Generalized Extension Principle

Authors:
Hsien-Chung Wu
Affiliations:
Department of Mathematics, National Kaohsiung Normal University, Kaohsiung, Taiwan 802
Venue:
Fuzzy Optimization and Decision Making
Year:
2010

Citing 1
Cited 2

On generalization on Nguyen's theorem

Fuzzy Sets and Systems

Hahn-Banach extension theorems over the space of fuzzy elements

Fuzzy Optimization and Decision Making
Generalized representation theorem and its application to the construction of fuzzy sets: Existence and uniqueness

International Journal of Approximate Reasoning

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Abstract

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.