Microsoft Word - cet-01.docx CHEMICAL ENGINEERING TRANSACTIONS VOL. 46, 2015 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Peiyu Ren, Yanchang Li, Huiping Song Copyright © 2015, AIDIC Servizi S.r.l., ISBN 978-88-95608-37-2; ISSN 2283-9216 A Multiple Fuzzy Evaluation Model of Physical Education in General Colleges and Universities for Knowledge Engineering Yue Zhang Sport Department, Jiangsu University, Jiangsu, Zhenjiang, 212001, China. zyuehome@163.com In response to the fact that the physical education evaluation is unitary in evaluation content, has unclear target, fails to address comprehensive indexes and reaches general conclusion, this paper discusses the multiple evaluation of physical education in general colleges and universities. Firstly, based on the multiple intelligence theory, this paper analyzes the evaluation process of physical education and proposes a new evaluation index system for physical education in general colleges and universities. Secondly, by dealing with different indexes under the system and based on the fuzzy system theory, this paper constructs a multiple fuzzy evaluation model and obtains the fuzzy distance and fuzzy similarity between measured values of indexes and their corresponding classic domains, thus knowing the physical education ability and level in general colleges and universities. Last but not the least, a case involving physical education in a given university is discussed to verify the efficacy of the model. 1. Introduction With quality education is applied to general colleges and universities, physical education have played an increasing role in higher education. The development of physical ability is becoming a key fa ctor of measuring education quality of general colleges and universities. Physical quality has been a dominant indicator for measuring the effect of talent nurturing. Therefore, it is necessary to evaluate physical education in general colleges and universities and adopt reasonable and scientific mechanism and strategies to promote physical education quality [Xue et al (2010), Huang (2014) and Li (2014) reported]. Currently, studies on the evaluation of physical education in colleges and universities have reached fruitful results, promoting the improvement of teaching effect and efficiency [He (2013), Wang et al (2013), Wang et al (2011) and Zhang et al (2011) reported]. However, the evaluation work is still in its infancy and previous researches have certain limitations. For example the evaluation is unitary in evaluation content, has unclear target, fails to take teaching effect into consideration, overlooks key section in the teaching process, or the evaluation model and method may be objective and general. Therefore, based on the multiple intelligence theory [Nalan et al (2011) and Vîrtop (2014) reported], this paper analyzes the evaluation system of physical education in general colleges and universities and proposes a multiple fuzzy evaluation index system. At the same time, by using the fuzzy system theory [Hoseyn et al (2011), Kaveh et al (2013) and Chee et al (2015) reported], it constructs a multiple fuzzy evaluation model to evaluate physical education in general colleges and universities. 2. The Fuzzy Evaluation Index System of Physical Education in General Colleges and Universities This paper analyzes eight dimensions of the multiple intelligence theory and specifies the evaluation indicator according to influential factors of physical education in colleges and universities. Table 1 shows the multiple evaluation index system. DOI: 10.3303/CET1546099 Please cite this article as: Zhang Y., 2015, A multiple fuzzy evaluation model of physical education in general colleges and universities for knowledge engineering, Chemical Engineering Transactions, 46, 589-594 DOI:10.3303/CET1546099 589 Table 1: The multiple evaluation index system of physical education in general colleges and universities target layer criteria layer indictor layer The fuzzy evaluation index system of physical education in general colleges and universities Verbal-linguistic intelligence Effectiveness of teaching content Effectiveness of teaching method Mastery degree of knowledge Learning attitude Musical-rhythmic intelligence Teaching planning Progress control of leaning Rhythm control Logical-mathematical intelligence Development of