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Nowadays, the intensification of a competitive environment in markets in conjunction with sustainability issues has forced organizations to concentrate on designing sustainable closed-loop supply chains. In this study, a sustainable closed-loop supply chain network is configured under uncertain conditions based on fuzzy theory. The proposed network is a multi-product multi-period problem which is formulated by a bi-objective mixed-integer linear programming model with fuzzy demand and return rate. The objectives are to maximize the supply chain profit and customer satisfaction at the same time. Moreover, the carbon footprint is included in the first objective function in terms of cost (tax) to affect the total profit and treat the environmental aspect. Fuzzy linear programming and Lp-metric method are then applied to deal with the uncertainty and bi-objectiveness of the model, respectively. In order to validate the methodology, a case study problem in the dairy industry is investigated where the proposed Lp-metric is also compared to goal attainment method. The obtained results demonstrate the superiority of Lp-metric against goal attainment method as well as the applicability and efficiency of the proposed methodology to treat a real case study problem. Furthermore, from the management perspective, outsourcing the production during high-demand periods is highly recommended as an efficient solution.

This study demonstrated the effectiveness of fuzzy method in decision-making and recommends the integration of fuzzy methods in decision-making in production, transportation, power production and distribution and utility maintenance in Nigeria companies.

Large-scale disasters occur worldwide, with a continuing surge in the frequency and severity of disruptive events. Researchers have developed several optimization models to address the critical challenges of disaster relief supply chains (e.g., emergency material reserving and scheduling inefficiencies). However, most developed algorithms are proven to have low fault tolerance, which makes it difficult for disaster relief supply chain managers to obtain optimal solutions and meet the emergency distribution requirements within a limited time frame. Considering the uncertainty and ambiguity of disaster relief information and using Interval Type-2 Fuzzy Set (IT2TFS), this paper presents a collaborative optimization model based on an integrative emergency material supplier evaluation framework. The optimal emergency material suppliers are first selected using a multi-attribute group decision-making ranking method. Multi-objective fuzzy optimization is then run in three emergency phases: early -, mid-, and late-disaster relief stages. Focusing on a massive flash flood disaster event in Yunnan Province as a case study, a comprehensive numerical analysis tests and validates the developed model. The results revealed that the proposed optimization method can optimize emergency material planning while ensuring that reserve material safety inventory is always maintained at a reasonable level. The presented method suggests a fuzzy interval to prevent emergency materials’ safety inventory shortage and minimize continuous life/property losses in disaster-affected areas.

Fuzzy data envelopment analysis (FDEA) is one of the most applicable approaches for performance assessment of peer decision making units under ambiguity which is evolving rapidly and gaining popularity under uncertain data envelopment analysis field. The goal of this paper is to review some FDEA models based on applied possibility, necessity, credibility, general fuzzy measures and chance-constrained programming to deal with data ambiguity. The study presents a comprehensive and structured literature review of fuzzy chance-constrained data envelopment analysis (FCCDEA) studies including 87 studies from 2000 to 2020. The main contributions of this research include the following details: (1) Review of fuzzy chance-constrained programming, (2) Survey of FCCDEA models based on different fuzzy measures, (3) Analysis of FCCDEA applications and features, (4) Classification of FCCDEA studies from modeling and uncertainty type viewpoints, (5) Bibliometric analysis of FCCDEA literature, and (6) Extraction of main research gaps and guidelines for future research directions.

Supply chain disruptions compel professionals all over the world to consider alternate strategies for addressing these issues and remaining profitable in the future. In this study, we considered a four-stage global supply chain and designed the network with the objectives of maximizing profit and minimizing disruption risk. We quantified and modeled disruption risk as a function of the geographic diversification of facilities called supply density (evaluated based on the interstage distance between nodes) to mitigate the risk caused by disruptions. Furthermore, we developed a bi-criteria mixed-integer linear programming model for designing the supply chain in order to maximize profit and supply density. We propose an interactive fuzzy optimization algorithm that generates efficient frontiers by systematically taking decision-maker inputs and solves the bi-criteria model problem in the context of a realistic example. We also conducted disruption analysis using a discrete set of disruption scenarios to determine the advantages of the network design from the bi-criteria model over the traditional profit maximization model. Our study demonstrates that the network design from the bi-criteria model has a 2% higher expected profit and a 2.2% lower profit variance under disruption than the traditional profit maximization solution. We envisage that this model will help firms evaluate the trade-offs between mitigation benefits and mitigation costs.

