Application of Fuzzy Sets to Aggregate Production Planning With Multiproducts and Multitime Periods
ABSTRACT The objective of this study is to develop a fuzzy mathematical programming method to solve aggregate production planning (APP) decision problems that involve multiproducts and multitime periods in a fuzzy environment. The fuzzy APP model that is developed here attempts to minimize total cost with respect to inventory carrying levels, available labor levels, machine capacity and warehouse space, and the constraint of available budget. The proposed APP method evaluates monetary interest of related operating cost categories and provides greater computational efficiency and flexibility by adopting triangular fuzzy numbers and piecewise linear membership functions to represent both imprecise data and fuzzy goals. The actual performance of an industrial company was used to demonstrate the feasibility of applying the proposed method to real-world APP decisions. The proposed method yields an efficient solution and presents overall decision-maker satisfaction with the given goal values. This paper also presents several significant management implications that are related to the practical application of the proposed method.
Conference Paper: On modeling and solving fuzzy mathematical programming[Show abstract] [Hide abstract]
ABSTRACT: Mathematical programming approach has been employed extensively as a means to enhance the decision-making process in science and engineering. One of the fields that has been benefiting from the employing mathematical programming is the production planning and scheduling in both the industry and service sectors. Most of these applications assume deterministic situations in which the parameters used to develop the model are known in advanced and will remain unchanged. Undesirably, real-world decision-making problems are not deterministic, and in fact; they are fuzzy in nature. This research work is mainly concerned with enhancing the decision-making in production planning through adaptation of the concept of fuzzy programming. This paper reports on the development of a mathematical programming model that involves fuzzy parameters. In addition and besides presenting the fuzzy mathematical model, our paper will present, compare and discuss among two solution procedures that can deal with the fuzzy multi-objective linear programming problems.Statistics in Science, Business, and Engineering (ICSSBE), 2012 International Conference on; 01/2012
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ABSTRACT: Recently, gradual numbers have been introduced as a means of extending standard interval computation methods to fuzzy and gradual intervals. However, it is well known that the practical use of standard interval arithmetic operators, just like their fuzzy extension, gives results that are more imprecise than necessary and, in some cases, even counterintuitive. In this paper, we combine the concepts of gradual numbers and Kaucher arithmetic on extended intervals to define extended gradual interval arithmetic, where subtraction and division operators are, respectively, the inverse operators of the addition and the multiplication. They are applied to the inversion of a linear regressive model and to a control problem that is based on the inversion of a linear model.IEEE Transactions on Fuzzy Systems 03/2012; · 5.48 Impact Factor
Article: RFRR: Robust Fuzzy Rough Reduction[Show abstract] [Hide abstract]
ABSTRACT: This paper proposes a robust method of dimension reduction using fuzzy rough sets, in which the reduction results can reflect the reducts obtained on all of the possible parameters. Here, the reducts being obtained on all of the possible parameters mean that all of the reducts are obtained on different degrees of robustness to handle noise. This method is completely different from the existing methods of fuzzy rough reduction. The differences are shown in three aspects: the concept, the tool, and the algorithm. First, the key concept of attribute reduction is redefined in a new way. That is, the robust fuzzy rough reduct, which is shortened to a robust reduct, is proposed to reflect the classical reducts obtained on all of the possible parameters. The new “robust reduct” is not a crisp subset of condition attributes; rather, it is a fuzzy subset, whose most interesting property is that any cut set of the robust reduct is a classical reduct on a certain parameter. Second, the tool used to measure the discernibility power is different from the existing discernibility measures. In this paper, the robustness of each attribute to handle misclassification and perturbation is considered. By considering both the robustness and the discernibility, a robust fuzzy discernibility matrix is designed. Finally, the algorithms used to find the robust reducts are designed based upon the robust fuzzy discernibility matrix, which is completely different from the existing algorithms used to find the classical reducts.IEEE Transactions on Fuzzy Systems 01/2013; 21(5):825-841. · 5.48 Impact Factor