A SEMANTIC BASE FOR THE FUZZY EXTENSION-PRINCIPLE

A distance-semantic is attached to fuzzy acceptabilities. Within the f rame of this semantic, a modified version of the extension principle p roves to be obligatory. It is derived without referring to fuzzy logic and coincides only under certain assumptions with the usual version o f the extension principle. Over that, it is shown under not very restr icting assumptions that membership-functions which are compatible with the above semantic have to be automatically of that triangle- or trap ezoid type which is so popular in fuzzy applications.