Computing with words and its relationships with fuzzistics
Information Sciences: an International Journal
New geometric inference techniques for type-2 fuzzy sets
International Journal of Approximate Reasoning
Information Sciences: an International Journal
Information Sciences: an International Journal
α-plane representation for type-2 fuzzy sets: theory and applications
IEEE Transactions on Fuzzy Systems
A spatio-temporal fuzzy logic system for process control
SMC'09 Proceedings of the 2009 IEEE international conference on Systems, Man and Cybernetics
Overview of Type-2 Fuzzy Logic Systems
International Journal of Fuzzy System Applications
On type-2 fuzzy sets and their t-norm operations
Information Sciences: an International Journal
Uncertainty degree and modeling of interval type-2 fuzzy sets: Definition, method and application
Computers & Mathematics with Applications
On type-2 fuzzy relations and interval-valued type-2 fuzzy sets
Fuzzy Sets and Systems
Channel equalization using quasi type-2 fuzzy strategies
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Interval type-2 fuzzy sets (IT2 FS) play a central role in fuzzy sets as models for words and in engineering applications of T2 FSs. These fuzzy sets are characterized by their footprints of uncertainty (FOU), which in turn are characterized by their boundaries-upper and lower membership functions (MF). The centroid of an IT2 FS, which is an IT1 FS, provides a measure of the uncertainty in the IT2 FS. The main purpose of this paper is to quantify the centroid of a non-symmetric IT2 FS with respect to geometric properties of its FOU. This is very important because interval data collected from subjects about words suggests that the FOUs of most words are non-symmetrical. Using the results in this paper, it is possible to formulate and solve forward problems, i.e., to go from parametric non-symmetric IT2 FS models to data with associated uncertainty bounds. We provide some solutions to such problems for non-symmetrical triangular, trapezoidal, Gaussian and shoulder FOUs.