Measures of Uncertainty Based on Gaussian Kernel for Type-2 Fuzzy Information Systems

In data processing, measurement of uncertainty is one of the significant evaluation tools, which can describe the uncertainty essence of data. So far, there are few measurable tools to study the uncertainty of type-2 fuzzy information systems (TFISs-2) (the expanded models of fuzzy information systems). This paper is devoted to looking for effective indicators to describe the uncertainty of TFISs-2. The fuzzy T-cos-similarity relations are first introduced, which are generated by TFISs-2 based on Gaussian kernel. Then, the fuzzy information structures are defined on account of this fuzzy T-cos-similarity relation. Next, two measures constructed from the upper and lower approximations are given for TFISs-2, that is, delta-accuracy and delta-roughness, which are used to reflect the degree of accuracy and inaccuracy of information by numerical form. Furthermore, by combining roughness and entropy, the delta-rough entropy is investigated. Finally, the practicability of proposed measures is tested by a numerical experiment. The experimental results show that the delta-rough entropy is efficacious and applicable for TFISs-2.

Automated summary

This paper introduces effective indicators for describing the uncertainty of TFISs-2, including fuzzy T-cos-similarity relations, fuzzy information structures, and measures such as delta-accuracy and delta-roughness. Experimental results demonstrate the efficacy and applicability of delta-rough entropy for TFISs-2.