Label of a linguistic value in a universe of discourse and the truth values of fuzzy propositions

Due to objects described by a linguistic value with unsharp or fuzzy boundary, meaning of a linguistic value means different things to different people, the relation between the linguistic value and membership functions as its meaning is one-to-many rather than one-to-one. How to precisiate meaning of a linguistic value and even determine the truth values of fuzzy propositions remain open problems in computing with words (CW). In the paper, label of a linguistic value in its universe of discourse is proposed to formalize a possible position of objects described by the linguistic value, which is determined by a part of objects that can be and can not be described by the linguistic value via a group of users' commonsense knowledge. Then confidence degree of a membership function relative to a linguistic value is presented by measuring “the membership function is close to label of the linguistic value”, which can be used to precisiate meaning of a linguistic value and determine the truth values of fuzzy propositions. Finally, the truth value approximate reasoning of fuzzy propositions in the framework of the generalized modus ponens is provided and employed to evaluate the students' educational achievement. Comparative analysis with educational achievement based on Aliev's Z-interpolation approach and Zadeh's compositional rule of inference show that label of a linguistic value and confidence degree of a membership function relative to the linguistic value are effective and useful tools for CW.