Some extensions of fuzzy sets such as interval-valued fuzzy sets, intuitionistic fuzzy sets, interval-valued intuitionistic fuzzy sets, type n-fuzzy sets, and neutrosophic sets provided powerful and practical tools for dealing with uncertainty in decision-making problems. Neutrosophic set is defined with three-dimensional membership functions to describe the degrees of truth, indeterminacy, and falsity. Neutrosophic set theory is a useful instrument to handle incomplete, inconsistent, and indeterminate information. In this paper, we first propose a modified score function for ranking single-valued neutrosophic numbers. Then, we suggest a TOPSIS method based on the proposed function for decisionmaking under group recommendation. The method is applied to deal with the hotel location selection problem, where the decision values of the attributes for alternatives and the weights of the attributes are given by decisionmakers based on single-valued neutrosophic sets. Finally, numerical experiments are done. They show that the given method is more efficient as well as more reasonable tool for decision-making in contrast to the other existing methods.

In developing countries, the demand for old aged people requiring private health care at home is dramatically growing with the improvement of living standards. Since vehicles are used for transferring the medical staff (or doctors) to patient homes, it may be interesting to select a vehicle type based on the cost, capacity, and environmental sustainability (fuel consumption and CO2 gas emission per unit of distance) to maximize profits and social responsibility. In this paper, the first contribution, a new green home health care network for location, allocation, scheduling, and routing problems is developed with uncertain conditions. Another novelty, the time window to serve patients is also considered. In this regard, a novel grey flexible linear programming model is developed to cope with the uncertain nature of costs and capacity parameters that is as one important novelty. Due to this model’s high complexity and difficulty in large-scale instances, this research develops two novel hybrid algorithms. The first hybrid strategy called the HSEOSA algorithm combines the Social Engineering Optimizer algorithm with the Simulated Annealing method. In terms of contribution to the related solution methodology, additionally, the Keshtel Algorithm is incorporated with the Genetic Algorithm called the HGAKA algorithm as the second new hybrid metaheuristic. An extensive comparison among the proposed algorithms is performed to find the most efficient one for the application of home healthcare in real practice. To validate the proposed model, a novel real case study is illustrated in the home healthcare services in Tehran/Iran.

This paper presents a new method for group multi-attribute decision-making (GMADM) based on interval neutrosophic sets, where decision makers determine the weights and the evaluating values of the attributes with respect to the available alternatives by using interval neutrosophic values. In comparison with other existing methods involving group multi-attribute decision making, that only consider crisp or incomplete information, the proposed method, based on interval neutrosophic sets, can handle not only incomplete information but also indeterminate and inconsistent information which is common in real-world situations. Therefore, the method presented in this paper can be more effective and efficient than other decision-making methods.

One of the main topics discussed in a supply chain is the production-distribution problem. Producing and distributing the products plays a key role in reducing the costs of the chain. To design a supply chain, a network of efficient management and production-distribution decisions is essential. Accordingly, providing an appropriate mathematical model for such problems can be helpful in designing and managing supply chain networks. Mathematical formulations must be drawn close to the real world due to the importance of supply chain networks. This makes those formulations more complicated. In this study, a novel multi-objective formulation is devised for the production-distribution problem of a supply chain that consists of several suppliers, manufacturers, distributors, and different customers. Also, a Mixed Integer Linear Programming (MILP) mathematical model is proposed for designing a multi-objective and multi-period supply chain network. In addition, grey flexible linear programming (GFLP) is done for a multi-objective production-distribution problem in a supply chain network. The network is designed for the first time to cope with the uncertain nature of costs, demands, and capacity parameters. In this regard, due to the NP-hardness and complexity of problems and the necessity of using meta-heuristic algorithms, NSGA-II and Fast PGA algorithm are applied and compared in terms of several criteria that emphasize the quality and diversity of the solutions.