Training course assessment with Shannon Entropy and Fuzzy TOPSIS

Document Type : Original Article


1 Ph.D in Environmental Science at Dept. of Environmental Science, Natural Resource Faculty, University of Gorgan, Gorgan, Iran.

2 MSc in Educational administration at Dept. of Educational administration, University of Shahid Beheshti, Tehran, Iran

3 MSc in Environmental Science at Dept. of Environmental Science, Natural Resource Faculty, University of Tarbiat modarres, Noor, Iran

4 MSc in Computer Science at Guilan Azad University, Rasht, Iran



Objective:Performance appraisal is a systematic, data-driven approach to organizational management whose results can be effective in achieving organizational excellence, the quality of moving from status to desirable status, enhancing performance and improving service delivery. This study defines the issue of educational quality assessment in Rasht municipality in the form of a multi-criteria decision-making problem with 9 criteria and 11 alternatives. This paper is intended to analyze training courses and determine the orders of them based of some criteria in order to be used in future training programs.
Methods:For solving the problem, Shannon entropy is developed to determine subjective weights and TOPSIS method is used for finding the preferences among alternative (courses).
Results:the results shows that in this municipality on the basis of criteria used in the study, the educational quality of firefighting course is the highest level and this state in transport and traffic management course is the lowest level.
Conclusion:This paper is intended to analyze training courses and determine the orders of them based of some criteria in order to be used in future training programs. The results shows that the mentioned methods can be used in organizational performance appraisal if they are defined in a multi-criteria decision making problems.


