Abstract
Uncertainty measurement (UM) can offer new visual angle for data analysis. A fuzzy set-valued information system (FSVIS) indicates an information system (IS) where its information values are fuzzy sets. This article investigates UM for fuzzy set-valued data based on Chebyshev distance. First, the distance between information values is founded in a given subsystem. After that, the tolerance relation induced by this subsystem is obtained by means of this distance. Moreover, the information structure of this subsystem is proposed. Next, the uncertainty of a FSVIS are measured. Eventually, to show the feasibility of the proposed measures, effectiveness analysis is carried out from a statistical view. The obtained outcomes may be helpful for comprehending the nature of uncertainty in a FSVIS.
Highlights
4) This paper investigates uncertainty measurement (UM) for a fuzzy set-valued information system (FSVIS)
We propose the definition of FSVIS below
It can be concluded that the uncertainty of a FSVIS can be evaluated by θ -information granulation displayed in Definition 20
Summary
Brought forward by Pawlak [23], [25], [26], is a significant approach for managing imprecision, vagueness, and specially uncertainty This theory is developed around the concept of an information system (IS). Zhang et al [35] explored uncertainty measures in a fully fuzzy IS; Beaubouef et al [4] come up with a method for measuring the uncertainty of rough sets; Li et al [17], [21], [22] studied information structures and UM in covering and fuzzy relation ISs. B.
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