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Ananthanarayanan, M.
- A Study on Comparison between Fuzzy Assignment Problems Using Trapezoidal Fuzzy Numbers with Average Method
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PDF Views:123
Authors
Affiliations
1 Department of Mathematics, R.K.M. Vivekananda College, Chennai-600 005, IN
2 Department of Mathematics, A.M. Jain College, Chennai-600 114, IN
1 Department of Mathematics, R.K.M. Vivekananda College, Chennai-600 005, IN
2 Department of Mathematics, A.M. Jain College, Chennai-600 114, IN
Source
Indian Journal of Science and Technology, Vol 5, No 4 (2012), Pagination: 2610-2613Abstract
Assignment problem is very often used in solving problems of engineering and management science. In this paper, trapezoidal fuzzy numbers are considered which are more realistic and general in nature. The fuzzy assignment problem has been transformed into crisp assignment problem in the LPP form solved by using LINGO 9.0 and the results were compared with average method. Subject classification: Fuzzy Logic- 03B52Keywords
Fuzzy Sets, Fuzzy Numbers, Fuzzy Assignment Problem, Fuzzy Ranking, Hungerian MethodFull Text
References
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- Solving Fuzzy Assignment Problem using Ranking of Generalized Trapezoidal Fuzzy Numbers
Abstract Views :182 |
PDF Views:0
Authors
Affiliations
1 Department of Mathematics, Jeppiaar Engineering College, Chennai - 600119, IN
2 Department of Mathematics, A. M. Jain College, Chennai - 600114, IN
1 Department of Mathematics, Jeppiaar Engineering College, Chennai - 600119, IN
2 Department of Mathematics, A. M. Jain College, Chennai - 600114, IN
Source
Indian Journal of Science and Technology, Vol 9, No 20 (2016), Pagination:Abstract
Background/Objectives: The fuzzy optimal solution is totally based on ranking or comparing fuzzy numbers. Ranking fuzzy numbers play an vital role in decision making problems, data analysis and socio economics systems. The aim is to optimize the total cost of assigning all the jobs to the available persons. Ranking fuzzy number offers an powerful tool for handling fuzzy assignment problems. Methods/Statistical analysis: In this paper we used Hungarian method for solving fuzzy assignment problems using generalized trapezoidal fuzzy numbers. By using the ranking procedure we convert the fuzzy assignment problem to a crisp value assignment problem which then can be solved using Hungarian Method to find the fuzzy optimal solution. We presented the method which is not only simple in calculation but also gives better approximation and satisfactory results which is illustrated through the numerical examples. Findings: We propose a new ranking method which discriminates the fuzzy numbers where as few of the existing method fails to discriminates the fuzzy numbers. This method ranks all types of fuzzy numbers i.e. normal and generalized fuzzy numbers. Both triangular and trapezoidal fuzzy numbers). It is evident from the numerical examples that the proposed ranking measure for a fuzzy assignment problem is easy to compute and cost effective and gives much more optimal value. Applications/Improvements: The proposed ranking procedure can be applied in various decision making problems. This ranking method could also be used to solve other types of problems like game theory, project schedules, transportation problems.Keywords
Fuzzy Assignment Problem, Ranking Function, Trapezoidal Fuzzy Numbers.Full Text