Three-level And Three-way Uncertainty Measurements For Interval-valued Decision Systems

Uncertainty measurements underlie system interaction and data learning.They become full for single-valued decision systems,but they are worth deeply investigating for interval-valued decision systems.Thus,three-level and three-way uncertainty measurements of interval-valued decision systems are implemented,it mainly by systematically constructing a criss-crossed information network of weighted entropiesas well as their basic properties.The concrete contents are organized as follows.Firstly,three-level analyses of interval-valued decision systems,we can see it is endowed with three-level structures,including Micro-Bottom,Meso-Middle,Macro-Top.Then,the existing conditional entropy in interval-valued decision systems is decomposed by three-way probabilities.The three-level decomposition of the existing conditional entropy makes a new uncertainty measurement method established in the interval-valued decision system,which is verified by an example.It lays a foundation for the construction of three-way weighted entropies in the subsequent interval-valued decision system.Then,in the context of the three-level structure of the interval-valued decision system,three weighted entropies are systematically and hierarchically constructed,and the hierarchical,systematic,algorithmic,bounded,and granular monotonicity/non-monotonic of the three weighted entropies are achieved.At the Micro-Bottom,the boundedness and monotonicity/non-monotonicity of the three-weighted entropies are proved.The boundedness and monotonicity/non-monotonicity of the three weighted entropies at the Meso-Middle and the Macro-Top are also proved,This proof is obtained by integrating the three weighted entropies At the Micro-Bottom,and verified by an example.The three-level and three-way weighted entropies deepen and extend the conditional entropy,and they complete the novel criss-crossed informatization for interval-valued decision systems.Finally,the effectiveness of the three-way weighted entropies in the interval-value decision systems is verified by examples and data experiments.