Decision of a Fuzzy Inventory with Fuzzy Backorder Model Under Cloudy Fuzzy Demand Rate

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.Mathematics Subject Classification. 03E72, 90B50.

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“…Appendix (De and Mahata [32], De and Beg [33,34]): Suppose x is a crisp number then under non-randomly uncertainties it will be "around x".…”

Section: Conflict Of Interestmentioning

confidence: 99%

A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment

Maity

Chakraborty

et al. 2020

RAIRO-Oper. Res.

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“…2.2 Cloudy normalized triangular fuzzy number [33,35] Definition 1 LetÃ be the fuzzy set whose components are the elements of R Â R, R being the set of real numbers with the membership grade satisfying the functional relation l : R Â R ! 0; 1 ½ .…”

Section: Normalized General Triangular Fuzzy Number (Ngtfn)mentioning

confidence: 99%

“…*For correspondence Alternatively, De and Beg [33,34] introduced dense fuzzy approach to capture the degree of learning experiences in recent times. De and Mahata [35] extended the dense fuzzy set to cloudy fuzzy set and gave a new formula for defuzzification. Several attempts on the application of dense fuzzy rule were studied by De [36], Karmakar et al [37,38] and Maity et al [39] extensively.…”

Section: Introductionmentioning

confidence: 99%

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A comprehensive study of an economic order quantity model under fuzzy monsoon demand

Mahata

2019

Sādhanā

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This article deals with a classical economic order quantity (EOQ) model under monsoon type fuzzy demand rate. It is nothing but the generalization of cloudy fuzzy model. We split the EOQ model into three parts according to the real-time fuzzy components of the demand rate. To defuzzify the model we develop an algorithm and the solution is obtained with the help of a nonlinear optimization technique that requires maximum aspiration level of the fuzzy membership of the objective function. Moreover, for comparative study we take numerical results of the crisp, general fuzzy and cloudy fuzzy model also. By this study we have shown that the decision maker might have to choose the monsoon type fuzzy environment all the time to control the proposed inventory. Moreover, sensitivity analysis and graphical illustrations are made to justify the new fuzzy approach. adhana(0123456789().,-volV)FT3 ](0123456789().,-volV)

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“…They developed the triangular dense fuzzy set (TDFS) along with the new defuzzification methods first then applied it in a triangular dense fuzzy neutrosophic set (TDFNS) explicitly. Subsequently, De and Mahata [12] applied this concept with new addition in the name of cloudy fuzzy sets to discuss a backorder EOQ model. In their study they choose a Cauchy sequence which might converges to zero.…”

Section: Introductionmentioning

confidence: 99%

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

Maity

Pal

2018

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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.

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Decision of a Fuzzy Inventory with Fuzzy Backorder Model Under Cloudy Fuzzy Demand Rate

Cited by 51 publications

References 35 publications

A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment

A comprehensive study of a backlogging EOQ model with nonlinear heptagonal dense fuzzy environment

A comprehensive study of an economic order quantity model under fuzzy monsoon demand

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

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