Aalianvari, A., Katibeh, H., Sharifzadeh, M., (2012), Application of fuzzy Delphi AHP method for the estimation and classification of Ghomrud tunnel from groundwater flow hazard, Arab Journal of Geosciences 5(2), 275–284.
Abbasiann, A., Salimi, G., Azin , R., (2008), Evaluation of engineering training: Survey the effectiveness of resistant welding training course based on Kirkpatrick model, Irankhodro Co. as a case Study, Iranian Journal of Engineering Educational, 10(39), 37–62.
Abdi, A., Alipour, M., Abdollahi, J., (2008), Measuring the effectiveness of training courses, Tadbir, 200, 26–32.
Abiodun, E.J.A. (1999) Human Resources management, an overview. Concept Publication, Shomolu, Lagos. P. 110-121.
Afzalkhani, M., Nejabat, S., (2013), Strategies to Increase In-service Terms of Teachers and Personnel in Semnan Education Organization, Journal of New Approach in Educational Administration 4(3), 83–98.
Ahmadi, E., Setorg, T., (2007), Investigating the relationship between organizational culture and creativity and organizational effectiveness in middle schools in Marvdasht, Quarterly Journal Of Educational Leadership & Administration, 3(4), 133-53.
Al-Mughairi, A. M., (2018), The evaluation of training and development of employees : the case of a national oil and gas industry, s.l.:Brunel University London - Unpublished PhD thesis.
Aryadoust, V., (2016), Adapting levels 1 and 2 of Kirkpatrick’s model of training evaluation to examine theeffectiveness of a tertiary-level writing course, Pedagogies: an international journal, 12(2), 151-179
Armstrong, M., (1991), A handbook of personnel management practice, Kogan page, London.
Boella, M., Steven, G. T., (2005), Human resources Management in the hospitality industry: An introductory guide, 8th edition, Butterworth-Heinemann.
Cajot, S., Mirakyan, A., Koch, A., Maréchal, F., (2017), Multicriteria Decisions in Urban Energy System Planning: A Review, Frontiers in Energy Research, 5(10)
Campbell JP., (1988), Training design and performance improvement, In: Productivity in Organizations: New Perspectives from Industrial and OrganizationaL Psychology, Jossey-Bass, San Francisco, CA) Chapter 8.
Chaghooshi, J. A., Fathi, M. R., Kashef, M., (2012), Integration of fuzzy shannon’s entropy with fuzzy TOPSIS for industrial robotic system selection, Journal of industrial engineering and management, 5(1), 102-114
Chattopadhayay, R., & Ghosh , A. K., (2012), Performance appraisal based on a forced distribution system: its drawbacks and remedies, International journal of productivity and performance management, 61 (8), 881-896.
Chang, Y. H., Yeh, C. H., (2002), A survey analysis of service quality for domestic airlines, European Journal of operational research, 139, 166-177.
Chang, Y. H., Chung, H. Y., and Wang, S. Y., (2007), A survey and optimization-based evaluation of development strategies for the air cargo industry, International journal of production economics, 106, 550-562.
Chu, A.T.W., Kalaba, R.E., & Spingarn, K., (1979), A comparison of two methods for determining the weights of belonging to fuzzy sets, Journal of optimiz. theor., 27, 531–538.
Decouza, D. A., & Robbins, S. P., (1996), Human resource practice, 5th edition. New York: John Wiley & Sons Inc.
Dehdasht, G., Ferwati, M. S., Mohamadzin, R., Zainulabidin, N., A hybrid approach using entropy and TOPSIS to select key drivers for a successful and sustainable lean construction implementation, Plos one, 15(2) : e0228746.
Deng, H., Yeh, C. H., Willis, R. J., (2000), Inter-company comparison using modified TOPSIS with objec­tive weights, Computers and Operations Research, 27(10), 963–973.
Diakoulaki, D., Mavrotas, G., Papayannakis, L., (1995), Determining objective weights in multiple criteria problems: the CRITIC method, Computers and Operations Research, 22(7), 763–770.
Fan, Z.P., (1996), Complicated multiple attribute decision making: Theory and applications, Ph.D Dissertation; Northeastern University, Shenyang, China.
Goldstein IL, Buxton VM., (1982), Training and human performance, In: Human Performance and Productivity, Ed: EA Fleischman, Erlbaum, Hillsdale, NJ, Chapter 5.
Gosti, M. and Wilson, A., (2001), corporate reputation management: living the brand, Management Decision, 39( 2) , 99-104.
Güneralpa, B., Gertnera, G., Mendozaa, G., & Anderson, A., (2007), Evaluating probabilistic data with a possibilistic criterion in land-restoration decision-making: Effects on the precision of results, Journal of fuzzy set systems, 158, 1546–1560.
Helm, S., (2011), Employees’ awareness of their impact on corporate reputation, Journal of Business Research, Elsevier, vol. 64(7), pages 657-663, July,64(7), 657-663
Hsieh, T. Y., Lu, S. T., and Tzeng, G. H., (2004), Fuzzy MCDM approach for planning and design tenders selection in public office buildings, International journal of project management, 22(7), 573-584.
Hwang, C. L., and Yoon, K. S., (1981), Multiple attributes decision making: Methods and applications, Berlin: Spring-Verlag. , New York.
Hwang, C.L., Lin, M.J., (1987), Group decision making under multiple criteria: methods and applications Springer: Berlin, Heidelberg.
