Modelling and analysis of an interval type-2 Mamdani fuzzy PID controller

Praharaj, Manoranjan; Sain, Debdoot; Mohan, B.M.

doi:10.1016/j.ifacol.2022.04.119

Cited by 1 publication

(3 citation statements)

References 17 publications

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“…Other extensions to IT2FS can also be improved in the future by using the ICOG method as their defuzzification method. For example, future studies can improve the IT2 fractional fuzzy inference systems, 44 the IT2 fuzzy controllers that use nonuniformly distributed fuzzy sets, 45 and the IT2 fuzzy inference systems that attempt to optimize the system parameters. [48][49][50][51][52] The T2FSs and their extensions, like, the Constraint T2FSs, better model the uncertainty than the T1FSs.…”

Section: Discussionmentioning

confidence: 99%

“…For example, the IT2 fractional fuzzy inference systems introduced in Mazandarani and Xiu 44 use the EKM algorithm for type reducing and the average method for defuzzifying IT2 fractional fuzzy sets. An IT2 fuzzy controller formed based on nonuniformly distributed fuzzy sets uses the center of sets type‐reducer and average defuzzifier 45 . A fuzzy control method proposed for the IT2 Takagi–Sugeno fuzzy interconnected systems uses a weighted average defuzzifier 46 .…”

Section: Literature Reviewmentioning

confidence: 99%

“…An IT2 fuzzy controller formed based on nonuniformly distributed fuzzy sets uses the center of sets type-reducer and average defuzzifier. 45 A fuzzy control method proposed for the IT2 Takagi-Sugeno fuzzy interconnected systems uses a weighted average defuzzifier. 46 In Tabakov et al, 47 a classification procedure related to Mamdani type fuzzy inference is introduced that uses the center-of-set type reducer using the KM algorithm.…”

Section: Defuzzificationmentioning

confidence: 99%

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A simple noniterative method to accurately calculate the centroid of an interval type‐2 fuzzy set

Arman

2022

Int J of Intelligent Sys

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An interval type‐2 fuzzy set (IT2FS) contains the infinite number of embedded membership functions (MFs) defined as type‐1 fuzzy sets. The center of gravity (COG) of an IT2FS is obtained by integrating the centroids of all these MFs. However, obtaining the COG of an IT2FS in a continuous domain is impossible because the number of embedded MFs is infinite and, in a discrete domain, comes with exponential time complexity. Therefore, different algorithms were proposed to find the center of centroids (COCs) instead of the COG. These algorithms do not necessarily obtain the exact value of COC; they compete to find a more accurate result in less time. In this study, we propose a simple noniterative method to obtain the COG of IT2FSs. This method only considers the MFs which form the boundary values, that is, the lower MF (LMF) and upper MF (UMF), and obtains their centroids separately. We show that the COG of an IT2FS is equal to the weighted sum of the centroids of its LMF and UMF if the relative areas of LMF and UMF are considered their corresponding weights. We call this method the Indirect COG (ICOG) method because it indirectly obtains the COG of an IT2FS. This method finds the accurate COG of an IT2FS by considering only two MFs instead of infinite MFs. It can also obtain the accurate COG of an uncommon polygonal IT2FS schematically. We use numerical examples to illustrate that the ICOG obtains the accurate COG of an IT2FS very fast in a nonexponential time. We also develop a new triangular interval type‐2 fuzzy analytical hierarchy process that uses the ICOG method to accurately defuzzify the IT2 fuzzy weights.

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