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Modelling on Lecturers‟ Performance with Hotteling-Harmonic-Fuzzy

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Modelling on Lecturers‟ Performance with Hotteling-Harmonic-Fuzzy Proceedings of ”The 6th SEAMS-UGM Conference 2011” Topic, pp. xx–xx. Modelling On Lecturers‟ Performance with Hotteling-Harmonic-Fuzzy 1ST H.A PARHUSIP, 2ND A. SETIAWAN Abstract. This paper is a brief research on modelling of lecturers' performance with modified Hotelling- Fuzzy. The observation data is considered to be as a fuzzy set which is obtained from students survey at Mathematics Department of Science Mathematics Faculty in SWCU in the year 2008-2009. The modified Hotelling relies on a harmonic mean instead of an arithmetic mean which is normally used in a literature. The used charaterization function is an exponential function which identifies the fuzziness. The result will be a general measurement of lecturers' performance. Based on the 4 variables used in the analysis (Utilizes content scope and sequence planning, Clearness of assignments and evaluations, Systematical in lecturing, and Encourages students attendance) we obtain that lecturers' performance are fair, poor, fair, and poor respectively. Keywords and Phrases : Hotelling, harmonic mean, fuzzy, exponential function, characteristic function. 1. INTRODUCTION University is one of post investments for human development in education which most activities based on the learning process during in a university. This process relies on interaction between lecturers and students. After some period of time, students may adopt some knowledge which may determine their futures. Therefore lecturers require to transfer their knowledge such that students capable to reproduce their knowledge obtained in their universities as a support for themselves in their working places. Since a lecturer becomes an important agent in the effort of human development in a university, some necessary conditions must be satisfied as a lecturer. This paper will propose some results on lecturers' performance based on students survey. Students evaluate a lecturer by some questions (some are adopted from a literature given in a web which are listed on Table 1 and these are considered the same items in Indonesian that have been used as instruments in the observation for this paper. According to Yusrizal [1], the items are validated which is not done in this paper. We have used these items to evaluate lecturers‟ performance. Each item will be quantified as 0, 1, 2 or 3 which means poor, fair, satisfactory and good respectively. Since all students did not meet with all lecturers in 1 semester then the research is simply made as a general evaluation for all lecturers in the Department. ________________________________ 2010 Mathematics Subject Classification : 03B50, 03C65 , 62H25. 1 2 HAP AND ADS (H.A PARHUSIP AND ADI SETIAWAN) TABLE I QUESTIONS FOR STUDENTS OBSERVATION TO EVALUATE A LECTURER HELD DURING IN A CLASS No Questions 1 Utilizes content scope and sequence planning 2 Clearness of assignments and evaluations 3 Systematical in lecturing 4 Encourages students attendance 5 Demonstrates accurate and current knowledge in subject field 6 Creates and maintains an environment that supports learning 7 Clearness to answer the question from a student 8 Attractiveness of the lecture 9 Clearness of purpose on each assignment 10 Lecturer‟s competence on stimulating students excitement 11 Lecturer‟s competence on delivering idea 12 Does teacher have available time to help students for the related topic outside the class? 13 Effectiveness of time used in the class 14 Provides relevant examples and demonstrations to illustrate concepts and skills 15 The quality of lecturer‟s feedback due to the given assignment. 16 Score the overall the lecturer‟s performance maxwell, G = gauss, Oe = oersted; Wb = weber, V = volt, s = second, The used Tdata = tesla, here m = meter,are Aobtained = ampere, J =from joule, kgstudents = kilogram, survey H = henry. in Mathematics Department in Science and Mathematics Faculty, Satya Wacana Christian University in the year 2008-2009. Furthermore, the lecturers‟ performance can not be exactly in one of the values 0,1, 2 or 3. Therefore data can be considered nonprecise and hence we refer to fuzzy in presenting the analysis. The remaining paper is organized as follows. The used theoretical background is shown in Section 2. Procedures to analyze the obtained data are shown on Section 3. The analysis is then shown in Section 4 and finally some conclusion and remark are written in the last Section of this paper. II. MODELLING HOTELLING-HARMONIC-FUZZY ON LECTURERS’ PERFORMANCE 2.1 Review Stage Some authors have proposed a quality evaluation based on some mathematical approaches such as using fuzzy set. Teacher performance is studied with fuzzy system [2] to generate an assesment criteria. In complex system such as cooling process of a metal, the combined PCA (Principal Component Analysis) algorithm and T2 -Hotteling are used to define quality index after all data are normalized in a range -1 and 1 [3]. The other instrument for lecturers‟ performance have been developed and validitated using variable analysis . Lecturers‟ strictness are also estimated using intuitionistic fuzzy [4]. There are several standards can also be used to indicate a quality of a teacher which are more a qualitative approach which are easily found through internet. In a strategic planning, SWOT is one of the most pointed references. In SWOT analysis some uncertainties can be encountered and therefore using fuzzy will renew the classical SWOT by presenting the internal and external variables in 3 HAP AND ADS (H.A PARHUSIP AND ADI SETIAWAN) the sense of fuzzy as shown by Ghazinoory, et.all[5]. It is assumed that the given data contain non-precision. Thus the representation data will be as a fuzzy set [6]. The fuzzy data are indicated by a characteristic function. There are some well-known characteristic functions. In this research, we apply an exponential characteristic function ,i.e q q 2 L(x), x m1 1 x m2 with x m1 and (x) 1, m x m L(x) exp R(x) exp 1 2 a a 1 2 R(x), x m2 . (1) There are 6 parameters in Eq.(1), i.e m1,a1,q1 and m2 ,a2 ,q2 that must be determined. An illustration of this characteristic function is depicted in Figure 1. Figure 1 shows us that a single value x*=0.5 can be considered that the value may vary in the interval 0.25 x* 1.5. This allows us to tolerate that the given value is not exactly 0.5 but it can be in this interval which indicates its non-precision. However, if this tolerance is too big, one introduces a parameter which varies in 0 1 such that our tolerance can be chosen freely. For example, if 0.2 then the tolerance for saying is reduced as illustrated in Figure 1. We may say that 0.35 x* 0.85. Fig 1. (x) with the given data is 0.5 (denoted by star on the peak) , and the value of each parameter m1,a1,q1 is 0.4980, 0.1 , 2 respectively and the value of each parameter m2 ,a2 ,q2 is 0.2, 0.502 , 0.8 respectively. The tolerance for x* is reduced. The corresponding cut is also shown as a horizontal line for 0.2. A problem appears here that the determination of parameters becomes time consuming for each value. Up to now, there exists no optimization procedure to find the best values of parameters here. Therefore we may vary parameters based on the given data. Let us consider by this following example. Example 1: Let the given data be a vector x [0.5 0.67 0.83 1. 1.17 1.33 1.5 1.67 1.83 2] T . Let the vector x be an element in the observation space M X . We want to express this vector in the sense of fuzzy. By trial and error we try to use the value of each parameter. This means that each value in the vector has its own characteristic function. We will also define the average value of this vector by the harmonic mean and the characteristic function of this average value. The used parameters for all characteristic functions are a1 0.1,q1 q2 2, a2 0.2. These parameters are chosen freely. The illustration of characteristic functions is depicted in Figure 2a. The values of m1 and m2 are taken from the given vector. The characteristic function of the harmonic average is obtained as L(x), x 1.039 2 with x 1.039 and (x) 1, x 1.039 L(x) exp 0.1 R(x), x 1.309 4 HAP AND ADS (H.A PARHUSIP AND ADI SETIAWAN) x 1.039 2 R(x) exp . 0.2 Thus the characteristic function is defined after the harmonic mean is obtained. The statistical test for multivariate data is based on the T 2 named as Hotelling [7] in a classical sense that 2 T 1 nX 0 S (X 0 ) (2) T where X (x1, x2 ,......, x p ) is a vector of an arithmetic mean of each n variable, 1 is an arithmetic mean for the k-th item. It is also xk xki n i 1 known from Wikipedia or [7] that TABLE II STUDENTS SURVEY FOR 6 LECTURERS BASED ON 4 VARIABLES THE SYMBOL D j INDICATES THE NAME OF J-TH LECTURER. Row Harmonic No Questions D1 D2 D3 D4 D5 D6 Average Utilizes content scope and sequence 1 planning 3.0 1.67 1.89 1.71 1.62 2.2 1.92 Clearness of assignments and 1.84 2 evaluations 3.0 1.51 2.00 1.57 1.58 2.05 Systematical in 3 lecturing 3.0 1.72 1.11 1.29 2.01 1.83 1.65 Encourages students 4 attendance 2.0 1.41 1.78 1.14 2.48 1.83 1.69 Column-Harmonic Average 2.75 1.57 1.61 1.39 1.86 1.97 1.77 TOTAL AVERAGE 2 2 n p 2 ~ Tp,n1 or ~ F .
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