Document Type : Research Paper
Department of Mathematical Sciences, University of Peloponnese, Graduate TEI of Western Greece, Greece.
The present work focuses on two directions. First, a new fuzzy method using triangular / trapezoidal fuzzy numbers as tools is developed for evaluating a group’s mean performance, when qualitative grades instead of numerical scores are used for assessing its members’ individual performance. Second, a new technique is applied for solving Linear Programming problems with fuzzy coefficients. Examples are presented on student and basket-ball player assessment and on real life problems involving Linear Programming under fuzzy conditions to illustrate the applicability of our results in practice. A discussion follows on the perspectives of future research on the subject and the article closes with the general conclusions.
- Klir, G. J. & Folger, T. A. (1988). Fuzzy sets, Uncertainty and information. Prentice-Hall, London.
- Voskoglou, M. Gr. (2017). Finite markov chain and fuzzy logic assessment models: emerging research and opportunities. Createspace independent publishing platform, Amazon, Columbia, SC, USA.
- Voskoglou, M. G. (2019). An essential guide to fuzzy systems. Nova science publishers, New York, USA.
- Voskoglou, M. G. (2011). Measuring students modeling capacities: a fuzzy approach. Iranian journal of fuzzy systems, 8(3), 23-33.
- Voskoglou, M. Gr. (2012). A study on fuzzy systems. American journal of computational and applied mathematics, 2(5), 232-240.
- Voskoglou, M. G. (2019). Methods for assessing human–machine performance under fuzzy conditions. Mathematics, 7(3), 230.
- Van Broekhoven, E., & De Baets, B. (2006). Fast and accurate center of gravity defuzzification of fuzzy system outputs defined on trapezoidal fuzzy partitions. Fuzzy sets and systems, 157(7), 904-918.
- Sakawa, M. (2013). Fuzzy sets and interactive multiobjective optimization. Springer science & business media. Plenum press, NY and London.
- Kaufman, A., & Gupta, M. M. (1991). Introduction to fuzzy arithmetic. New York: Van Nostrand Reinhold Company.
- Dubois, D. J. (1980). Fuzzy sets and systems: theory and applications(Vol. 144). Academic press, New York.
- Dinagar, D. S., & Kamalanathan, S. (2017). Solving fuzzy linear programming problem using new ranking procedures of fuzzy numbers. International journal of applications of fuzzy sets and artificial intelligence, 7, 281-292.
- (2014). Center of mass: A system of particles. Retrieved October 10, 2014, from http://en.wikipedia.org/wiki/Center_of_mass#A_system_of_particles
- Wang, M. L., Wang, H. F., & Lin, C. L. (2005). Ranking fuzzy number based on lexicographic screening procedure. International journal of information technology & decision making, 4(04), 663-678.
- Wang, Y. J., & Lee, H. S. (2008). The revised method of ranking fuzzy numbers with an area between the centroid and original points. Computers & mathematics with applications, 55(9), 2033-2042.
- Dantzig, G. B. (1951). Maximization of a linear function of variables subject to linear inequalities. Activity analysis of production and allocation, 13, 339-347.
- Dantzig, G.B. (1951). Maximization of a linear function of variables subject to linear inequalities. In T. C. Koopmans (Eds.), Activity analysis of production and allocation (pp. 339–347). Wiley& Chapman - Hall, New York, London.
- Dantzig, G. B. (1983). Reminiscences about the origins of linear programming. In Mathematical programming the state of the art(pp. 78-86). Springer, Berlin, Heidelberg.
- Taha, H. A. (1967). Operations research – an introduction, Second Edition. Collier Macmillan, N. Y.,
- Tanaka, H., & Asai, K. (1984). Fuzzy linear programming problems with fuzzy numbers. Fuzzy sets and systems, 13(1), 1-10.
- Verdegay, J. L. (1984). A dual approach to solve the fuzzy linear programming problem. Fuzzy sets and systems, 14(2), 131-141.
- Voskoglou, M. G. (2018). Solving linear programming problems with grey data. Oriental journal of physical sciences, 3(1), 17-23.