International Journal of Applied Engineering and Technology, cilt.4, sa.3, ss.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.