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As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication . Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. In this paper, a novel method to find the solutions in which 0 is not the inner point of supports, of fully fuzzy linear systems (shown as FFLS ) is proposed, if they exist by an analytic approach. The system's parameters were splitted into two groups of nonpositive and nonnegative by solving a multi objective linear programming problem, MOLP , and employing an embedding method to transform n× n FFLS to 2n× 2n parametric form linear system and hence, transforming operations on fuzzy numbers to operations on functions. And finally, numerical examples are used to illustrate this approach. Keywords: Fuzzy Numbers, Fully Fuzzy Linear System, Systems of Fuzzy Linear Equations, Embedding Method, Splitting Method.

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Regarding the fact that getting a suitable combination of the human resources and service stations is one of the important issues in the most service and manufacturing environments, In this paper, we have studied the two models of planning queuing systems and its effect on the cost of the each system by using two fuzzy queuing models of M/M/1 and M/E2/1. In the first section, we have compared two different fuzzy queuing models based on the costs of each model and fuzzy ranking methods are used to select optimal model due to the resulted complexity. This paper results in a new approach for comparing different queuing models in the fuzzy environment (regarding the obtained data from the real conditions) that it can be more effective than deterministic queuing models. Also a sensitivity analysis is carried out to help the decision maker in selecting the optimal model. Keywords: Cost Analysis, Fuzzy Queuing Systems, Fuzzy Ranking Methods

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Recovery of used products is receiving much attention recently due to growing environmental concerns.In this paper, we address the carbon footprint basedon problem arising in closed-loop supply chain where returned products are collected from customers. These returned products can either be disposed or be remanufactured to be sold as new ones again. Here, we formulate a comprehensive closed-loop model for the logistics planning considering profitability and ecological goals. In this way, we can achieve the ecological goalreducing the overall amount of CO2.Moreover, the profitability criterion can be supported in the cyclic network with the minimum costs and maximum service level. To validate the model a numerical experiment is worked out.

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Data envelopment analysis (DEA) is a useful tool for identifying well-performing (efficient) decision-making units (DMUs). In DEA, those units that are not placed on the efficiency frontier are considered to be inefficient units. Identifying inefficiency sources can help turn the units into more efficient ones. Therefore, studying inefficiencies is of utmost importance. The present paper aims to propose a cost production possibility set in a non-competitive environment (where prices can vary from one DMU to another). We compare the three PPSs so that we can introduce a new inefficiency source for DMUs based on the inappropriate choice of price by evaluating DMUs and comparing them with the existing cost production-possibility set frontier. And as a result, optimizing these price vectors can remove or, at least, reduce inefficiencies and create more efficient units.
 

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In today’s competitive business environment, the supply chain plays a crucial role in maintaining an organization’s competitive advantage. However, environmental uncertainties, unpredictable delays, and various risks pose significant challenges to the sustainability of these systems. This study aims to present an analytical model based on Fuzzy Data Envelopment Analysis (FDEA) to assess the supply chain system's sustainability capabilities against different types of risks. The proposed model seeks to enhance supply chain flexibility and resilience under dynamic environmental conditions by utilizing fuzzy data. To achieve this goal, supply chain risks were initially identified and categorized into three levels: strategic, tactical, and operational. Subsequently, FDEA was employed to evaluate the impact of these risks on supply chain performance. The research findings indicate that increasing environmental uncertainties, over reliance on specific suppliers, reduced inventory levels, and inefficiencies in demand forecasting are key factors contributing to decreased supply chain sustainability. The results further suggest that adopting multidimensional risk management approaches and leveraging strategic management theories such as the resource based view (RBV) and dynamic capabilities can effectively mitigate risks and enhance supply chain flexibility. Additionally, a comparative analysis of the proposed model with traditional risk management approaches demonstrated that applying FDEA improves risk assessment accuracy and enhances decision making efficiency within organizations. Ultimately, this study underscores the importance of utilizing advanced decision making tools in supply chain management and recommends that organizations continuously evaluate their current status and adopt advanced analytical methods for managing potential risks. The proposed model not only provides a systematic, data driven approach for assessing supply chain sustainability but also serves as a practical tool for managers in developing risk mitigation strategies and optimizing supply chain processes.