Keywords
Optimization
Triangular dense fuzzy
Pentagonal dense fuzzy
Trapezoidal dense fuzzy
How to Cite
Abstract
In this project work, we deal with an economic order quantity inventory model of deteriorating items under non-random uncertain demand. Here we consider the customers screen the fresh items during the selling period. After a certain period of time, the deteriorated items are sold at a discounted price. Firstly, we solve the crisp model, and then the model is converted into a fuzzy environment. Here we consider the pentagonal dense fuzzy, trapezoidal dense fuzzy, and triangular dense fuzzy for a comparative study. We have taken the numerical result using LINGO 18.0 software. Finally, sensitivity analysis and graphical illustration have been given to check the validity of the model.
References
Felix and A.V. Devadoss, A new decagonal fuzzy number under uncertain linguistic environment. Int. J. Math. App. 3 (2015) 9-97.
A.S. Sudha and S. Karunambigai, Solving a transportation problem using a Heptagonal fuzzy number. Int. J. Adv. Res. Sci. Eng. Technol. 4 (2017) 3118-3115.
Asady, The revised method of ranking LR fuzzy number based on deviation Degree. Expert Syst. App. 37 (2010) 5056-5060.
C.H. Cheng, A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95 (1998) 307-317.
D.P. Filev and R.R. Yager, A generalized defuzzification method via BADD Distributions. Int. J. Intell. Syst. 6 (1991) 687-697.
E. Shekarian, E.U. Olugu, S.H. Abdul-Rashid and E. Bottani, A fuzzy reverse logistics inventory system integrating economic order/production quantity models. Int. J. Fuzzy Syst. 18 (2016) 1141-1161
E. Shekarian, E.U. Olugu, S.H. Abdul-Rashid and N. Kazemi, Analyzing optimization techniques in inventory models: the case of fuzzy economic order quantity problems. In: Int. Conference on Industrial Engineering and Operations Management. Kuala Lumpur, Malaysia, March 8-10 (2016) 1229-1240.
E. Shekarian, E.U. Olugu, S.H. Abdul-Rashid and N. Kazemi, An economic order quantity model considering di_erent holding costs for imperfect quality items subject to fuzziness and learning. J. Intell. Fuzzy Syst. 30 (2016) 2985-2997.
E. Shekarian, N. Kazemi, S.H. Abdul-Rashid and E.U. Olugu, Fuzzy inventory models: a comprehensive review. Appl. Soft Comput. 55 (2017) 588-621.
K. Rathi and S. Balamohan, A mathematical model for subjective evaluation of alternatives in Fuzzy multi-criteria group decision making using COPRAS method. Int. J. Fuzzy Syst. 19 (2017) 1290-1299.
K. Rathi and S. Balamohan, Comparative study of arithmetic nature of Heptagonal fuzzy numbers. Appl. Math. Sci. 8 (2016) 4309-4321.
K. Rathi, S. Balamohan, M. Revathi and B. Ananthi, A fuzzy approach for unequal workers-task assignment with heptagonal fuzzy numbers. Int. J. Recent Innov. Trends Comput. Commun. 4 (2016) 564-569.
L.A. Zadeh, Fuzzy sets. Inf. Control 8 (1965) 338-353.
L.H. Chen and H.W. Lu, An approximate approach for ranking fuzzy numbers based on left and right dominance. Comput. Math. Appl. 41 (2001) 1589-1602.
L.H Chen and H.W. Lu, The preference order of fuzzy numbers. Comput. Math. Appl. 4(2002) 1455-1465.
N.I. Namarta, N. Thakur and U.C. Gupta, Ranking of heptagonal fuzzy numbers using incentre of centroids. Int. J. Adv. Technol. Eng. Sci. 5 (2017) 248-255.
N. Kazemi, E.Shekarian, L.E. C_ardenas-Barron and E.U. Olugu, Incorporating human learning into a fuzzy EOQ inventory model with backorders. Comput. Ind. Eng. 87 (2015) 540-542.
