Computing with words and its relationships with fuzzistics
Information Sciences: an International Journal
A vector similarity measure for linguistic approximation: Interval type-2 and type-1 fuzzy sets
Information Sciences: an International Journal
Reduced-set vector-based interval type-2 fuzzy neural network
WSEAS Transactions on Computers
Information Sciences: an International Journal
Information Sciences: an International Journal
Reduced-set vector learning based on hybrid kernels for interval type 2 fuzzy modeling
ICS'08 Proceedings of the 12th WSEAS international conference on Systems
IEEE Transactions on Fuzzy Systems
Fuzzy filter based on interval-valued fuzzy sets for image filtering
Fuzzy Sets and Systems
Computing with words in decision making: foundations, trends and prospects
Fuzzy Optimization and Decision Making
IEEE Transactions on Fuzzy Systems
Color image segmentation based on type-2 fuzzy sets and region merging
ACIVS'07 Proceedings of the 9th international conference on Advanced concepts for intelligent vision systems
Comparative study of type-2 fuzzy sets and cloud model
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Study on enhanced Karnik-Mendel algorithms: Initialization explanations and computation improvements
Information Sciences: an International Journal
Journal of Mathematical Imaging and Vision
On interval type-2 rough fuzzy sets
Knowledge-Based Systems
On characterization of generalized interval type-2 fuzzy rough sets
Information Sciences: an International Journal
Overview of Type-2 Fuzzy Logic Systems
International Journal of Fuzzy System Applications
A closed form type reduction method for piecewise linear interval type-2 fuzzy sets
International Journal of Approximate Reasoning
On type-2 fuzzy sets and their t-norm operations
Information Sciences: an International Journal
Fixed charge transportation problem with type-2 fuzzy variables
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
Some proportional 2-tuple geometric aggregation operators for linguistic decision making
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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Interval type-2 fuzzy sets (T2 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). In this two-part paper, we focus on symmetric interval T2 FSs for which the centroid (which is an interval type-1 FS) provides a measure of its uncertainty. Intuitively, we anticipate that geometric properties about the FOU, such as its area and the center of gravities (centroids) of its upper and lower MFs, will be associated with the amount of uncertainty in such a T2 FS. The main purpose of this paper (Part 1) is to demonstrate that our intuition is correct and to quantify the centroid of a symmetric interval T2 FS, and consequently its uncertainty, with respect to such geometric properties. It is then possible, for the first time, to formulate and solve forward problems, i.e., to go from parametric interval T2 FS models to data with associated uncertainty bounds. We provide some solutions to such problems. These solutions are used in Part 2 to solve some inverse problems, i.e., to go from uncertain data to parametric interval T2 FS models (T2 fuzzistics)