Higher Order Fuzzy Rule Interpolation

Abstract

Fuzzy inference is an effective means for representing and handling vagueness and imprecision. As a particular type of fuzzy inference, fuzzy rule interpolation enhances the performance of the inference when a given observation has no overlap with the antecedent values of any of the existing rules. In such cases, conventional fuzzy inference methods cannot derive a conclusion, but fuzzy rule interpolation methods can still obtain a certain conclusion. Unfortunately, very little of the existing work on fuzzy rule interpolation can conjunctively handle more than one form of uncertainty in the rules or observations. In particular, the difficulty in defining the required precise-valued membership functions for the fuzzy sets that are used by conventional fuzzy rule interpolation techniques significantly restricts their application. In this thesis, a novel framework termed “higher order fuzzy rule interpolation” is proposed in an attempt to address such difficulties. The proposed framework allows the representation, handling and utilisation of different types of uncertainty in knowledge. This allows transformation-based fuzzy rule interpolation techniques to harness and utilise the additional uncertainty in order to implement a fuzzy interpolative reasoning system. Final conclusions can then be derived by performing higher order interpolation over this representation. The techniques for the representation and handling of uncertainty are organised in this framework such that in circumstances when different types of uncertainty are encountered the inference process can deal with them in an appropriate way. A rough-fuzzy set based rule interpolation approach is proposed in this work, by exploiting the concept of rough-fuzzy sets and generalising scale and move transformation-based fuzzy interpolation. A type-2 fuzzy set based interpolation approach is also presented as an alternative implementation of the framework. The effectiveness of this work in improving the robustness of fuzzy rule interpolation is demonstrated through the practical application to the prediction of disease rates in remote villages. Moreover, this framework is also further evaluated with application to other realistic decision making problems. The resultant accuracy reveals the efficacy of this research

Date of Award	27 May 2015
Original language	English
Awarding Institution	Aberystwyth University
Supervisor	Qiang Shen (Supervisor) & Richard Jensen (Supervisor)