A Method of Calculating the Matrix of Attainment Order Relation in the Analysis of Fuzzy Item Relational Structure

Abstract

The process of teaching-learning is generally divided into three phases of planning, executino and evaluation.Evaluation is the phase at which the learners' attainment of the learning objective, the teacher's teaching plan and its execution and others are evaluated. This phase requires a method mainly of analyzing the attainment order of test items on the basis of the learners' response patterns in the test items.So far we have developed the FIRS(Fuzzy Item Relational Structure) analysis by which the learning traits of respective learners and groups, as well as the common trait of the whole class, can be analyzed, with the data on the marks obtained in the test items having a value of [0,1]. In the present paper we give a short description of the FIRS analysis and then discuss in detail Procedure 2 in which a matrix of the learners' attainment order is calculated on the set of test items. Since the results obtained in the procedure may have a significant effect on later analysis, we devote an extended discussion to what influence the selection of a main membership function used to calculate the attainment order relation may have on the decision of the attainment order relation.