Plithogenic Fuzzy Expert System, Neuro-Plithogenic Fuzzy System, and Plithogenic Fuzzy Cognitive Maps with Upside-down Logic

Abstract

Neuro–Fuzzy Systems combine fuzzy rule–based inference with neural learning, adapting memberships and rule parameters from data for interpretable modeling. Fuzzy Expert Systems map crisp inputs to outputs via fuzzification, T–norm/implication inference, aggregation, and defuzzification. Fuzzy Cognitive Maps capture causal relations on weighted directed graphs with iterative fuzzy updates. We extend these to the plithogenic setting: the Plithogenic Fuzzy Expert System (PFES), the Neuro–Plithogenic–Fuzzy System (NPFS), and Plithogenic Fuzzy Cognitive Maps (PFCM). We formalize a contradiction–aware operator and an Upside–Down transform with contradiction reset that flips memberships/edge–contributions above a threshold and neutralizes the anchor contradiction. We prove PFES, NPFS, and PFCM strictly generalize their classical counterparts and induce valid plithogenic fuzzy structures. Numerical examples illustrate context–dependent reasoning, learning consistency, and robustness under conflicting attributes.