A Novel Approach to Generate Type-1 Fuzzy Triangular and Trapezoidal Membership Functions to Improve the Classification Accuracy

Muhammad Hamza Azam,Said Jadid Abdulkadir,Saima Hassan,Mohd Hilmi Hasan

doi:10.3390/sym13101932

Muhammad Hamza Azam, Said Jadid Abdulkadir + Show 2 more

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https://doi.org/10.3390/sym13101932

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Abstract

Fuzzy logic is an approach that reflects human thinking and decision making by handling uncertainty and vagueness using fuzzy membership functions. When a human is engaged in the design of a fuzzy system, symmetric properties are naturally preferred. Fuzzy c-means clustering is a clustering algorithm that can cluster datasets to produce membership matrix and cluster centers, which results in generating type-1 fuzzy membership functions. However, fuzzy c-means algorithm has a limitation of producing only a single membership function type, Gaussian MF. Generation of multiple fuzzy membership functions is of immense importance as it provides more efficient and optimal solutions to a problem. Therefore, an approach to generate multiple type-1 fuzzy membership functions through fuzzy c-means is required for the optimal and improved results of classification datasets. Hence, to overcome the limitation of the fuzzy c-means algorithm, an approach for the generation of type-1 fuzzy triangular and trapezoidal membership function through fuzzy c-means is considered in this study. The approach is used to calculate and enhance the accuracy of classification datasets called iris, banknote authentication, blood transfusion, and Haberman’s survival. The proposed approach of generating MFs using FCM produce asymmetric MFs, whose results are compared with the MFs produced from grid partitioning (GP), which are symmetric MFs. The results show that the proposed approach of generating type-1 fuzzy membership function through fuzzy c-means is effective and can be adopted.

Highlights

The objective of this paper is to describe the generation of type-1 fuzzy triangular and trapezoidal membership function (MF) using Fuzzy C-Means (FCM) and to present a comparative analysis to prove the accuracy of the proposed approach
A type-1 fuzzy set (T1FS) F can be described as follows; assuming X is the universe with collections of x objects, a fuzzy set F is defined as the following: F = (x, μF (x))|x ∈ X, μF (x) ∈ [0, 1]
FIS based on proposed type-1 fuzzy triangular and trapezoidal MFs as well as FCM-based Gaussian and grid partitioning (GP)-based triangular and Gaussian MFs were developed and tested against the test dataset, and the classification accuracy was calculated for each fold

Summary

Introduction

A type-1 fuzzy set (T1FS) F can be described as follows; assuming X is the universe with collections of x objects, a fuzzy set F is defined as the following:. The notation μF(x) in Equation (1) is a MF, which contains the membership degree of each element in X. The value of membership degree is within the range of 0 and 1. A T1FLS theory is used to map crisp input into outputs in a type-1 fuzzy logic system (T1FLS). A T1FLS contains four key functions called fuzzifier, fuzzy rule base, fuzzy inference engine and defuzzifier.

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