An efficient algorithm for fuzzy weighted average
Fuzzy Sets and Systems
Centroid of a type-2 fuzzy set
Information Sciences: an International Journal
Numerical Methods Using MATLAB
Numerical Methods Using MATLAB
Fuzzy weighted averages revisited
Fuzzy Sets and Systems - Information processing
Computing with words and its relationships with fuzzistics
Information Sciences: an International Journal
Uncertainty measures for interval type-2 fuzzy sets
Information Sciences: an International Journal
An efficient centroid type-reduction strategy for general type-2 fuzzy logic system
Information Sciences: an International Journal
Information Sciences: an International Journal
Enhanced Karnik-Mendel algorithms
IEEE Transactions on Fuzzy Systems
α-plane representation for type-2 fuzzy sets: theory and applications
IEEE Transactions on Fuzzy Systems
Perceptual reasoning for perceptual computing: a similarity-based approach
IEEE Transactions on Fuzzy Systems
Computing with words for hierarchical decision making applied to evaluating a weapon system
IEEE Transactions on Fuzzy Systems - Special section on computing with words
Perceptual Computing: Aiding People in Making Subjective Judgments
Perceptual Computing: Aiding People in Making Subjective Judgments
Toward general type-2 fuzzy logic systems based on zSlices
IEEE Transactions on Fuzzy Systems
Uncertainty measures for general Type-2 fuzzy sets
Information Sciences: an International Journal
Type-2 Fuzzy Logic: A Historical View
IEEE Computational Intelligence Magazine
Dynamical optimal training for interval type-2 fuzzy neural network (T2FNN)
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
IEEE Transactions on Fuzzy Systems
Computing derivatives in interval type-2 fuzzy logic systems
IEEE Transactions on Fuzzy Systems
A Comparison of Discrete Algorithms for Fuzzy Weighted Average
IEEE Transactions on Fuzzy Systems
Type-2 Fuzzistics for Symmetric Interval Type-2 Fuzzy Sets: Part 1, Forward Problems
IEEE Transactions on Fuzzy Systems
IEEE Transactions on Fuzzy Systems
Aggregation Using the Linguistic Weighted Average and Interval Type-2 Fuzzy Sets
IEEE Transactions on Fuzzy Systems
Aggregation Using the Fuzzy Weighted Average as Computed by the Karnik–Mendel Algorithms
IEEE Transactions on Fuzzy Systems
A closed form type reduction method for piecewise linear interval type-2 fuzzy sets
International Journal of Approximate Reasoning
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Computing the centroid of an interval type-2 fuzzy set is an important operation in a type-2 fuzzy logic system, and is usually implemented by Karnik-Mendel (KM) iterative algorithms. By connecting KM algorithms and continuous KM algorithms together, this paper gives theoretical explanations on the initialization methods of KM and Enhanced Karnik-Mendel (EKM) algorithms, proposes exact methods for centroid computation of an interval type-2 fuzzy set, and extends the Enhanced Karnik-Mendel (EKM) algorithms to three different forms of weighted EKM (WEKM) algorithms. It shows that EKM algorithms become a special case of the WEKM algorithms when the weights of the latter are constant value. It also shows that, in general, the weighted EKM algorithms have smaller absolute error and faster convergence speed than the EKM algorithms which make them very attractive for real-time applications of fuzzy logic system. Four numerical examples are used to illustrate and analyze the performance of WEKM algorithms.