International Journal of Scientific & Engineering Research, Volume 4, Issue 6, June-2013 1525 ISSN 2229-5518 IJSER © 2013 http://www.ijser.org A Novel Method to Find the Optimism Index of Examiner in Students’ Evaluation Shilpa Ingoley, Jagdish Bakal Abstract— This paper presents a novel method to find out the optimism index of the examiner. Optimism index gives us the idea about the type of examiner. Optimism index is used by some authors Wang and Chen (2008, 2009) in evaluating student answersheet using fuzzy numbers. There are different types of examiners such as lenient, strict and normal. These examiners may be strict or lenient but their degree of strictness and leniency will be different. This paper proposed a method to find the optimism index of examiner which can be helpful in evaluating students’ answersheets more accurately. It makes use of fuzzy logic to do so. Index Terms— Fuzzy Logic, Fuzzy Set, Fuzzy Inference System (FIS), Optimism Index, Student’s Evaluation, Fuzzification, Defuzzification. ——————————  —————————— 1 INTRODUCTION N recent years, many researchers have started using fuzzy logic, fuzzy sets, fuzzy inference system (FIS), fuzzy logic controller (FLC) in educational grading and evaluation sys- tems. Biswas [2] highlighted the importance of evaluation in education system. He used fuzzy set theory in student evalua- tion and is finer than awarding grades or numbers when eval- uating answerscipts. The method presented by him are fem and generalized fem. Chen and Lee[3] extended Biswas’s work and presented methods which removes drawbacks of his’ methods. Their methods do not transfer the different fuzzy marks into same letter grade and perform calculations in much faster manner and don’t require complicated matching operations. Bai and Chen [16] uses fuzzy grading system which utilizes students’ and instructor’s performance measures in order to modify a set of collectively approved, a priori fuzzy grades, so as to produce a “fair” mark distribu- tion. James Nolan [7] applied FL in an expert classification system for supporting the grading of student writing samples. Later on [9] proposed method for evaluating student answer- scripts using fuzzy numbers associated with degree of confi- dence. They have considered degree of confidence of evaluator when awarding satisfaction level to questions of student an- swerscripts. Bai and Chen [15] proposed a method for auto- matically constructing grade membership functions of lenient- type grade, strict-type grade and normal-type grades given by teachers for students’ evaluation. [1] Proposed a method for automatically generating the weights for several attributes with fuzzy reasoning capability. Fuzzy synthetic decision method through composite operations, in evaluating student’s academic achievement for high school students is used by [19], in Taiwan. Combined effect of difficulty, complexity, im- portance on students’ answersheet is considered by [4] and evaluation is done by using FIS. Concept of vagueness of ques- tion paper is introduced by [12]. Model of students’ evalution system is given in [20], their design shows the recommended flow of students’ evaluation system. In [21] used two- node structure in students’ evaluation without considering “time” factor. Wang and Chen have proposed fuzzy evaluation methods with degree of confidence of evaluator along with satisfaction level of examiners [9] and interval-value grade methods [17]. Experimental result shows that their proposed methods are more stable and flexible than Biswas’s [2] and Chen and Lee’s [3] methods used in evaluating students answersheets using fuzzy numbers. Method proposed by Wang and Chen using fuzzy satisfac- tion levels in [9] and [17] respectively, has drawback– how to find the optimism index of examiner is not specified. As per them in [9] and [17], an index of optimism λ determined by the evaluator is used to indicate the degree of optimism of evaluator, where λ ϵ [0, 1]. That indicates the examiner will decide the value of index of optimism. We emphasize that it will be very much subjective decision because one may think that he/she may be very strict, but actually examiner may be less or much more strict than what he/she thinks. Examiner may be considering him/her as lenient but actually may be- long to normal category. As per particular examiner he may be strict with optimism index value λ = 0.4 but actually he can be very strict with value of optimism index λ = 0.3 or λ = 0.2. Lenient examiner will consider that his/her optimism index is λ = 0.6 but actually that examiner may be very lenient with optimism index λ = 0.8 and vice a versa. This paper proposed a new method in determining the val- ues of optimism index. It makes uses of fuzzy logic to solve the above problem. The rest of paper is organized as follows. In section 2, we briefly review Wang and Chen method of students’ evaluation using fuzzy numbers associated with degree of confidence from [9]. In Section 3, we present a new method to find out index of optimism of evaluator which is required for methods proposed in [9] and [17]. Experimental results are shown in section 4. The conclusions are discussed in section 5. 2 A REVIEW OF WANG AND CHEN METHOD In this section, we briefly reviews the Wang and Chen’s meth- od for students answersheets evaluation using fuzzy numbers associated with degree of confidence from [9]. For fuzzy as- sessment they have used triangular membership functions and nine satisfaction levels. Nine satisfaction levels are used to I