A Non-Iterative Reasoning Algorithm for Fuzzy Cognitive Maps based on Type 2 Fuzzy Sets

A Fuzzy Cognitive Map (FCM) is a causal knowledge graph connecting concepts using direc-tional and weighted connections making it an effective approach for reasoning and deci-sion making. However, the modelling and reasoning capabilities of a conventional FCM for real world problems in the presence of uncertain data is limited as it relies on Type 1 Fuzzy Sets (T1FSs). In this work, we extend the capability of FCMs for capturing greater uncertainties in the interrelations of the modelled concepts by introducing a new reason-ing algorithm that uses Type 2 Fuzzy Sets based on z slices (zT2FSs) for the modelling of uncertain weights connecting FCM's concepts. These Type 2 Fuzzy Sets are generated using interval valued data from surveyed participants and aggregated using the Interval Agreement Approach method. Our algorithm performs late defuzzification of the FCM's values at the end of the reasoning process, preserving the uncertainty in values for as long as possible. The proposed algorithm is applied to the evaluation of the performance of modules of an undergraduate Mathematical programme. The results obtained show a greater correlation to domain experts' subjective knowledge on the modules' performance than both a corresponding FCM with weights modelled using T1FS and a statistical method currently used for evaluating the modules' performance. Sensitivity analysis conducted demonstrates that the new algorithm effectively preserves the propagation of uncertainty captured from input data. (c) 2022 Elsevier Inc. All rights reserved.

Automated summary

A Fuzzy Cognitive Map (FCM) is an effective approach for reasoning and decision making, but its capability for handling uncertain data is limited. In this work, a new reasoning algorithm is introduced, which uses Type 2 Fuzzy Sets based on z slices for modelling uncertain weights connecting FCM's concepts. The algorithm preserves uncertainty in values as long as possible and shows better correlation to experts' subjective knowledge compared to traditional methods and statistical approaches.