REPRESENTATION THEOREM FOR FUZZY FUNCTIONS Graded Form

摘要

In this contribution, we will extend results relating to representability of a fuzzy function using a crisp function. And additionally, we show for which functions there exist fuzzy function of a specific form. Our notion of fuzzy function has a graded character. More precisely, any fuzzy relation has a property of being a fuzzy function that is expressed by a truth degree. And it consists of two natural properties: extensionality and functionality. We will also provide a separate study of these two properties.