fuzzy mathematical programming

In this paper, the property of fuzzy sets is used as approach to instrument for the construction and finding the value of “multi-objective linear fractional programming problem” (MOLFPP) and applied complementarity condition on such problems which is one of regulation of order problems which cover by fuzzy dealings. Introduce a technique to convert and solve the problem by symmetric fuzzy approach. Suggest an algorithm and show how fuzzy LFPP can be answered without rising the Arithmetic potency. Our technique is used to convert complementarity multi-objective linear fractional programming problem (CMOLFPP) to LP through symmetric fuzzy linear fractional problem (SFLFP). To demonstrate the efficacy of the suggested technique, a numerical example is presented. then compared the result with other techniques fuzzy linear fractional programming (FLFP) which are solved by using computer applications to test the algorithm of the above method to indicate that the results obtained by such approach are promising.

Fuzzy multiobjective linear bilevel programming (FMOLBP) problems are studied in this paper. The existing methods replace one or some deterministic model(s) instead of the problem and solve the model(s). Doing this work, we lose much information about the compromise decision, and it does not make sense for the uncertain conditions. To overcome the difficulties, Zadeh’s extension principle is applied to solve the FMOLBP problems. Two crisp multiobjective linear three-level programming problems are proposed to find the lower and upper bound of its objective values in different levels. The problems are reduced to some linear optimization problems using one of the scalarization approaches, called the weighting method, the dual theory, and the vertex enumeration method. The lower and upper bounds are estimated by the resolution of the corresponding linear optimization problems. Hence, the membership functions of compromise objective values are produced, which is the main contribution of this paper. This technique is applied for the problem for the first time. This method applies all information of a fuzzy number and does not estimate it by a crisp number. Hence, the compromise decision resulted from the proposed method is consistent with reality. This point can minimize the gap between theory and practice. The results are compared with the results of existing approaches. It shows the efficiency of the proposed approach.

The purpose of this study is to develop a dairy global supply chain planning model in which operational and financial dimensions are appropriately integrated in order to adjust the credit sale strategy. In order to evaluate the financial performance of the dairy supply chain, economic value-added index and some financial ratios are used. The proposed model is compared to traditional approaches, which usually use the profit maximization as an objective function. Also, the amount of credit sales is considered as a decision variable for the first time in this research. The developed model utilized a new risk measure, i.e., the fuzzy CVaR, to cope with the uncertainty of the exchange rate and the quality and quantity of returned products. The effectiveness and efficiency of the proposed model are analyzed and assessed using the data of a real dairy supply chain. The analysis of results obtained from the developed fuzzy mathematical model shows an increase in profit and a reduction in semi-variance compared to previously developed models. Also, some numerical experiments analyses index and the impact of credit sales strategy.

Ordering on fuzzy quantities have been attracted a wide domains of studies in fuzzy sets theory in the two last decades. In many practical situations as well as fuzzy mathematical programming, it is necessary to the decision makers consider L-R fuzzy numbers according to their aims. But in the most of methods which are presented to order fuzzy numbers, the authors have been considered a special kind of fuzzy numbers such as triangular fuzzy numbers, trapezoidal fuzzy numbers and etc. But as we know the L-R fuzzy numbers as a general kind of these numbers have not been discussed. Hence in this paper, we focus on a general L-R fuzzy number and propose a new approach to order them as an extension of the method which is given by Nasseri in [14]. For validity of the proposed method, we will illustrate this method based on a convenient examples which is appeared in the literature of fuzzy ordering. Furthermore, we emphasize that the proposed method will be useful for evaluating the optimality conditions in the fuzzy primal simplex algorithms and the other related algorithms such as the fuzzy dual simplex algorithm and the fuzzy two phase simplex algorithm, fuzzy transportation models, fuzzy interval linear programming and etc.

In this research, we address the application of uncertainty programming to design a multi-site, multi-product, multi-period, closed-loop supply chain (CLSC) network. In order to make the results of this article more realistic, a CLSC for a case study in the iron and steel industry has been explored. The presented supply chain covers three objective functions: maximization of profit, minimization of new product's delivery time, collection time and disposal time of used products, and maximizing flexibility. To solve the proposed model, an interactive hybrid solution methodology is adopted through combining a hybrid fuzzy-stochastic programming method and a fuzzy multi-objective approach. Finally, the numerical experiments are given to demonstrate the significance of the proposed model and the solution approach.