Abstract
Fuzzy relations are simple mathematical structures that enable a very general representation of fuzzy knowledge, and fuzzy relational calculus offers a powerful machinery for approximate reasoning. However, one of the most relevant limitations of approximate reasoning is the efficiency bottleneck. In this paper, we present two implementations for fast fuzzy inference through relational composition, with the twofold objective of being general and efficient. The two implementations are capable of working on full and sparse representations respectively. Further, a wrapper procedure is capable of automatically selecting the best implementation on the basis of the input features. We implemented the code in GNU Octave because it is a high-level language targeted to numerical computations. Experimental results show the impressive performance gain when the proposed implementation is used.
Highlights
Fuzzy Set Theory (FST) is widely recognized as a valid mathematical tool for representing and processing imprecise and gradual knowledge11
From the implementation for full matrices, the internal loop in this implementation does not necessarily cycle m times; rather, the number of cycles is reduced when zero elements occur in the columns of A or B involved in the computation
All the algorithms have been coded in C++, by using the libraries required for integrating with Octave
Summary
Fuzzy Set Theory (FST) is widely recognized as a valid mathematical tool for representing and processing imprecise and gradual knowledge. FST is capable to represent the semantics of concepts that are usually expressed with natural language terms, which are inherently imprecise In this way, FST enables the formal representation of linguistically quantified knowledge and provides a mathematical machinery for approximate reasoning. The objective of such tools is to enable knowledge engineers and/or end-users to develop fuzzy expert systems that can be applied in a variety of application domains. As regards the software approaches, either restrictive assumptions on the involved relations need to be made (e.g. only fuzzy rules are allowed) or efficient algorithms for general inference must be devised. In this paper we present two implementations for fast inference in approximate reasoning that have the twofold objective of being both general and efficient.
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