Linguistic Hedge Based Constrained Representation of Interval Type-2 Fuzzy Sets

Karadeniz S., Ulu C.

International Journal of Applied Engineering and Technology, vol.4, no.3, pp.11-19, 2022 (Scopus)


In general representation, a type-2 fuzzy set is defined as being composed of all its embedded type-1 fuzzy sets (ET1-FSs) which can be non-convex, subnormal, and/or discontinuous. However, interval type-2 fuzzy sets (IT2-FSs) are constructed by blurring a baseline type-1 membership function form in many applications, and thus, uncertainties are actually modeled by using only ET1-FSs which preserve the similar meaningful functional form. Therefore, the derived results can be too generic in such cases when all ET1-FSs are included in type-2 fuzzy computations. In this study, a new constrained representation of IT2-FSs is proposed for the above mentioned formation. In this representation, IT2-FSs are defined as being composed of only convex, normal and continuous ET1-FSs by using linguistic hedges. This constrained representation provides ease of computation and more precise results in interval type-2 fuzzy computations. The proposed constrained representation is applied to the centroid computation which is the most important uncertainty measure of IT2-FSs and also an important task in interval type-2 fuzzy logic systems (IT2-FLSs). It is shown that the centroid of the proposed constrained IT2- FS is calculated in closed form without the need of any iterative algorithm. In this way, the computational burden of the centroid type reduction process is removed. The effectiveness of the proposed constrained representation is shown through an illustrative example.