A Fast Inference and Type-Reduction Process for Constrained Interval Type-2 Fuzzy Systems

DrAlterio, Pasquale; Garibaldi, Jonathan M.; John, Robert; Wagner, Christian

doi:10.1109/tfuzz.2020.3018379

Cited by 7 publications

(2 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Although their algorithm obtains the centroid value approximately, it is significantly slower than the KM algorithm. Therefore, D'Alterio presented a new and faster type‐reduction procedure for finding the centroid of a Constrained IT2FS based on the concept of switch indices 41 …”

Section: Literature Reviewmentioning

confidence: 99%

“…Therefore, D'Alterio presented a new and faster type-reduction procedure for finding the centroid of a Constrained IT2FS based on the concept of switch indices. 41 T2FSs and IT2FSs have many real applications introduced in Doostparast Torshizi et al, 23 including control systems, health care, clustering, logic system, pattern classification, neural network, and decision making. Some type-reduction and defuzzification methods proposed for these fuzzy sets are more compatible for some applications.…”

Section: Defuzzificationmentioning

confidence: 99%

See 1 more Smart Citation

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

Arman

2022

Int J of Intelligent Sys

View full text Add to dashboard Cite

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.

show abstract

Section: Literature Reviewmentioning

confidence: 99%

Section: Defuzzificationmentioning

confidence: 99%

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

Arman

2022

Int J of Intelligent Sys

View full text Add to dashboard Cite

show abstract

Type-2 Fuzzy Sets Including Word Models

Mendel

2024

Explainable Uncertain Rule-Based Fuzzy Systems

View full text Add to dashboard Cite

T2RFIS: type-2 regression-based fuzzy inference system

Wiktorowicz

2023

Neural Comput & Applic

View full text Add to dashboard Cite

This article discusses a novel type-2 fuzzy inference system with multiple variables in which no fuzzy rules are explicitly defined. By using a rule-free system, we avoid the serious disadvantage of rule-based systems, which are burdened with the curse of dimensionality. In the proposed system, Gaussian membership functions are used for its inputs, and linearly parameterized system functions are used to obtain its output. To obtain the system parameters, a genetic algorithm with multi-objective function is applied. In the presented method, the genetic algorithm is combined with a feature selection method and a regularized ridge regression. The objective functions consist of a pair in which one function is defined as the number of active features and the other as the validation error for regression models or the accuracy for classification models. In this way, the models are selected from the Pareto front considering some compromise between their quality and simplification. Compared to the author’s previous work on the regression-based fuzzy inference system, a new inference scheme with type-2 fuzzy sets has been proposed, and the quality has been improved compared to the system based on type-1 fuzzy sets. Four experiments involving the approximation of a function, the prediction of fuel consumption, the classification of breast tissue, and the prediction of concrete compressive strength confirmed the efficacy of the presented method.

show abstract

A Fast Inference and Type-Reduction Process for Constrained Interval Type-2 Fuzzy Systems

Cited by 7 publications

References 21 publications

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

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

Type-2 Fuzzy Sets Including Word Models

T2RFIS: type-2 regression-based fuzzy inference system

Contact Info

Product

Resources

About