Extending Similarity Measures of Interval Type-2 Fuzzy Sets to General Type-2 Fuzzy Sets

Similarity measures provide one of the core tools that enable reasoning about fuzzy sets. While many types of similarity measures exist for type-1 and interval type-2 fuzzy sets, there are very few similarity measures that enable the comparison of general type-2 fuzzy sets. In this paper, we introduce a general method for extending existing interval type-2 similarity measures to similarity measures for general type-2 fuzzy sets. Specifically, we show how similarity measures for interval type-2 fuzzy sets can be employed in conjunction with the zSlices based general type-2 representation for fuzzy sets to provide measures of similarity which preserve all the common properties (i.e. reflexivity, symmetry, transitivity and overlapping) of the original interval type-2 similarity measure. We demonstrate examples of such extended fuzzy measures and provide comparisons between (different types of) interval and general type-2 fuzzy measures.Comment: International Conference on Fuzzy Systems 2013 (Fuzz-IEEE 2013

Connectionism and psychological notions of similarity

Kitcher (1996) offers a critique of connectionism based on the belief that connectionist information processing relies inherently on metric similarity relations. Metric similarity measures are independent of the order of comparison (they are symmetrical) whereas human similarity judgments are asymmetrical. We answer this challenge by describing how connectionist systems naturally produce asymmetric similarity effects. Similarity is viewed as an implicit byproduct of information processing (in particular categorization) whereas the reporting of similarity judgments is a separate and explicit meta-cognitive process. The view of similarity as a process rather than the product of an explicit comparison is discussed in relation to the spatial, feature, and structural theories of similarity

How to select combination operators for fuzzy expert systems using CRI

A method to select combination operators for fuzzy expert systems using the Compositional Rule of Inference (CRI) is proposed. First, fuzzy inference processes based on CRI are classified into three categories in terms of their inference results: the Expansion Type Inference, the Reduction Type Inference, and Other Type Inferences. Further, implication operators under Sup-T composition are classified as the Expansion Type Operator, the Reduction Type Operator, and the Other Type Operators. Finally, the combination of rules or their consequences is investigated for inference processes based on CRI