Generalized Extension Principle

The conventional extension principle was established on the Euclidean space and defined by considering the minimum or t-norm operator. The generalized extension principle proposed in this paper is established on the Hausdorff space and defined by considering an operator that is more general than the t-norm operator. On the other hand, based on the topological structure, we also discuss the properties of 0-level sets by considering the closure. Many interesting and useful equalities considering the 0-level sets will be obtained in this paper.