N. Kazemi, E.U. Olugu, A.-R. SalwaHanim and R.A.B.R. Ghazilla, A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters: an emperical study. Comput. Ind. Eng. 96 (2016) 140-148.
N. Kazemi, E.U. Olugu, A.-R. SalwaHanim and R.A.B.R. Ghazilla, Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters. J. Intell. Fuzzy Syst. 28 (2015) 2377-2389.
P. Das, S.K. De and S.S. Sana, An EOQ model for time dependent backlogging over idle time: a step order fuzzy approach. Int. J. Appl. Comput. Math. 1 (2014) 1-17.
Q. Song and R.P. Leland, Adaptive learning defuzzi_cation techniques and applications. Comput. Math. Appl. 81 (1996) 321-329.
R. Patro, M. Acharya, M.M. Nayak and S. Patnaik, A fuzzy EOQ model for deteriorating items with imperfect quality using proportionate discount under learning effects. Int. J. Manage. Decis. Making 17 (2018) DOI: 10.1504/IJMDM.2018.092557
R.R. Yager, Knowledge-based defuzzi_cation. Fuzzy Sets Syst. 80 (1996) 177-185.
S. Abbasbandy and B. Asady, Ranking of fuzzy numbers by sign distance. Inf. Sci. 176 (2006) 2405-2416.
S. Abbasbandy and T. Hajjari, A new approach for ranking of trapezoidal fuzzy Numbers. Comput. Math. Appl. 57 (2009) 413-419.
S. Abbasbandy and T. Hajjari, An improvement on centroid point method for ranking of fuzzy numbers. J. Sci. I.A.U. 78 (2011) 109-119.
S. Halgamuge, T. Runkler and M. Glesner, On the neural defuzzi_cation Methods. In: Proceeding of the 5th IEEE International Conference on Fuzzy Systems (1996) 463-469.
S.J. Chen and S.M. Chen, A new method for handling multicriteria fuzzy decision making problems using FN-IOWA operators. Cybern. Systems. 34 (2003) 109-137.
S.J. Chen and S.M. Chen, Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl. Intell. 26 (2007) 1-11.
S. Karmakar, S.K. De and A. Goswami, A pollution sensitive dense fuzzy economic production quantity model with cycle time dependent production rate. J. Cleaner Prod. 154 (2017) 139-150.
S. Karmakar, S.K. De and A. Goswami, A pollution sensitive remanufacturing model with waste items: triangular dense fuzzy lock set approach. J. Cleaner Prod. 187 (2018) 789-803.
S.K. De, A. Goswami and S.S. Sana, An interpolating by pass to Pareto optimality in intuitionistic fuzzy technique for a EOQ model with time sensitive backlogging. App. Math. Comput. 230 (2014) 664-674.
S.K. De and G.C. Mahata, Decision of a fuzzy inventory with fuzzy backorder model under cloudy fuzzy demand rate. Int. J. Appl. Comput. Math. 3 (2017) 2593-2609.
S.K. De and I. Beg, Triangular dense fuzzy Neutrosophic sets. Neutrosophic Sets Syst. 13 (2016) 1-12.
S.K. De and I. Beg, Triangular dense fuzzy sets and new defuzzication methods. J. Intell. Fuzzy Syst. 31 (2016) 467-479.
S.K. De and S.S. Sana, An EOQ model with backlogging. Int. J. Manage. Sci. Eng. Manage. 11 (2016) 143-154.
S.K. De and S.S. Sana, An alternative fuzzy EOQ model with backlogging for selling price and promotional effort sensitivedemand. Int. J. Appl. Comput. Math. 1 (2015) 69-86.
S.K. De and S.S. Sana, Backlogging EOQ model for promotional effort and selling price sensitive demand-an intuitionistic fuzzy approach. Ann. Oper. Res. 233 (2013) 57-76.
S.K. De and S.S. Sana, Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index. Econ. Model. 31 (2013) 351-358.
