Perfectly normal type-2 fuzzy interpolation B-spline curve

Abstract

In this paper, we proposed another new form of type-2 fuzzy data points(T2FDPs) that is perfectly normal type-2 data points(PNT2FDPs). These kinds of brand-new data were defined by using the existing type-2 fuzzy set theory(T2FST) and type-2 fuzzy number(T2FN) concept since we dealt with the problem of defining complex uncertainty data. Along with this restructuring, we included the fuzzification(alpha-cut operation), type-reduction and defuzzification processes against PNT2FDPs. In addition, we used interpolation B-soline curve function to demonstrate the PNT2FDPs.

On defining complex uncertainty data points by type-2 fuzzy number: two specials cases

“…For T2FDPs which has left and right footprint uncertainty, the membership function values are equal were called perfectly normal T2FDPs which has been discussed on the previous research paper [23]. In this case of T2FDPs, the illustration of the phenomenon on getting the crisp T2FDPs solution from T2FDPs are shown in Table 6.3.…”

“…are left-right, right and right-right T2FDPs respectively [23,24]. This can be illustrated as in Fig.…”

“…This Section 5 will discuss about the T2FDPs of footprint uncertainty definition were also known as perfectly normal T2FDPs which mentioned in [23]. Therefore, T2FDPs of footprint uncertainty definition can be given as the perfectly normal T2FDPs which involving the fuzzification, type-reduction and defuzzification process's definitions.…”

“…Therefore, T2FDPs of footprint uncertainty definition can be given as the perfectly normal T2FDPs which involving the fuzzification, type-reduction and defuzzification process's definitions. A a result, the definition of T2FDPs of footprint uncertainty can be referred to [23].…”

Fuzzy Interpolation Curve Modelling of Earthquake Magnitude Data

“…The research that combined fuzzy set theory and geometric modeling had many done due to the requirement of specifically on modeling and defining the uncertain problem IOP Publishing doi:10.1088/1755-1315/1103/1/012029 2 including uncertain data [8][9][10][11][12]. Those studies are none other rather than is intended to model the uncertainty data points which the existing function is unable to do so.…”