtain a precise or sufficient level of knowledge about the problem domain and hence must provide multiple answers with interval values to depict them. This makes cognizing and decision making very difficult. To address this issue, this paper proposes a novel cognitive information-based decision-making algorithm with interval-valued q-rung picture fuzzy (IVq-RPtF) numbers. We first define the concept of the IVq-RPtF set, including the basic definition, operational laws, a score function, and an accuracy function. Considering the interrelationship between attributes, we then present the IVq-RPtF Heronian mean (IVq-RPtFHM) operators using the new operational laws. Moreover, we discuss the properties of IVq-RPtFHM operators, such as monotonicity, commutativity, and idempotency. Finally, we use a numerical example to verify the viability of the proposed method. The results show that the proposed method effectively expresses multiple types of interval cognitive information. The sensitivity analysis of the parameters shows that the ranking results are susceptible to parameter changes, but regardless of how the parameters change, the score values of the four alternatives in our example are in the range of [1.27, 1.66], within the basic scoring range of [1.352–1.472] for the four alternatives. Therefore, our proposed method based on IVq-RPtFHM operators has a stronger information aggregation ability than other methods. Compared with other methods, the proposed cognitive information-based decision-making algorithm is more widely applicable, avoids loss of cognitive information, and conducts a reasonable decision-making process.