This paper deals with an adaptation of an application of nonlinear heptagonal dense fuzzy number. The concept of linear and as well as non-linear for both symmetric and asymmetric heptagonal dense fuzzy number is introduced here. We develop a new ranking method for non-linear heptagonal dense fuzzy number also. Considering a backorder inventory model with non-linear heptagonal dense fuzzy demand rate we have utilized a modified centroid method for defuzzification. For decision maker’s aspects, numerical examples, comparative study with other dense fuzzy numbers and a sensitivity analysis show the superiority of the nonlinear heptagonal dense fuzzy number. Finally, graphical illustrations are made to justify the model followed by a conclusion.
Keywords: Heptagonal dense fuzzy number, centroid method, inventory problem, optimization
@article{RO_2020__54_1_267_0,
author = {Maity, Suman and Chakraborty, Avishek and De, Sujit Kumar and Mondal, Sankar Prasad and Alam, Shariful},
title = {A comprehensive study of a backlogging {EOQ} model with nonlinear heptagonal dense fuzzy environment},
journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
pages = {267--286},
year = {2020},
publisher = {EDP Sciences},
volume = {54},
number = {1},
doi = {10.1051/ro/2018114},
mrnumber = {4062456},
zbl = {1444.03155},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2018114/}
}
TY - JOUR AU - Maity, Suman AU - Chakraborty, Avishek AU - De, Sujit Kumar AU - Mondal, Sankar Prasad AU - Alam, Shariful TI - A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2020 SP - 267 EP - 286 VL - 54 IS - 1 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/ro/2018114/ DO - 10.1051/ro/2018114 LA - en ID - RO_2020__54_1_267_0 ER -
%0 Journal Article %A Maity, Suman %A Chakraborty, Avishek %A De, Sujit Kumar %A Mondal, Sankar Prasad %A Alam, Shariful %T A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment %J RAIRO - Operations Research - Recherche Opérationnelle %D 2020 %P 267-286 %V 54 %N 1 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/ro/2018114/ %R 10.1051/ro/2018114 %G en %F RO_2020__54_1_267_0
Maity, Suman; Chakraborty, Avishek; De, Sujit Kumar; Mondal, Sankar Prasad; Alam, Shariful. A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 1, pp. 267-286. doi: 10.1051/ro/2018114
[1] and , A new decagonal fuzzy number under uncertain linguistic environment. Int. J. Math. App. 3 (2015) 9–97.
[2] and , Solving a transportation problem using a Heptagonal fuzzy number. Int. J. Adv. Res. Sci. Eng. Technol. 4 (2017) 3118–3115.
[3] , The revised method of ranking LR fuzzy number based on deviation Degree. Expert Syst. App. 37 (2010) 5056–5060. | DOI
[4] , A new approach for ranking fuzzy numbers by distance method. Fuzzy Sets Syst. 95 (1998) 307–317. | MR | Zbl | DOI
[5] and , A generalized defuzzification method via BADD Distributions. Int. J. Intell. Syst. 6 (1991) 687–697. | Zbl | DOI
[6] , , and , A fuzzy reverse logistics inventory system integrating economic order/production quantity models. Int. J. Fuzzy Syst. 18 (2016) 1141–1161. | MR | DOI
[7] , , and , 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.
[8] , , and , An economic order quantity model considering different holding costs for imperfect quality items subject to fuzziness and learning. J. Intell. Fuzzy Syst. 30 (2016) 2985–2997. | Zbl | DOI
[9] , , and , Fuzzy inventory models: a comprehensive review. Appl. Soft Comput. 55 (2017) 588–621. | DOI
[10] and , 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. | DOI
[11] and , Comparative study of arithmetic nature of Heptagonal fuzzy numbers. Appl. Math. Sci. 8 (2016) 4309–4321.
[12] , , and , A fuzzy approach for unequal workers-task assignment with heptagonal fuzzy numbers. Int. J. Recent Innov. Trends Comput. Commun. 4 (2016) 564–569.
[13] , Fuzzy sets. Inf. Control 8 (1965) 338–353. | MR | Zbl | DOI
[14] and , An approximate approach for ranking fuzzy numbers based on left and right dominance. Comput. Math. Appl. 41 (2001) 1589–1602. | MR | Zbl | DOI
[15] and , The preference order of fuzzy numbers. Comput. Math. Appl. 44 (2002) 1455–1465. | MR | Zbl | DOI
[16] , and , Ranking of heptagonal fuzzy numbers using incentre of centroids. Int. J. Adv. Technol. Eng. Sci. 5 (2017) 248–255.
[17] , , and , Incorporating human learning into a fuzzy EOQ inventory model with backorders. Comput. Ind. Eng. 87 (2015) 540–542. | DOI
[18] , , and , A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters: an emperical study. Comput. Ind. Eng. 96 (2016) 140–148. | DOI
[19] , , and , 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. | MR | DOI
[20] , and , An EOQ model for time dependent backlogging over idle time: a step order fuzzy approach. Int. J. Appl. Comput. Math. 1 (2014) 1–17. | MR | Zbl
[21] and , Adaptive learning defuzzification techniques and applications. Comput. Math. Appl. 81 (1996) 321–329.
