Clustering is more popular than the expert knowledge approach in Interval Fuzzy Type-2 membership function construction because it can construct membership function automatically with less time consumption. Most research proposed a two-fuzzifier fuzzy C-Means clustering method to construct Interval Fuzzy Type-2 membership function which mainly focused on producing Gaussian membership function. The other two important membership functions, triangular and trapezoidal, are constructed using the grid partitioning method. However, the method suffers a drawback of not being able to represent actual data composition in the underlying dataset. Some research proposed triangular and trapezoidal membership functions construction using readily formed Fuzzy Type-1 membership functions, which means it remains unclear how the membership functions are heuristically constructed using fuzzy C-Means outputs. The triangular and trapezoidal membership functions are important because previous works have shown that they may produce superior performance than Gaussian membership function in some applications. Therefore, this paper presents a structured literature review on generating triangular and trapezoidal Interval Fuzzy Type-2 membership functions using fuzzy C-Means. Initially, 110 related manuscripts were collected from Web of Science, Scopus, and Google Scholar. These manuscripts went through the identification, screening, eligibility, and inclusion processes, and as a result, 21 manuscripts were reviewed and discussed in this paper. To ensure that the review also covers the important components of fuzzy logic, this paper also reviews and discusses another 49 manuscripts on fuzzy calculation and operation. Furthermore, this paper also discusses the contributions of the conducted review to the body of knowledge, future research directions and challenges, with the aim to motivate the future works of constructing the methods to generate Interval Fuzzy Type-2 triangular and trapezoidal membership functions using fuzzy C-Means. The methods imply flexibility in choosing membership function type, hence increasing the effectiveness of fuzzy applications through leveraging the advantages that each of the three membership function types could provide.

Fuzzy C-Means (FCM) is one of the mostly used techniques for fuzzy clustering and proven to be robust and more efficient based on various applications. Image segmentation, stock market and web analytics are examples of popular applications which use FCM. One limitation of FCM is that it only produces Gaussian membership function (MF). The literature shows that different types of membership functions may perform better than other types based on the data used. This means that, by only having Gaussian membership function as an option, it limits the capability of fuzzy systems to produce accurate outcomes. Hence, this paper presents a method to generate another popular shape of MF, the trapezoidal shape (trapMF) from FCM to allow more flexibility to FCM in producing outputs. The construction of trapMF is using mathematical theory of Gaussian distributions, confidence interval and inflection points. The cluster centers or mean (μ) and standard deviation (σ) from the Gaussian output are fully used to determine four trapezoidal parameters; lower limit a, upper limit d, lower support limit b, and upper support limit c with the assistance of function trapmf() in Matlab fuzzy toolbox. The result shows that the mathematical theory of Gaussian distributions can be applied to generate trapMF from FCM.

No abstract

This paper focuses on the application of knowledge based systems for child performance analysis in an online Montessori module. Using knowledge based techniques, the system generates an automatic analysis based on the teacher's answers to a variety of questions about a child's performance of a specific Montessori activity. The questions were created through a study of the criteria used to assess the level of a child's performance and achievement. This prototype is designed as a proof-of-concept, to show how the knowledge base technique could be applied. To design the prototype, we conducted literature reviews on the delivery of Montessori methods and the knowledge base technique, and compared rule-based and case-based reasoning. We selected rule-based reasoning for the concept prototype since it is suitable for Montessori activities which are well defined and easy to acquire.