New results about the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule
Information SciencesPublished 19 April 2006
Jerry M. Mendel, Hongwei Wu
Citations157
SJR quartileQ1
SJR score1.80
SNIP1.98
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
The centroid of an interval type-2 fuzzy set (IT2 FS) provides a measure of the uncertainty of such a FS. Its calculation is very widely used in interval type-2 fuzzy logic systems. In this paper, we present properties about the centroid of an IT2 FS. We also illustrate many of the general results for a T2 fuzzy granule (FG) in order to develop some understanding about the uncertainty of the FG in terms of its vertical and horizontal dimensions. At present, the T2 FG is the only IT2 FS for which it is possible to obtain closed-form formulas for the centroid, and those formulas are in this paper.
Keywords
Computer ScienceDecision Sciences
Fuzzy Sets and SystemsToward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic
2,875 Citations1997Lotfi A. Zadeh
M Modes of information granulation (IG) in which the granules are crisp (c-granular) play important roles in a wide variety of methods, approaches and techniques, but this does not reflect the fact that in almost all of human reasoning and concept formation thegranules are fuzzy (f- Granular).
IEEE Transactions on Fuzzy SystemsType-2 fuzzy sets made simple
2,533 Citations2002Jerry M. Mendel, Robert John
Establishing a small set of terms that let us easily communicate about type-2 fuzzy sets and also let us define such sets very precisely, and presenting a new representation for type- 2 fuzzy sets, and using this new representation to derive formulas for union, intersection and complement of type-1 fuzzy sets without having to use the Extension Principle.
IEEE Transactions on Fuzzy SystemsInterval type-2 fuzzy logic systems: theory and design
1,954 Citations2000Qi‐Lian Liang, Jerry M. Mendel
Uncertain Rule-Based Fuzzy Logic Systems: Introduction and New Directions
1,911 Citations2001Jerry M. Mendel
This chapter discusses Type-2 Fuzzy Sets, a New Direction for FLSs, and Relations and Compositions on different Product Spaces on Different Product Spaces, as well as operations on and Properties of Type-1 Non-Singleton Type- 2 FuzzY Sets.
IEEE Transactions on Fuzzy SystemsType-2 fuzzy logic systems
1,619 Citations1999N.N. Karnik, Jerry M. Mendel +1 more
A type-2 fuzzy logic system (FLS) is introduced, which can handle rule uncertainties and its implementation involves the operations of fuzzification, inference, and output processing, which consists of type reduction and defuzzification.
Information SciencesCentroid of a type-2 fuzzy set
1,197 Citations2001Nilesh N. Karnik, Jerry M. Mendel
The centroid and generalized centroid of a type-2 fuzzy set are introduced, and how to compute them is explained, and examples are given that compare the exact computational results with the approximate results.
IEEE Transactions on Fuzzy SystemsA Hierarchical Type-2 Fuzzy Logic Control Architecture for Autonomous Mobile Robots
1,007 Citations2004Hani Hagras
A novel reactive control architecture for autonomous mobile robots that is based ontype-2 FLC to implement the basic navigation behaviors and the coordination between these behaviors to produce a type-2 hierarchical FLC is presented.
Introduction to type-2 fuzzy logic systems
558 Citations2002N.N. Karnik, Jerry M. Mendel
A robust fuzzy logic system is introduced, one that can handle rule uncertainties and make use of type-2 fuzzy sets for this purpose, and a new operation that is called type-reduction is introduced.
IEEE Transactions on Fuzzy SystemsUncertainty bounds and their use in the design of interval type-2 fuzzy logic systems
500 Citations2002Hongwei Wu, Jerry M. Mendel
This work derives inner- and outer-bound sets for the type-reduced set of an interval type-2 fuzzy logic system (FLS), based on a new mathematical interpretation of the Karnik-Mendel iterative procedure for computing thetype-reducing set, and demonstrates that the resulting system can operate without type- Reduction and can achieve similar performance to one that uses type- reduction.
IEEE Transactions on Fuzzy SystemsEqualization of nonlinear time-varying channels using type-2 fuzzy adaptive filters
341 Citations2000Qi‐Lian Liang, Jerry M. Mendel
This filter is applied to equalization of a nonlinear time-varying channel and it is demonstrated that it can implement the Bayesian equalizer for such a channel, has a simple structure, and provides fast inference.
