Credibility of a Membership Function Related to a Linguistic Value to Improve Computing With Words

The relation between a linguistic value and its meaning is one-to-many rather than one-to-one. How to precisiate meaning of a linguistic value and even fuzzy linguistic propositions or rules remain open problems in computing with words (CW). In this article, according to a linguistic value describes a class of objects with unsharp or fuzzy boundary, label of the linguistic value in its universe of discourse is proposed to formalize a possible position of objects described by the linguistic value via a group of subjects' commonsense cognition. Then, credibility of a membership function related to a linguistic value is presented by measuring “objects in its support are close to label of the linguistic value,” which can be used to determine whether the membership function can be regarded as representation of meaning of the linguistic value. By combining credibility of a membership function related to a linguistic value with overlap indices between two membership functions, an alternative method is provided to precisiate meaning of a linguistic value and deduce fuzzy truth values of meaning rules of fuzzy If–Then linguistic rules, all of these can be exploited to improve test-score semantics of
CW
. Finally, a case in designing fuzzy linguistic estimator is employed to show useful and effective improvement of
CW
.