Enhancing Fuzzy Inference System-Based Criterion-Referenced Assessment with a Similarity Reasoning Technique

Introduction

Education assessment is an important yet complicated task for assessors (lecturers, teachers, tutors, evaluators or etc) as it would influence students in their learning process outcomes directly (Ma & Zhou, 2000). Assessments in higher education can be conducted by using a criterion-referenced assessment (CRA) approach. It determines students’ grades by comparing their achievements with a clearly stated criterion for learning outcomes and the standards for particular levels of performance are also clearly stated. It can be a simple pass-fail grading schema, a series of key criteria rather than as a single grade or percentage (Sadler, 2005). For CRA, there is a possibility for all students within a particular group to get high or low grades depending on the individual’s performance against the established criteria and standards. Another popular education assessment approach, Norm-referenced assessment (NRA) ranks each student with respect to the achievement of others in broad areas of knowledge and discriminates between high and low achievers (Popham, 1975).

Scoring rubric is a descriptive scoring instrument developed by assessors to guide the analysis of the products or processes of students’ efforts (Brookhart, 1999). There are two types of scoring rubrics, i.e., holistic rubric and analytic rubric. A holistic rubric requires the assessor to give score to the overall process or product as a whole, without judging the component parts separately (Nitko, 2001). On the other hand, an analytic rubric requires the assessor to give a score to each part of the product or performance, and a total-score is obtained by adding the scores. (Moskal 2000; Nitko, 2001). In this chapter, the focus is on CRA with holistic scoring rubrics.

With regards to fuzzy inference system (FIS), it is also known as fuzzy rule-based system, or fuzzy if-then model. An FIS can be viewed as a method where a multi-input model can be constructed in an easy manner (Jang, Sun, & Mizutani, 1997). One of the success key factors is its ability to incorporate human/expert knowledge where information is described using vague and imprecise statements. Furthermore, the behavior of an FIS is also expressed in a language that can be easily interpreted by humans. FIS is widely applied in many application domains, for example, it has been applied to calculate the resonant frequencies of rectangular microstrip antenna (MSAs) with thin and thick substrates (Guney & Sarikaya, 2009). Besides that, it has been applied to failure mode and effect analysis (FMEA) methodology, i.e., fuzzy FMEA methodology (Tay & Lim, 2006, 2008a, 2008b, 2010).

Recent advances in FIS modeling mainly focus on the use of Similarity Reasoning (SR) as a solution to the incomplete rule base. Two typical SR schemes are Analogical Reasoning (AR) (Turksen, & Zhong, 1988) and Fuzzy Rule Interpolation (FRI) (Kóczy & Hirota, 1997). Obtaining a complete rule base is sometimes infeasible, especially for multi-input FIS models, owing to the large number of rules required (Kóczy & Hirota, 1997). A fuzzy rule consists of an antecedent and a consequent. For an incomplete rule base, some consequents are unknown or missing. A conventional FIS model assumes that the unknown consequents are zero (Hsiao, Chen, & Lee, 1998). This assumption may not always be true or appropriate; and this is the so-called “tomato classification problem” (Hsiao, Chen & Lee, 1998).

SR is explained as a type of qualitative reasoning for an FIS model by Zadeh (1989). An example adopted from Zadeh (1989) is as follows:

Therefore, if pressure is medium, then volume iswhere