S.K. De and S.S. Sana, The (p; q; r; l) model for stochastic demand under intuitionistic fuzzy aggregation with bonferroni mean. J. Intell. Manuf. 29 (2018) 1753-1771.
S.K. De, EOQ model with natural idle time and wrongly measured demand rate. Int. J. Inventory Control Manage. 3 (2013)329-354.
S.K. De, Triangular dense fuzzy lock set. Soft Comput. 22 (2018) 7243-7254.
S.K. Sharma and S.M. Govindaluri, An analytical approach for EOQ determination using trapezoidal fuzzy function. Int. J. Procurement Manage. 11 (2018) 356-369.
S. Maity, S.K. De and M. Pal, Two decision makers' single decision over a back order EOQ model with dense fuzzy demand rate. Finance Market 3 (2018) 1-11.
S.M. Chen and J.H. Chen, Fuzzy risk analysis based on the ranking of generalized fuzzy numbers with different heights and different spreads. Expert Syst. App. 36 (2009) 6833-6842.
S. Selvakumari and S. Lavanya, Fuzzy game problem with payoffs as linguistic variables, Int. J. Eng. Sci. Manage. Res. 3 (2016) 18-24.
S.S.L. Chang and L.A. Zadeh, On fuzzy mappings and control. IEEE Trans. Syst. Man Cybern. 2 (1972) 30-34
T. Chu and C. Tsao, Ranking fuzzy numbers with an 1 area between the centroid point and original point. Comput. Math. Appl. 43 (2002) 111-117.
T. Jiang and Y. Li, Generalized defuzzi_cation strategies and their parameter learning procedure. IEEE Trans. Fuzzy Syst. 4 (1996) 64-71.
T. Hajjari, On deviation degree methods for ranking fuzzy numbers. Aust. J. Basic App. Sci. 5 (2011) 750-758.
T. Hajjari, Ranking of fuzzy numbers based on ambiguity degree. Aust. J. Basic App. Sci.. 5 (2011) 62-69.
U. Chanda and A. Kumar, Optimisation of fuzzy EOQ model for advertising and price sensitive demand model under dynamic ceiling on potential adoption. Int. J. Syst. Sci.: Oper. Logist. 4 (2017) 145-165.
X.W. Liu and. S.L. Han, Ranking fuzzy numbers with preference weighting function expectation. Comput. Math. Appl. (2005) 1455-1465.
Y. Deng and Q. Liu, A TOPSIS-based centroid index ranking method of fuzzy numbers and its application in decision-making. Cybern. Syst. 36 (2005) 581-595.
Y. Deng, Z.F. Zhu and Q. Liu, Ranking fuzzy numbers with an area method using of gyration. Comput. Math. Appl. 51 (2006)1127-1136.
Y.J. Wang and H.S. Lee, The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput. Math. Appl. 55 (2008) 2033-2042.
Z.X. Wang, Y.J. Liu, Z.P. Fan and B. Feng, Ranking L-R fuzzy numbers based on deviation degree. Inf. Sci. 176 (2009) 2070-2077.
S. Maity, S.K. De and M. Pal and S.P. Mondal, A study of an EOQ model with public-screened discounted items under cloudy fuzzy demand rate, Journal of Intelligent & Fuzzy Systems, 41(6) 2021, 6923-6934.
S. Maity, S.K. De and M. Pal and S.P. Mondal, A study of an EOQ model of growing items with parabolic dense fuzzy lock demand rate, Applied System Innovation, 4(4), 2021, 81.
S. Maity, S.K. De and S.P. Mondal, A Study of an EOQ Model under Lock Fuzzy Environment, Mathematics, 2019, https://doi.org/10.3390/math7010075.
S. Maity, S.K. De and S.P. Mondal, A Study of a Backorder EOQ Model for Cloud-Type Intuitionistic Dense Fuzzy Demand Rate, Int. J. Fuzzy Syst, 2019, https://doi.org/10.1007/s40815-019-00756-1.
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