Sine-square Embedded Fuzzy Sets

Abstract

Type-2 fuzzy sets minimize the effects of uncertainties that cannot be modeled using type-l fuzzy sets. However, the computational complexity of the type-2 fuzzy sets is very large and it is more difficult to use and understand than are type-l fuzzy sets. This paper proposes sine-square embedded fuzzy sets and gives a comparison with type-2 and nonstationary fuzzy sets. The sine-square embedded fuzzy sets consist of type-l fuzzy sets and sine function. The footprint of uncertainty in the type-2 fuzzy sets is provided with amplitude and frequency of sine-square function in the proposed algorithm. The proposed sine-square embedded fuzzy sets are very simpler than the type-2 fuzzy sets and the nonstationary fuzzy sets. Finally, the simulation results are carried out to demonstrate the effectiveness of the proposed fuzzy sets.