Z-number based neural network structured inference system

Abstract

Z-number based Neural Network structured Inference System (ZNIS) with rule-base consisting of linguistic Z-terms trainable with Differential Evolution with Constraints (DEC) optimization algorithm is suggested. The inference mechanism of the multi-layered ZNIS consists of a fuzzifier, fuzzy rule base, inference engine, and output processor. Due to the use of extended fuzzy terms, each processing layer implements appropriate extended fuzzy operations, including computation of fuzzy valued rule firing strengths, fuzzy Level-2 aggregate outputs, and two consecutive Center of Gravity (COG) defuzzification procedures. The experiments with different versions of ZNIS have demonstrated that it is a universal modeling tool suitable for dealing with both approximate reasoning and functional mapping tasks. Random experiments on benchmark examples (among which are simple functional mapping, Parkinson disease, and non-linear system identification) have shown that ZNIS performance is equivalent to or better than FLS Type 2 and far superior to FLS Type 1, showing on average 2–3 times lower MSE. Along with this, the main advantages of ZNIS over other inference systems are better semantic expressing power, higher degree of perception and interpretability of the linguistic rules by humans, and a higher confidence in the reliability of achieved decision due to the transparency of the underlying decision-making mechanism.