An integrated production policy with defective items and stock-out based substitution under triangular dense fuzzy lock set environment

Abstract

Brand substitution is common observed phenomenon in daily life. It is the decision makers' economic understanding and potential scheme for business-industries. Also, it provides the flexibility in management and increases the ability to control the production. This paper proposes an integrated supplier-retailer inventory model for substitutable products. Two supplier with two different brand product with their corresponding demand are involved and one retailer sells each of the products. To nullify the complexities of the joint optimization problem, we first develop a deterministic model for three cases: no substitution, partial substitution and full substitution, then we go for its fuzzification. Keeping the financial constraint of each producer, we have studied over the elasticity of the cost parameters by means of triangular dense fuzzy lock set approach with its locking and unlocking property for final decision making. Finally, sensitivity analysis and graphical illustration are made to justify the model.

Linguistic single‐valued neutrosophic soft sets with applications in game theory

“…The existence of equilibrium in this twoperson (nonconstant sum) game is judged. By using Equations ( 30) and (31), we obtain that ≥ υ x y υ x y ( , ) = 0.9303 ( , )…”

“…In the following years, the literature of FS theory was expanded by introducing many generalized versions of FSs such as the Pythagorean fuzzy set (PyFS) [3][4][5] and q-rung fuzzy set (q-ROFS). 6,7 By means of these set theories, the uncertainty was allowed to be described from different perspectives, and thus many issues including uncertainty such as decision making, [8][9][10][11][12][13] multiattribute decision making, [14][15][16][17] game theory, [18][19][20][21][22][23] medical diagnosis, [24][25][26] pattern recognition, [27][28][29] supplier-retailer inventory model, 30,31 economic order quantity model, 32,33 clustering analysis, 34,35 and supplier selection 36,37 were discussed. Smarandache 38 introduced the neutrosophic set, taking into account the degrees of membership, nonmembership, indeterminacy and hesitation simultaneously.…”