Picture inference system: a new fuzzy inference system on picture fuzzy set

In this paper, we propose a novel fuzzy inference system on picture fuzzy set called picture inference system (PIS) to enhance inference performance of the traditional fuzzy inference system. In PIS, the positive, neutral and negative degrees of the picture fuzzy set are computed using the membership graph that is the combination of three Gaussian functions with a common center and different widths expressing a visual view of degrees. Then, the positive and negative defuzzification values, synthesized from three degrees of the picture fuzzy set, are used to generate crisp outputs. Learning in PIS including training centers, widths, scales and defuzzification parameters is also discussed. The system is adapted for all architectures such as the Mamdani, the Sugeno and the Tsukamoto fuzzy inferences. Experimental results on benchmark UCI Machine Learning Repository datasets and an example in control theory - the Lorenz system are examined to verify the advantages of PIS.