This article presents an algorithm for solving fully fuzzy multi-objective linear fractional (FFMOLF) optimization problem. Some computational algorithms have been developed for the solution of fully fuzzy single-objective linear fractional optimization problems. Veeramani and Sumathi (Appl Math Model 40:6148–6164, 2016) pointed out that no algorithm is available for solving a single-objective fully fuzzy optimization problem. Das et al. (RAIRO-Oper Res 51:285–297, 2017) proposed a method for solving single-objective linear fractional programming problem using multi-objective programming. Moreover, it is the fact that no method/algorithm is available for solving a FFMOLF optimization problem. In this article, a fully fuzzy MOLF optimization problem is considered, where all the coefficients and variables are assumed to be the triangular fuzzy numbers (TFNs). So, we are proposing an algorithm for solving FFMOLF optimization problem with the help of the ranking function and the weighted approach. To validate the proposed fuzzy intelligent algorithm, three existing classical numerical problems are converted into FFMOLF optimization problem using approximate TFNs. Then, the proposed algorithm is applied in an asymmetric way. Since there is no algorithm available in the existing literature for solving this difficult problem, we compare the obtained efficient solutions with corresponding existing methods for deterministic problems.

Epistemic uncertainty such as fuzzy based linear programming problem with equality constraints has been considered here. Fuzziness presents in system parameters are modelled using Trapezoidal Fuzzy Number (TrFN). In the considered problem the coefficients are defined as crisp while the decision variables as well as the right-hand side of the constraints are taken as fuzzy. Accordingly, a new method to solve the problem based on the fuzzy centre and radius has been proposed here. First the problem is solved for fuzzy centre and next the bounds of the fuzzy variable are replaced in terms of fuzzy centre and radius. Then using the obtained fuzzy centre solution there one can have the radius of the solution. Finally using the results for centre and radius one can get the final solution. For the implementation of this proposed methodology LINGO 18.0 software has been used. Consequently, optimal fuzzy feasible solution has been obtained to get the optimal value (maximum/minimum) of the fuzzy objective function. Moreover, various numerical examples have been solved using the proposed method and the obtained solutions are compared with the solution of existing methods for validation. Moreover, it has been observed that present methods overcome the limitations of Maleki (Maleki in Far East J Math Sci 4:283–301, 2002), Nasseri (Nasseri in Appl Math Sci 2:2473–2480, 2008), Mahdavi-Amiri and Nasseri (Mahdavi-Amiri and Nasseri in Fuzzy Sets Syst 158:1961–1978, 2007) and Saati et al. (Saati et al. in Int J Inf Decis Sci 7:312–333, 2015), and clearly the advantages of the proposed method are discussed in conclusion section.

This study proposes a fuzzy clustering-based vertical stacking strategy (FVSS) to reduce weight variance and enhance operational efficiency in container terminal operations. To address inefficiencies from reshuffling, defined as unnecessary container movements during retrieval, the FVSS method classifies containers into multiple weight classes using Fuzzy C-means (FCM) clustering based on historical container data. Stacking spaces are then proportionally allocated according to cluster sizes, and each stack is assigned a weight reference value to guide real-time container stacking. This enables flexible vertical stacking that dynamically adapts to weight similarities and uncertainty. The proposed strategy was evaluated against existing approaches including hybrid sequence stacking (HSS), random stacking strategy (RSS), and GMM-based methods. Numerical experiments using real-world terminal data demonstrate that FVSS outperforms other strategies, achieving up to 78% reduction in weight variance. Furthermore, performance remains stable even under uncertain weight conditions. These results highlight the practical advantage of integrating fuzzy optimization into stacking strategies, offering a robust and computationally efficient solution for container yard operations.

Nowadays, many inventory practitioners give special attention to green inventory problems incorporating carbon emission issues throughout the world. In this study, a green inventory model is considered where the demand rate depends on selling price, stock and green concern level. The holding cost is considered a quadratic function of time, and preservation technology has been utilized to control carbon emissions. First of all, a profit maximization crisp model is developed. Then, due to market flexibility, the demand rate assumes uncertainty in nature, where the concept of membership value and nonmembership value exists. So, a fuzzy model is developed where the demand rate is assumed to be a pentagonal intuitionistic dense fuzzy number. A novel defuzzification technique and a solution algorithm have been presented to solve the proposed model. In the numerical illustration, a comparative study is given among crisp and other fuzzy environments. For numerical computation, LINGO 18.0 software has also been utilized. Findings reveal that the green concern is a vital factor for model optimization under uncertain system. Finally, graphical illustration and sensitivity analysis have been made to justify the proposed model.

In this paper, the convex nonsmooth optimization problem with fuzzy objective function and both inequality and equality constraints is considered. The Karush–Kuhn–Tucker necessary optimality conditions are proved for such a nonsmooth extremum problem. Further, the exact l 1 penalty function method is used for solving the considered nonsmooth fuzzy optimization problem. Therefore, its associated fuzzy penalized optimization problem is constructed in this approach. Then, the exactness property of the exact l 1 penalty function method is analyzed if it is used for solving the considered nonsmooth convex fuzzy optimization problem.