Abstract
Constrained interval type-2 (CIT2) fuzzy sets are a class of type-2 fuzzy sets that has been recently proposed as a way to extend type-1 membership functions to interval type-2 (IT2) while keeping a semantic connection between the IT2 fuzzy set and the concept it models. Recent work has shown how their mathematical properties can be used to design CIT2 fuzzy logic systems that are able to provide explanations for their outputs. Although the CIT2 representation can be a valuable alternative to the IT2 one, no software library for their implementation is available for the research community. The aim of this paper is to introduce a new Java library, Juzzy Constrained, that has been developed as an extension of the popular type-1 and type-2 Java toolkit Juzzy, adding support for CIT2 sets and systems. Throughout the paper, the main classes and the structure of the new library are described, together with a working example that illustrates how to build a CIT2 fuzzy system from scratch and how it can be used to produce explanations for the output.
Highlights
The use of interval type-2 (IT2) [1] fuzzy sets and systems has rapidly grown over time
The aim of this paper is to present the first software library, named Juzzy Constrained, that implements constrained interval type-2 (CIT2) fuzzy sets and systems and to collect constructive feedback on the CIT2 representation from the research community
Constrained type-2 (CT2) and constrained interval type-2 (CIT2) fuzzy sets were proposed [15] as a new way to model vague concepts using T2 and IT2 fuzzy sets starting from a T1 set modeling the same word or concept
Summary
The use of interval type-2 (IT2) [1] fuzzy sets and systems has rapidly grown over time. By the imposition of additional mathematical constraints on the footprint of uncertainty (FOU) and the shape of the embedded sets (ES), they establish a standard process to “extend” T1 fuzzy sets to IT2 ones while keeping a strong semantic relation between the constrained set and the concept it models It has been shown [13], [14] how the additional constraints make it easier to explain the interval centroid produced by CIT2 FLS thanks to the use of embedded sets with a “meaningful” shape. These properties make CIT2 FLSs a valuable alternative to IT2 FLSs in contexts in which producing explainable outputs is important (e.g. XAI applications).
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