High-Dimensional Discrete Fuzzy Numbers and their Application in Ranking Multi-Channel Uncertain Discrete Digital Information

In this paper, some issues related to high-dimensional discrete fuzzy numbers are studied. Firstly, an enhancement has been made to the previously established theorem concerning the representation of one-dimensional, discrete fuzzy numerical entities, and the definition of high-dimensional discrete fuzzy numbers has been given based on the idea of this improved representation theorem. Then, we proposed a sufficient condition for a fuzzy set of [Formula: see text] to be an n-dimensional discrete fuzzy number in order to be used conveniently in application, and a special high-dimensional discrete fuzzy number is introduced based on this result. Subsequently, we derive the average computation formula for an n-cell discrete fuzzy number that arises from the combination of trapezoidal-shaped and triangular-shaped fuzzy numbers, and introduce a partial ordering relation within the n-dimensional discrete fuzzy number domain. In the end, we provide a case to clarify how our obtained findings can be harnessed to establish a priority order for objects that are characterized by multi-channel uncertain discrete digital data.