EXTENDING SET FUNCTIONS AND RELATIONS

Abstract

Zadeh's extension principle is applicable to functions defined upon elements of a set. A new extension principle is developed for functions defined upon power sets. Another extension is proposed for relations between sets, such as subsethood. A formal relation connects the two new extension principles. The new extension principles are not a consequences of Zadeh's original.

INDEX TERMS:

• Fuzzy sets
• extension principle
• cutworthy

Notes

Mark Wierman is an Assistant Professor of Computer Science at Creighton University in Omaha, Nebraska. Dr. Wierman received his Ph.D. in Systems Science from Binghainton University. He also has a B.S. in mathematics from SUC at Purchase. He has worked in both government and industrial research. Dr. Wierman's research interests include systems modeling, genetic algorithms, fuzzy set theory, and optimization techniques. He is a member of the IEEE and NAFIPS.

Additional information

Notes on contributors

MARK J. WIERMAN

E-mail: [email protected].