A new fuzzy criterion-referenced assessment with a fuzzy rule selection technique and a monotonicity-preserving similarity reasoning scheme

Abstract

The use of a Fuzzy Inference System (FIS) as a part of Criterion-referenced Assessment (CRA) is not new. Nevertheless, there are several limitations in combining FIS models and CRA, as follows. (i) It is difficult to maintain the monotonicity property of the FIS-based CRA model; (ii) it is difficult and impractical to form a complete fuzzy rule base when the number of required rules is large, and (iii) reducing fuzzy rules may cause the “tomato classification” problem. In this paper, a practical solution to overcome these limitations is provided. We adopt the sufficient conditions (i.e., a mathematical foundation) as a set of governing equations for designing fuzzy membership functions and fuzzy rules to preserve the monotonicity property. In this paper, our works in [21] is extended and a new procedure that comprises of the sufficient conditions, fuzzy rule reduction and a monotonicity-preserving similarity reasoning (SR) is proposed. The new framework reduces the number of fuzzy rules gathered from an assessor (i.e., selected rules) with a proposed fuzzy rule selection approach. Selected rules are identified in such that the unselected rules can be deduced via a monotonicity-preserving SR technique. We formulate the process of minimizing the number of selected rules as a constrained optimization problem and a genetic algorithm (GA) technique is implemented. Unselected rules are predicted with a proposed monotonicity-preserving SR scheme. The proposed approach contributes to a solution to reduce the number of fuzzy rules to be gathered from an assessor while maintaining the monotonicity property. Besides, this paper also contributes to a new application of SR in education assessment. The proposed approach is evaluated with a case study relating to a lab assessment in Universiti Malaysia Sarawak (UNIMAS).