IEEE Transactions on Fuzzy SystemsType-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems
223 Citations2006Jerry M. Mendel, Hongwei Wu
The main purpose of this paper is to demonstrate that the intuition is correct and to quantify the centroid of a symmetric interval T2 FS, and consequently its uncertainty, with respect to such geometric properties, and to formulate and solve forward problems, i.e., to go from uncertainties to data with associated uncertainty bounds.
Granular Computing: An Emerging Paradigm
216 Citations2001Witold Pedrycz
This book discusses Granular Computing in Neural Networks, Fuzzy Clustering for Multiple-Model Approaches in System Identification and Control, and Induction of Rules about Complications with the Use of Rough Sets.
IEEE Transactions on Systems Man and Cybernetics Part C (Applications and Reviews)Connection admission control in ATM networks using survey-based type-2 fuzzy logic systems
207 Citations2000Jerry M. Mendel, N.N. Karnik +1 more
This paper presents a connection admission control (CAC) method that uses a type-2 fuzzy logic system (FLS) that can handle linguistic uncertainties and a methodology for representing the linguistic knowledge usingtype-2 membership functions and processing surveys using type-1 FLS.
Fuzzy Sets and SystemsFuzzy weighted average: An improved algorithm
157 Citations1992Tian‐Shy Liou, Mao‐Jiun J. Wang
A steepest descend/ascend method is proposed to facilitate steps (3) and (4) of the FWA to find the minimum/maximum of f(x1,x2,…,xn,w1,w2,….,wn) = Σi = 1n wixi/Σi=1n wi.
On the importance of interval sets in type-2 fuzzy logic systems
83 Citations2002Jerry M. Mendel
It is only for interval type-2 fuzzy sets that type- 2 FLSs are practical, and this paper explains why this is so.
IEEE Transactions on Circuits and Systems II Analog and Digital Signal ProcessingOvercoming time-varying co-channel interference using type-2 fuzzy adaptive filters
76 Citations2000Qilian Liang, Jerry M. Mendel
A method for overcoming time-varying co-channel interference (CCI) using type-2 fuzzy adaptive filters (FAF) and uses transversal equalizer and decision feedback equalizer structures to eliminate the CCI.
Computers & Electrical EngineeringFuzzy interval control of mobile robots
73 Citations1996Kung C. Wu
The FIC represents an adaptive FLC whose input-output relation is no longer deterministic and is designed for the applications in which limited or uncertain expert's experience is available and provides a practical implementation of a type 2 FLC to real applications.
Information SciencesOn a 50% savings in the computation of the centroid of a symmetrical interval type-2 fuzzy set
58 Citations2004Jerry M. Mendel
It is proved that if the footprint of uncertainty for an interval T2 FS is symmetrical about the primary variable y at y = m, then the centroid is also asymmetrical about y =m and its defuzzified value equals m.
Interval Type 2 Neuro-Fuzzy Systems Based on Interval Consequents
56 Citations2003Janusz T. Starczewski, Leszek Rutkowski
This paper presents a new neuro-fuzzy system of type 2 derived under the assumption that the rule antecedents are characterized by interval fuzzy membership grades and the consequents are intervals.
International Journal of Intelligent SystemsDesigning interval type-2 fuzzy logic systems using an SVD-QR method: Rule reduction
39 Citations2000Qilian Liang, Jerry M. Mendel
This paper presents a design method which can tremendously reduce rule number for interval type‐2 fuzzy logic systems using an SVD‐QR method, and demonstrates that tremendous rule number reduction ratio is achieved with very little performance degradation.
Centroid uncertainty bounds for interval type-2 fuzzy sets: forward and inverse problems
31 Citations2005Jerry M. Mendel, Hongwei Wu
The main purpose of this paper is to demonstrate that the intuition is correct and to quantify the centroid of an interval T2 FS with respect to these geometric properties of its FOU, which makes it possible to formulate and solve inverse problems, i.e., going from data to parametric T2FS models.
Studies in fuzziness and soft computingModeling MPEG VBR Video Traffic Using Type-2 Fuzzy Logic Systems
11 Citations2001Qilian Liang, Jerry M. Mendel
This chapter demonstrates that a type-2 fuzzy membership function, i.e., a Gaussian MF with uncertain variance, is most appropriate to model the log-value of I/P/B frame sizes in MPEG VBR video.