Some Extensions of Membership Graphs for Picture Inference Systems

In this paper, we have extended the fuzzy inference system (FIS) on picture fuzzy sets in order to get a new system called picture inference system (PIS). PIS is designed based on the membership graph together with the general picture inference scheme. A membership graph is the combination of three lines giving a visual view of the positive, neutral and negative degrees, which reflect the underlying principle of picture fuzzy sets. Some extensions of the membership graph including the triangle, trapezoid, Gaussian and Bell graphs are investigated. The findings of the paper suggest the most efficient membership graph(s) that can be used in the picture inference system.