Islam, S., Roy, T.K., (2006), A new fuzzy multi-objective programming: Entropy based geometric programming and its application of transportation problems, Eur. Journal Oper. Res., 173, 387–404.
Jozi, S. A., Shafiee, M., MoradiMajd, N., Saffarian, S., (2012), An integrated shannon’s entropy-TOPSIS methodology for environmental risk assessment of Helleh protected area in Iran, Environment monitoring assessment, 184, 6913-6922
Kahraman, C., Beskese, A., & Ruan, D., (2004), Measuring flexibility of computer integrated manufacturing systems using fuzzy cash flow analysis, Information Science, 168, 77-94.
Li, C. W., (2009), A Structure Evaluation Model for Technology Policies and Programs, PhD Dissertation, Institute of Management of Technology, National Chiao Tung University, Taiwan.
Mavi, R. K., Goh, M., & Mavi, N. K., (2016), Supplier selection with Shannon Entropy and fuzzy TOPSIS in the Context of Supply Chain Risk Management, Procedia-Social and Behavioral Sciences, 235, 216-225.
Mic, P., Antmen, Z. F., (2019), A healthcare facility location selection problem with fuzzy TOSIS method for a regional hospital, European Journal of Science and Technology, 16, 750-757
Mishra,S., Ayyub, B. M., (2019), Shannon entropy for quantifying uncertainty and risk in economic disparity, Risk Anal, 39, 2160-2181.
Noori, K., Yazdani, H., Khanifar, H., (2019), Choosing training needs assessment methods using with TOPSIS technique, Journal of Educational planning studies, 8(15), 96-120.
Nouri, I., Asadi, B., Rezazadeh, A., (2007), Evaluation of Training Quality with Fuzzy MCDM, Management Knowledgel, 20(78), 139-160.
Occupational Safety and Health Administration, (1988), Training requirements in OSHA standards and training guidelines, OSHA Rept. 2254, Occupational Safety and Health Administration, U.S. Department of Labor, Washington D.C.
Rohmatulloh R, Winarni S., (2014), Topsis mothod for determining the priority of strategic Training Program, Advanced Science Engineering Information Technology, 4(2)
Saaty, T. L., (1980), The analytic hierarchy process, New York: McGraw-Hill.
Sabaei, D., J. Erkoyuncu, R. Roy., (2015), A Review of Multi-Criteria Decision Making Methods for Enhanced Maintenance Delivery, Procedia CIRP, 37, 30-35.
Shyur, H. J., Shih, H. S., (2006), A hybrid MCDM model for strategic vendor selection, Mathematical and computer modeling, 44, 749-761
Stoner, J. A. F., Freeman, E., (1992), Management, 5th edition. England Cliffs, NJ: Prentice-Hall.
Sun, C. C., Lin, G. T. R., (2009), Using fuzzy TOPSIS method for evaluating the competitive advantages of shopping websites, Expert systems with applications, 36, 11764-11771.
Taheri, S., Mashinchi, M., (2013), Introduction Fuzzy probabilities and statistics, Kerman university Press.
Tannenbaum SI, Yukl G., (1992), Training and development in work organizations, Ann Rev Psychol 43, 399-441.
Tiwari, V., Jain, P. K., Tandon, P., (2017), An integrated shannon’s entropy and TOPSIS for product design concept evaluation based on bijective soft set, Journal intelligent manufacturing, 30(4), 1645-1658
Torrington, D., Chapman, J., (1983), Personnel management, 2th edition. Prentice-Hall international, London.
Wang, T. C., Chang, T. H., (2007), Application of TOPSIS in evaluating initial training aircraft under a fuzzy environment, Expert systems with applications, 33, 870-880.
Wang, J. J., Jing, Y. Y., Zhang, C. F., Zhao, J. H., (2009), Review on multi-criteria decision aid in sustainable energy decision-making, Renewable and Sustainable Energy Reviews, 13(9), 2263–2278.
Wang, T. C., & Lee, H. D., (2009), Developing a fuzzy TOPSIS approach based on subjective weights and objective weights, Expert systems with applications, 36, 8980-8985.
Xu, Z. S., and Chen, J., (2007), An interactive method for fuzzy multiple attributes group decision making, Information Sciences, 177, 248-263.
Yalcin, N., Unlu, U., (2016), A multi-criteria performance analysis of initial public offering (IPO) firms using CRITIC and VIKOR methods, Technological and economic development of economy, 24(2), 534-560
Yang, T., Hung, C. C., (2007), Multiple-attribute decision making methods for plant layout design problem, Robotics and computer-integrated manufacturing, 23, 126-137.
Zadeh, L.A., (1965), Fuzzy Sets, Information and Control, 8, 338–353
Zaied, A. N. H., (2012), Multi-criteria evaluation approach for E-learning technologies: selection criteria usisng AHP, international journal on E-learning, 11(4), 465-485
Zare Mehrjerdi, Y., (2015), Grey theory, VIKOR and TOPSIS approaches for strategic system selection with linguistic preferences: a stepwise strategy approach, Iranian Journal of Operations Research, 6(2), 36-57
Zhao, R., Govind, R., (1991), Algebraic characteristics of extended fuzzy numbers, Information science, 54, 103-130
Zavadskas, E. K., Antucheviciene, J., Chatterjee, P., (2019), Multiple-criteria Decision-making (MCDM) techniques for business process information management, Information, 10(4)
Zimmerman, H. J., (1996), Fuzzy sets theory and its applications, Boston: Kluwer Academic Publisher.