Implementation of the FATI hierarchical fuzzy inference system using the immutability decomposition method

Abstract

Most practical implementations of fuzzy inference systems chiefly encompass rule-based systems (FITA) due to their lower implementation cost. Classic fuzzy relational inference systems (FATI) are rarely used in practice. This paper presents a hierarchical architecture of the FATI system, which allows one to reduce the resources necessary for its software or hardware implementation. The system consists of single-input single-output (SISO) subsystems, which have the same architecture, but differ from each other in the contents of their knowledge in the form of fuzzy subrelations. These subrelations are created using decomposition of a global fuzzy relation of the primary classic multiple-input single-output (MISO) fuzzy inference system. Calculation of the global fuzzy relation, based on the knowledge base of the FITA system, is time-consuming and requires much memory to store it; therefore, decomposition has been moved to the linguistic level. Decomposition is a lossy operation; thus, the fuzzy inference result of the hierarchical system is fuzzier than the classic one. To avoid inference error, we present novel methods based on derivative linguistic values and partitioning of the primary knowledge base with immutability of its contents during the decomposition step, which can be used for any fuzzy inference system. An example of a FATI system proves the suitability of the developed methods in a real practical application.