Informative value of the possibilistic extension principle

Abstract

The present fuzzy arithmetic is based on possibilistic extension-principle of Zadeh. Fuzzy arithmetic is necessary to accomplish calculation in Computing with Words [6]. However, arithmetic operations carried out with the standard, possibilistic extension-principle often yield results which have small or no practical value. Sometimes the results are paradoxical ones. An example of such case is presented in the paper and also a new cardinality extension-principle in a version that enables regard for all additional constraints resulting from the context of the problem to be solved. The principle can be used only to fuzzy sets of numbers of probabilistic character which often occur in practical problems.