Congratulations to Professor Haitao Zhang, who co-authored the IEEE Transactions on Fuzzy Systems paper "A Constrained Representation Theorem for well-shaped IntervalType 2 Fuzzy Sets, and the Corresponding Constrained Uncertainty Measures" was selected as the 2019 IEEE CIS (Society for Computational Intelligence) highlight papers (a total of 8 papers from around the world,2 papers in TFuzzy field).
Proposing a constraint representation theorem (CRT) for IT2 FSS with regular shape in this paper, using only convex hull and conventional embedded T1 FSS. It is shown that IT2 FSS generated by three literal encoding methods and four word computing engines are all IT2 FSS with regular shape.Five constrained uncertainty parameters (centroid, cardinality, ambiguity, variance and skewness) for regular shape are also calculated using CRT.The proposed CRT and its associated constrained uncertain parameters have application value in word calculation, design of IT2 fuzzy logic systems using the uncertainty principle, and measurement of similarity between two well-shaped IT2 FSS.
The full paper links：https://ieeexplore.ieee.org/abstract/document/8481422
About the paper:
A Constrained Representation Theorem for Well-Shaped Interval Type-2 Fuzzy Sets, and the Corresponding Constrained Uncertainty Measures
Abstract—The representation theorem for interval type-2 fuzzy sets (IT2 FSs), proposed by Mendel and John, states that an IT2 FS is a combination of all its embedded type-1 (T1) FSs, which can be nonconvex and/or subnormal. These nonconvex and/or subnormal embedded T1 FSs are included in developing many theoretical results for IT2 FSs, including uncertainty measures, the linguistic weighted averages (LWAs), the ordered LWAs (OLWAs), the linguistic weighted power means (LWPMs), etc. However, convex and normal T1 FSs are used in most fuzzy logic applications, particularly computing with words. In this paper,we propose a constrained representation theorem (CRT) for well-shaped IT2 FSs using only its convex and normal embedded T1 FSs, and show that IT2 FSs generated from three word encoding approaches and four computing with words engines (LWAs, OLWAs, LWPMs, and perceptual reasoning) are all well-shaped IT2 FSs. We also compute five constrained uncertaintymeasures (centroid, cardinality, fuzziness, variance, and skewness) for well-shaped IT2 FSs using the CRT. The CRT and the associated constrained uncertaintymeasures can be useful in computing with words, IT2 fuzzy logic system design using the principlesof uncertainty, and measuring the similarity between two well-shaped IT2 FSs.