innovative ability Development of thinking ability Visual-spatial intelligence) Insight of sport actions Bodily-kinesthetic intelligence Effectiveness of teaching forms Performance ability Development of stamina Development of athletic skills Sport activity participation Body health Self-questioning intelligence Degree of completion of teaching tasks Mental health Social service Social satisfaction Interpersonal intelligence Development of coordination Development of cooperation and teamwork Naturalist intelligence Ability to reform Social adaption 3. Multiple Fuzzy Evaluation Model of Physical Education in General Colleges and Universities 3.1 Standardization of evaluation index There are qualitative indicators and quantitative indicators. The qualitative indicator can be expressed by fuzzy membership or qualitative language description. The quantitative indicator can be obtained through measured data. To have unified scale, these indicators need to be subject to standardization. (1) Standardization of qualitative indicator If the value j v of the qualitative indicator j can be obtained through fuzzy membership, suppose the corresponding fuzzy membership function is  x . There are:  j jv x (1) In particular, if the qualitative indicator has reverse membership, there is: C 1 C 11 c 12 c 13 c 14 c 2 C 21 c 22 c 23 c 3 C 31 c 32 c 4 C 41 c 5 C 51 c 52 c 53 c 54 c 55 c 56 c 6 C 61 c 62 c 63 c 64 c 7 C 71 c 72 c 8 C 81 c 82 c j 590  1j jv x  (2) If the value of the qualitative indicator can be obtained through fuzzy language description, it should be transformed to a value in the range 0-1. 1 refers to “excellent” and 0 refers to “poor”. So there are: , a b j j j v v v    , 0 1 a b j j v v   (3) (2) Standardization of quantitative indicator If the value j u of the quantitative indicator is measured data, the maximum value is sup j u and the minimum value is inf j u . When the quantitative indicator is a positive indicator, its value after standardization is: inf j j j sup inf j j u u v u u    (4) When the quantitative indicator is a negative indicator, its value after standardization is: sup j j j sup inf j j u u v u u    (5) In particular, if the value ju of the quantitative indicator is a measured interval, namely , a b j j j u u u    , expression (4) should be rewritten to the following form: , , a inf b inf j j j ja b j j j sup inf sup inf j j j j u u u u v v v u u u u              (6) Expression (5) should be rewritten to the following form: , , sup b sup a j j j ja b j j j sup inf sup inf j j j j u u u u v v v u u u u              (7) 3.2 Construction of classic domain The multiple fuzzy evaluation of physical education usually has several grades, each corresponding to different values. To conduct the multiple fuzzy evaluation effectively, it is necessary to establish different classic domains of different evaluation grades. Suppose there are m grades in the evaluation of physical education, the classic domain ijG of indicator j about evaluation grade i is: , a b ij ij ij G g g    , a b ij ij g g (8) The classic domain ijG is subject to standardization, as shown in Section 3.1 and gets: , a b ij ij ij H h h    , 0 1 a b ij ij h h   (9) 3.3 Weight of indicators This paper adopts the Analytic Hierarchy Process (AHP) to allocate weight of indicators. According to experts’ experience and knowledge, the ratio scale of 1-9 is used to compare two indicators in the same layer and score them. As a result, the comparative judgment matrix A can be obtained:   11 12 1 21 22 2 1 2 n n ks nxn n n nn a a a a a a a a a a              A (10) Where, 1 ks sk a a  . By computing the maximum eigenvalue of judgment matrix, the characteristic vector of can be obtained. j v j j j j v j jv j 591 max X XA (11)  1 2 1, , , ,n nX x x x x (12) The characteristic vector is standardized to obtain the weight vector W :  1 2 1 1 2 1 1 1 1 1 / , / , , / , / , , , , n n n n j j n j n j n n j j j j W x x x x x x x x w w w w                  (13) 3.4 Establishment of the evaluation model and realization of the algorithm Through abovementioned analysis, the unified measurement of indicator j of physical education evaluation can be obtained, which is , a b j j j v v v    . The classic domain of indicator j about evaluation grade i can be identified, , a b ij ij ij H h h    . Thus, the fuzzy Euclidean distance ijd between the