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Two decision makers’ single decision over a back order EOQ model with dense fuzzy demand rate

Suman Maity, Sujit Kumar De, Madhumangal Pal

Abstract


In this article we develop an economic order quantity (EOQ) model with backlogging where the decision is made jointly from two decision maker supposed to view one of them as the industrialist (developer) and the other one as the responsible manager. The problem is handled under dense fuzzy environment. In fuzzy set theory the concept of dense fuzzy set is quite new which is depending upon the number of negotiations/ turnover made by industrial developers with the supplier of raw materials and/or the customers.  Moreover, we have discussed the preliminary concept on dense fuzzy sets with their corresponding membership functions and appropriate defuzzification method. The numerical study explores that the solution under joint decision maker giving the finer optimum of the objective function. A sensitive analysis, graphical illustration and conclusion are made for justification the new approach.


Keywords


Backorder inventory; dense fuzzy set; dense fuzzy lock set; defuzzification; optimization

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References


Baez-Sancheza, A.D., Morettib, A.C., & Rojas-Medarc, M.A. (2012). On polygonal fuzzy sets and numbers, Fuzzy Sets and System. 209, 54-65.

Ban, A.I., & Coroianu, L. (2014). Existence, uniqueness and continuity of trapezoidal approximations of fuzzy numbers under a general condition. Fuzzy Sets and System, 257, 3-22.

Beg, I., & Ashraf, S. (2014). Fuzzy relational calculus. Bulletin of the Malaysian Mathematical Science Society. (2) 37(1), 203-237.

Bellman, R.E., &Zadeh, L.A., (1970). Decision making in a fuzzy environment. Management Sciences. 17(4), 141-164.

Chutia, R., Mahanta, S., &Baruah, H.K. (2010). An Alternative Method of Finding the Membership of a Fuzzy Number.International Journal of Latest Trends in Computing. 69 – 72.

Das, P., De, S.K.and Sana, S.S.(2014). An EOQ model for time dependent backlogging over idle time : A step order fuzzy approach.International Journal of Applied and Computational Mathematics. 1(2), 1-17. DOI: 10.1007/s40819-014-0001-y.

Deli, I., &Broumi, S. (2015). Neutrosophic soft matrices and NSM-decision making. Journal of Intelligent and Fuzzy System. 28(5), 2233-2241.

De, S.K., & Beg, I. (2016a). Triangular dense fuzzy sets and new defuzzication methods. Journal of Intelligent and Fuzzy System.31(1),467-479, DOI: 10.3233/IFS-162160.

De, S. K., & Beg, I.(2016b). Triangular dense fuzzy Neutrosophic sets, Neutrosophic Sets and Systems. 13, 1-12.

De, S.K. (2013). EOQ model with natural idle time and wrongly measured demand rate. International Journal of Inventory Control and Management. 3(1-2), 329-354.

De, S.K., Goswami, A., & Sana, S.S. (2014). An interpolating by pass to Pareto optimality in intuitionistic fuzzy technique for an EOQ model with time sensitive backlogging. Applied Mathematics and Computation. 230, 664-674.

De, S.K. and Mahata, G.C., (2016). Decision of a fuzzy inventory with fuzzy backorder model under cloudy fuzzy demand rate, International Journal of Applied and Computational Mathematics, DOI: 10.1007/s40819-016-0258-4.

De, S.K., & Sana, S.S. (2015). An EOQ model with backlogging. International Journal of Management Sciences and Engineering Management. Doi: 10.1080/17509653.2014.995736.

De, S.K., & Sana, S.S. (2013a). Backlogging EOQ model for promotional effort and selling price sensitive demand- an intuitionistic fuzzy approach. Annals of Operations Research. Doi: 10.1007/s10479-013-1476-3.

De, S.K., & Sana, S.S. (2013b). Fuzzy order quantity inventory model with fuzzy shortage quantity and fuzzy promotional index. Economic Modelling, 31, 351-358.

De, S.K., and Sana, S. S.(2014). An alternative fuzzy EOQ model with backlogging for selling price and promotional effort sensitive demand. Int. J. of Applied and Computational Mathematics. 1-20, DOI: 10.1007/s40819-014-0010-x.

De, S.K., and Sana S.S.(2016). The (p,q,r,l) model for stochastic demand under intuitionistic fuzzy aggregation with Bonferroni mean. Journal of Intelligent Manufacturing. 1-21, DOI: 10.1007/s10845-016-1213-2.

De, S.K. (2017). Triangular Dense Fuzzy Lock Set. Soft Computing. Doi: 10.1007/s00500-017-2726-0.

Diamond, P. & Kloeden, P.E. (1991). Parametrization of fuzzy sets by single valued mappings, Proc. 4th IFSA, Brussels, 42-45.

Diamond, P. (1989). The structure of type k fuzzy numbers, in the coming of age of fuzzy logic.J.C. Bezdek (ed.), Seattle, 671-674.

Diamond, P. (1990). A note on fuzzy star shaped fuzzy sets. Fuzzy Sets and Systems. 37

Diamond, P. &Kloeden, P.E. (1989). Characterization of compact sets of fuzzy sets. Fuzzy Sets and Systems. 29, 341-348.

Dubois, D., &Prade, H. (1978). Operations on fuzzy numbers. International Journal of System Science. 9(6), 613-626.

Goetschel, R., &Voxman, J. (1985). Eigen fuzzy number sets. Fuzzy Sets and System, 16(1), 75-85.

Heilpern, S.(1981). Fuzzy mappings and fixed point theorem. J. Math. Anal. Applns. 83, 566-569.

Kaufmann, A., & Gupta, M.M. (1985). Introduction of fuzzy arithmetic theory and applications. Van Nostrand Reinhold, New York.

Kazemi, N., Ehsani, E. and Jaber, M. (2010). An inventory models with backorders with fuzzy parameters and decision variables. International Journal of Approximate Reasoning, 51(8), 964-972.

Kazemi, N., Olugu, E. U., Salwa Hanim, A-R. and Ghazilla, R.A.B.R. (2015a). Development of a fuzzy economic order quantity model for imperfect quality items using the learning effect on fuzzy parameters. Journal of Intelligent and Fuzzy System. 28(5), 2377-2389.

Kazemi, N., Olugu, E. U., SalwaHanim, A-R. andGhazilla, R.A.B.R. (2016). A fuzzy EOQ model with backorders and forgetting effect on fuzzy parameters: an empericalstudy.Computers and industrial Engineering. 96, 140-148.

Kazemi, N., Shekarian, E., Cárdenas-Barrón, L.E., andOlugu, E.U.(2015b). Incorporating human learning into a fuzzy EOQ inventory model with backorders. Computer and Industrial Engineering. 87, 540–542.

Mahanta, S., Chutia, R., &Baruah, H. K. (2010). Fuzzy Arithmetic without Using the Method of α – Cuts.International Journal of Latest Trends in Computing. 73 – 80.

Piegat, A. (2005). A New Definition of Fuzzy Set. Appl. Math. Comput. Sci, 15(1), 125-140.

Roychoudhury, S. &Pedrycz, W.(2003). An Alternative Characterization of Fuzzy Complement Functional.Soft Computing – A Fusion of Foundations, Methodologies and Applications. 563 – 565.

Zadeh, L.A. (1965). Fuzzy sets. Information and Control. 8(3), 338-356.




DOI: http://dx.doi.org/10.18686/fm.v3i1.1061

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