Uncertainty Avoider Interval Type II Defuzzification Method

Sadegh Aminifar

doi:10.1155/2020/5812163

Abstract

One of the IT2FS (interval type-2 fuzzy system) defuzzification methods uses the iterative KM algorithm. Because of the iterative nature of KM-type reduction, it may be a computational bottleneck for the real-time applications of IT2FSs. There are several other interval type-2 defuzzification methods suffering from lack of meaningful relationship between membership function uncertainties and changing of system output due to lack of clearly defined variables related to uncertainty in their methods. In this paper, a new approach for IT2FS defuzzification is presented by reconfiguring interval type-2 fuzzy sets and how uncertainties are present in them. This closed-formula method provides meaningful relation between the presence of uncertainty and its effect on system output. This study investigates uncertainty avoidance that the output of IT2FS obtained by centroid or bisection methods in comparison with type-1 fuzzy system (T1FLS) moves to points with less uncertainty. Uncertainty can enter into T1FSs and affect system response. Finally, for proving the affectivity of the proposed defuzzification method and uncertainty avoidance, several investigations are done and a prototype two-input one-output IT2FS MATLAB code is enclosed.

Highlights

In recent years, there has been an increasing trend of using type-II fuzzy systems (T2FSs) in engineering works
If all intervals are determined to their corresponding decisive point, a membership function appeared that it is called decisive membership function (DMF)
Investigations. ese numerical investigations intend to show a comparative behaviour of the proposed defuzzification method

Summary

Introduction

There has been an increasing trend of using type-II fuzzy systems (T2FSs) in engineering works. To reduce the computational complexity of KM algorithms, Wu and Mendel [4] extended the IT2FS uncertainty bounds to estimate TR. E results showed that this method is considerably faster than the KM algorithm for the symmetric footprint of uncertainty (FOU) and for producing similar results. This method is yet to use as an algorithm and there is no hardware proof of its performance. E complexity of defuzzification calculations in general T2FSs is more than IT2FSs. A method is presented in [21] for reduction of complexity cost in general T2FS based on parametrized shadowed type-II membership functions. Ontiveros-Robles et al [22, 23] worked on decreasing the computational cost of general T2FS defuzzification. e extension of uncertainty avoider method to the general typeII fuzzy systems is found in [24]

Methodology

Proposed Defuzzifier and Its Property

Findings

Investigations and Discussion