fuzzy linear programming

This Evaluation of fuzzy networks with imprecise data is crucial. In this article, we propose fuzzy two-stage network models based on the structure of central resource allocation models. Firstly, we obtain the target for the fuzzy decision-making units in the two-stage network by using central resource allocation models, with a maximum of one two-phase model in each stage of the network. Then, we determine the overall target for the network. The probability function approach is used in the two-stage fuzzy network models to rephrase the proposed models and find the target. In conclusion, we calculate the target for Iranian airlines using fuzzy data and the proposed model.

In this study, we discussed a fuzzy programming approach to bi-level linear programming problems and their application. Bi-level linear programming is characterized as mathematical programming to solve decentralized problems with two decision-makers in the hierarchal organization. They become more important for the contemporary decentralized organization where each unit seeks to optimize its own objective. In addition to this, we have considered Bi-Level Linear Programming (BLPP) and applied the Fuzzy Mathematical Programming (FMP) approach to get the solution of the system. We have suggested the FMP method for the minimization of the objectives in terms of the linear membership functions. FMP is a supervised search procedure (supervised by the upper Decision Maker (DM)). The upper-level decision-maker provides the preferred values of decision variables under his control (to enable the lower level DM to search for his optimum in a wider feasible space) and the bounds of his objective function (to direct the lower level DM to search for his solutions in the right direction).

Recently, Srinivasan [On solving fuzzy linear fractional programming inmaterial aspects, Materials Today: Proceedings, https://doi.org/10.1016/j.matpr.2019.04.209] proposed a method to solve fractional linear programmingproblem under fuzzy environment based on ranking and decompositionmethods. Srinivasan also claimed that the proposed method solved fractionallinear programming problem with inequality and equality constraints. In thisnote, we point out that the paper entitled above suffers from certainmathematical mistakes for solving these problems. Hence, the mentionedmethod and example are not valid. Further the exact method is stated and solvedthe problem.