Abstract
This paper deals with a new fuzzy number namely, cloudy fuzzy number and its new defuzzification method for a classical economic order quantity (EOQ) inventory management problem. In fuzzy system, the measures of ambiguity depend upon the area of applicability and the observations of experimenters. The lack of insight over the set consideration causes the invention of new fuzzy set “cloudy fuzzy set”. The traditional assumptions over fuzziness were fixed over time, but in this study we see fuzziness can be removed as time progresses. Here the crisp model is solved first then taking the demand rate as general fuzzy as well as cloudy fuzzy number we have solved the problem under usual Yager’s index method and extension of Yager’s index method respectively. With the help of numerical example we have compared the objective values for all cases and the implication of the cloudy fuzzy number has been discussed exclusively. Graphical illustrations, sensitivity analysis are given for better justification of the model. Finally, a conclusion is made.
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Appendix
Appendix
We have the demand rate as fuzzy number \(\langle d_{1},d_{2},d_{3}\rangle = \langle 16,20,22\rangle \). The lower and upper bounds are \(L_{b}=16\) and \(U_{b}=22\) respectively. The mean is 19.333, the median is 20, so the mode (m) is \(3\times median-2\times mean =60- 38.666=21.334\). Therefore, \(d_{f}=\frac{1}{2m}(U_{b}-L_{b})=\frac{6}{42.668}=0.141\) and \(CI=\frac{Log(1+T)}{T}=\frac{Log(1+7)}{7}=0.129\).
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Karmakar, S., De, S.K., Goswami, A. (2018). A Study of an EOQ Model Under Cloudy Fuzzy Demand Rate. In: Ghosh, D., Giri, D., Mohapatra, R., Savas, E., Sakurai, K., Singh, L. (eds) Mathematics and Computing. ICMC 2018. Communications in Computer and Information Science, vol 834. Springer, Singapore. https://doi.org/10.1007/978-981-13-0023-3_15
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