Fuzzy Cognitive Maps with Type 2 Fuzzy Sets

  • Alya Al Farsi

    Student thesis: Doctoral ThesisDoctor of Philosophy


    A Fuzzy Cognitive Map (FCM) is a causal knowledge graph with feedback. Its robust characteristics make it an effective approach to reasoning and decision making in diverse application domains. However, the capabilities of a conventional FCM for modelling and
    reasoning real-world problems in the presence of uncertain data is limited as it relies on a Type 1 Fuzzy Set (T1FS). In this thesis, the capability of FCM for capturing more uncertainties is extended by introducing Type 2 Fuzzy Sets based on z slices (zT2FSs)
    which are capable of capturing higher degrees of uncertainties compared to T1FS. This extension is carried out through two stages. In Stage 1, the Interval Agreement Approach (IAA) is used to generate zT2FSs that model the weights of causal relations in the FCM. In this stage, the FCM’s reasoning is carried out using an iterative reasoning algorithm with the defuzzified values of generated zT2FSs. In Stage 2, a new reasoning algorithm is
    introduced for the FCM which is proposed in Stage 1, where the reasoning operates with the fuzzy values of the weights without defuzzification. To demonstrate the proposed FCM in Stage 1, a new case study for early diagnosis of autism was created. Using the secondary data for an autism diagnosis, published in the literature, the accuracy of the diagnosis is increased by 5.46% when the proposed FCM is used. The results demonstrate that the
    proposed method outperforms conventional FCMs used for the same purpose. To demonstrate the new reasoning algorithm developed in Stage 2, the proposed FCM in Stage 1 was applied with the new reasoning algorithm in a new created case study for the evaluation of module performances across mathematical modules in a higher education institution. It was found that the results obtained have a higher correlation with domain experts’ subjective knowledge than both an FCM with weights modelled using T1FS and statistics currently used for evaluating module performances. The correlation between the domain experts and the results obtained when the proposed reasoning algorithm is applied is 0.34, while in cases when a T1FS and currently used statistics are used it is 0.08 and 0.28, respectively. In addition, sensitivity analysis is conducted to investigate the propagation of uncertainty in the proposed reasoning algorithm. The results demonstrate that the FCM that uses the new reasoning algorithm preserves the propagation of uncertainty captured from input data effectively. It was observed that changes in uncertainties of zT2FS weighted links impacted the value of the decision concept in the
    FCM with different degrees depending on the structure of the FCM and its links. The contributions of this research, which are obtained from the abovementioned two stages, are: (1) new extensions of FCM where the weights represented by zT2FSs outperform the conventional FCM, and (2) a new non-iterative reasoning algorithm for FCM that effectively propagates the uncertainty while reasoning and hence enhances the capability
    of FCM for reasoning similar to human.
    Date of Award2022
    Original languageEnglish
    Awarding Institution
    • Coventry University
    SupervisorAmmar Al Bazi (Supervisor), Faiyaz Doctor (Supervisor) & Dobrila Petrovic (Supervisor)

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