In this paper, we introduce fuzzy mathematical programming (FMP) for decision-making related to software creation by selecting optimal commercial-off-theshelf (COTS) products in a modular software system. Each module in such software systems have different alternatives with variations in their properties, for example, quality, reliability, execution time, size and cost. Due to these variations, componentbased software developers generally deals with the problem of selecting appropriate COTS products. The development of COTS-based systems largely depends on the success of the selection process. Various crisp optimization models of COTS products selection have been proposed in literature. However, in real COTS products selection problem, it is difficult to estimate precisely the values of various model parameters due to lack of sufficient data and also because of measurement errors. Hence, instead of crisp optimization model, if we use flexible optimization model then we might obtain results which are more preferred by the decision maker. In this study, we use multiple methodologies such as quality model, analytical hierarchy process and FMP to develop fuzzy multiobjective optimization model of the COTS products selection. To determine a preferred compromise solution for the multiobjective optimization problem, an interactive fuzzy approach is used.

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The optimization techniques used in commercial-off-the-shelf (COTS) selection process faces challenges to deal with uncertainty in many important selection parameters, for example, cost, reliability and delivery time. In this paper, we propose a fuzzy optimization model for selecting the best COTS product among the available alternatives for each module in the development of modular software systems. The proposed model minimizes the total cost of the software system satisfying the constraints of minimum threshold on system reliability, maximum threshold on the delivery time of the software, and incompatibility among COTS products. In order to deal with uncertainty in real-world applications of COTS selection, the coefficients of the cost objective function, delivery time constraints and minimum threshold on reliability are considered fuzzy numbers. The fuzzy optimization model is converted into a pair of mathematical programming problems parameterized by possibility (feasibility) level α using Zadeh's extension principle. The solutions of the resultant problems at different α-cuts provide lower and upper bounds of the fuzzy minimum total cost which helps in constructing the membership function of the cost objective function. The solution approach provide fuzzy solutions instead of a single crisp solution thereby giving decision maker enough flexibility in maintaining cost-reliability trade-off of COTS selection besides meeting other important system requirements. A real-world case study is discussed to demonstrate the effectiveness of the proposed model in fuzzy environment.

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Due to the rapid growth of development of component based software systems, the selection of optimal commercial-off-the-shelf (COTS) components has become the key of optimization techniques used for the purpose. In this paper, the authors use fuzzy mathematical programming (FMP) for developing bi-objective fuzzy optimization models that aims to select the best-fit COTS components for a modular software system under multiple applications development task. The proposed models maximize the functional performance and minimize the total cost of the software system satisfying the constraints of minimum threshold on intra-modular coupling density and reusability of COTS components. The efficiency of the models is illustrated using a real-world scenario of developing two financial applications for two small-scale industries.

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