摘要：In this paper, we present two new methods for evaluating students’ answerscripts based on the similarity measure between vague sets. The vague marks awarded to the answers in the students’ answerscripts are represented by vague sets, where each element ui in the universe of discourse U belonging to a vague set is represented by a vague value. The grade of membership of ui in the vague set à is bounded by a subinterval [tÃ(ui), 1 – fà (ui)] of [0, 1]. It indicates that the exact grade of membership ìÃ(ui) of ui belonging the vague set à is bounded by tÃ(ui) ≤ ìÃ(ui) ≤ 1 – fÃ(ui), where tÃ(ui) is a lower bound of the grade of membership of ui derived from the evidence for ui, fÃ(ui) is a lower bound of the negation of ui derived from the evidence against ui, tÃ(ui) + fÃ(ui) ≤ 1, and ui U. An index of optimism ë determined by the evaluator is used to indicate the degree of optimism of the evaluator, where ë [0, 1]. Because the proposed methods use vague sets to evaluate students’ answerscripts rather than fuzzy sets, they can evaluate students’ answerscripts in a more flexible and more intelligent manner. Especially, they are particularly useful when the assessment involves subjective evaluation. The proposed methods can evaluate students’ answerscripts more stable than Biswas’s methods (1995).
关键词：Similarity functions, Students’ answerscripts, Vague grade sheets, Vague membership values, Vague sets, Index of optimism