indicator j and the classic domain of indicator j about evaluation grade i is:     2 2 a a b b ij j ij j ij d v h v h    (14) The fuzzy similarity ij  between the indicator j and the classic domain of indicator j about evaluation grade i is: 1 ij ij d   (15) Considering the weight j w of indicators, the weighed fuzzy similarity i   between the indicator j and the classic domain of indicator j about evaluation grade i is:   1 n i j ij j w      (16) The larger i   is, the closer the object under evaluation is to evaluation grade i . Thus, according to weighed fuzzy similarity i   , the evaluation grade of the object under evaluation can be identified. 4. Case Study and Model Verification To promote physical education in key colleges and universities and improve physical education quality, a phase assessment on physical education in general colleges and universities of a province is practiced and taken as an example. This paper combines the statistical analysis, questionnaires; exert comprehensive evaluation method and student comprehensive evaluation method to evaluate the education performance of key colleges and universities of a province according to the evaluation ind ex system. Table 2 shows relevant data for the evaluation. 592 Table 2: Evaluation indicators of physical education in general colleges and universities criteria layer Weight indicator layer Weight Value 1 C 0.125 0.321 0.85 0.321 0.80 0.228 0.85 0.130 0.75 2 C 0.125 0.600 0.80 0.200 0.50 0.200 0.60 3 C 0.125 0.500 0.40 0.500 0.40 4 C 0.125 1.000 0.75 0.161 0.80 5 C 0.125 0.161 0.75 0.045 0.90 0.045 0.80 55 c 0.294 0.90 0.294 0.80 6 C 0.125 0.200 0.90 0.200 0.90 0.300 0.90 0.300 0.80 7 C 0.125 0.333 0.60 0.667 0.80 8 C 0.125 0.500 0.50 0.500 0.75 According to the evaluation standard of physical education in general colleges and universities, there are four grades, namely excellent, good, mediocre and poor. After standardization of indicators, the classic domain is constructed, as shown in Table 3. Table 3: Classic domain of the evaluation of physical education in general colleges and universities Evaluation grade Classic domain Excellent 0.90-1.00 Good 0.75-0.90 Mediocre 0.50-0.75 Poor 0-0.50 According to the Euclidean distance and fuzzy similarity between the indicator and the classic domain, the fuzzy similarity of indicators is obtained. Similarly, according to the calculation model proposed in this paper, the comprehensive fuzzy similarity between evaluation criteria and evaluation grade is computed, as shown in Table 4. 11 c 12 c 13 c 14 c 21 c 22 c 23 c 31 c 32 c 41 c 51 c 52 c 53 c 54 c 56 c 61 c 62 c 63 c 64 c 71 c 72 c 81 c 82 c 593 Table 4: Fuzzy similarity between evaluation criteria and evaluation grade Evaluation criteria Evaluation grade Excellent Good Mediocre Poor 1 C 0.803 0.883 0.670 0.118 2 C 0.638 0.772 0.732 0.266 3 C 0.220 0.390 0.636 0.588 4 C 0.708 0.850 0.750 0.209 5 C 0.808 0.869 0.633 0.133 6 C 0.863 0.861 0.611 0.055 7 C 0.685 0.814 0.737 0.228 8 C 0.534 0.689 0.750 0.355 Comprehensive fuzzy similarity 0.657 0.766 0.689 0.244 From Table 5, it can be seen the performance of physical education in key colleges and universities of this province is labeled as “good”, which is in line with the real assessment result. The case proves the model proposed has efficacy and feasibility. 5. Conclusions This paper analyzes problems presenting in physical education and addresses the evaluation of physical education in general colleges and universities. It proposes an evaluation index system based on multiple intelligence theory. And according to the fuzzy system theory, this paper constructs a multiple fuzzy evaluation model to evaluate physical education in general colleges and universities. These two theories are proved to have good theoretical basis. The introduction of Euclidean distance reduces the com plexity of calculation and produces reliable computing results. Through a case study, the model is proved to be worthy of widely application. It provides an effective way of evaluation of physical education in general colleges and universities. References Akkuzu N., Akçay H. 2011. The design of a learning environment based on the theory of multiple intelligence and the study its effectiveness on the achievements, attitudes and retention of students [J]. 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