[22] , , and , A fuzzy EOQ model for deteriorating items with imperfect quality using proportionate discount under learning effects. Int. J. Manage. Decis. Making 17 (2018) | DOI
[23] , Knowledge-based defuzzification. Fuzzy Sets Syst. 80 (1996) 177–185. | MR | DOI
[24] and , Ranking of fuzzy numbers by sign distance. Inf. Sci. 176 (2006) 2405–2416. | MR | Zbl | DOI
[25] and , A new approach for ranking of trapezoidal fuzzy Numbers. Comput. Math. Appl. 57 (2009) 413–419. | MR | Zbl | DOI
[26] and , An improvement on centroid point method for ranking of fuzzy numbers. J. Sci. I.A.U. 78 (2011) 109–119.
[27] , and , On the neural defuzzification Methods. In: Proceeding of the 5th IEEE International Conference on Fuzzy Systems (1996) 463–469.
[28] and , A new method for handling multicriteria fuzzy decision making problems using FN-IOWA operators. Cybern. Systems. 34 (2003) 109–137. | Zbl | DOI
[29] and , Fuzzy risk analysis based on the ranking of generalized trapezoidal fuzzy numbers. Appl. Intell. 26 (2007) 1–11. | DOI
[30] , and , A pollution sensitive dense fuzzy economic production quantity model with cycle time dependent production rate. J. Cleaner Prod. 154 (2017) 139–150. | DOI
[31] , and , A pollution sensitive remanufacturing model with waste items: triangular dense fuzzy lock set approach. J. Cleaner Prod. 187 (2018) 789–803. | DOI
[32] , and , 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. | MR | Zbl | DOI
[33] and , Decision of a fuzzy inventory with fuzzy backorder model under cloudy fuzzy demand rate. Int. J. Appl. Comput. Math. 3 (2017) 2593–2609. | MR | Zbl | DOI
[34] and , Triangular dense fuzzy Neutrosophic sets. Neutrosophic Sets Syst. 13 (2016) 1–12.
[35] and , Triangular dense fuzzy sets and new defuzzication methods. J. Intell. Fuzzy Syst. 31 (2016) 467–479. | Zbl
[36] and , An EOQ model with backlogging. Int. J. Manage. Sci. Eng. Manage. 11 (2016) 143–154.
[37] and , An alternative fuzzy EOQ model with backlogging for selling price and promotional effort sensitive demand. Int. J. Appl. Comput. Math. 1 (2015) 69–86. | MR | Zbl | DOI
[38] and , Backlogging EOQ model for promotional effort and selling price sensitive demand-an intuitionistic fuzzy approach. Ann. Oper. Res. 233 (2013) 57–76. | MR | Zbl
[39] and , Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index. Econ. Model. 31 (2013) 351–358. | DOI
[40] and , The (p,q,r,l) model for stochastic demand under intuitionistic fuzzy aggregation with bonferroni mean. J. Intell. Manuf. 29 (2018) 1753–1771. | DOI
[41] , EOQ model with natural idle time and wrongly measured demand rate. Int. J. Inventory Control Manage. 3 (2013) 329–354. | DOI
[42] , Triangular dense fuzzy lock set. Soft Comput. 22 (2018) 7243–7254. | Zbl | DOI
[43] and , An analytical approach for EOQ determination using trapezoidal fuzzy function. Int. J. Procurement Manage. 11 (2018) 356–369. | DOI
[44] , and , Two decision makers’ single decision over a back order EOQ model with dense fuzzy demand rate. Finance Market 3 (2018) 1–11. | DOI
[45] and , Fuzzy risk analysis based on the ranking of generalized fuzzy numbers with different heights and different spreads. Expert Syst. App. 36 (2009) 6833–6842. | DOI
[46] and , Fuzzy game problem with payoffs as linguistic variables. Int. J. Eng. Sci. Manage. Res. 3 (2016) 18–24.
[47] and , On fuzzy mappings and control. IEEE Trans. Syst. Man Cybern. 2 (1972) 30–34. | MR | Zbl | DOI
[48] and , Ranking fuzzy numbers with an area between the centroid point and original point. Comput. Math. Appl. 43 (2002) 111–117. | MR | Zbl | DOI
[49] and , Generalized defuzzification strategies and their parameter learning procedure. IEEE Trans. Fuzzy Syst. 4 (1996) 64–71. | DOI
[50] , On deviation degree methods for ranking fuzzy numbers. Aust. J. Basic App. Sci. 5 (2011) 750–758.
[51] , Ranking of fuzzy numbers based on ambiguity degree. Aust. J. Basic App. Sci. 5 (2011) 62–69.
[52] and , 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.
[53] and , Ranking fuzzy numbers with preference weighting function expectation. Comput. Math. Appl. 49 (2005) 1455–1465. | MR | Zbl
[54] and , A TOPSIS-based centroid index ranking method of fuzzy numbers and its application in decision-making. Cybern. Syst. 36 (2005) 581–595. | Zbl | DOI
[55] , and , Ranking fuzzy numbers with an area method using of gyration. Comput. Math. Appl. 51 (2006) 1127–1136. | MR | Zbl | DOI
[56] and , The revised method of ranking fuzzy numbers with an area between the centroid and original points. Comput. Math. Appl. 55 (2008) 2033–2042. | MR | Zbl | DOI
[57] , , and , Ranking L-R fuzzy numbers based on deviation degree. Inf. Sci. 176 (2009) 2070–2077. | MR | Zbl | DOI
Cité par Sources :
