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Green supplier evaluation and selection plays a crucial role in the green supply chain management of any organization to reduce the purchasing cost of materials and increase the flexibility and quality of products. An interval neutrosophic set (INS)-which is a generalization of fuzzy sets, intuitionistic fuzzy sets (IFS) and neutrosophic sets (NS)-can better handle the incomplete, indeterminate and inconsistent information than the other sets. This paper proposes a new integrated Quality Function Deployment (QFD) in support of the green supplier evaluation and selection process. In the proposed approach, INS is used to assess the relative importance of the characteristics that the purchased product should have (internal variables "WHATs") in order to satisfy the company's needs, the relevant supplier assessment criteria (external variables "HOWs"), the "HOWs"-"WHATs" correlation scores, the resulting weights of the "HOWs" and the impact of each potential supplier. The normalized weighted rating is then defined and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is developed to obtain a final ranking of green suppliers. A case study is applied to demonstrate the efficiency and computational procedure of the proposed method.

Intuitionistic fuzzy sets (IFSs), including member and nonmember functions, have many applications in managing uncertain information. The similarity measures of IFSs proposed to represent the similarity between different types of sensitive fuzzy information. However, some existing similarity measures do not meet the axioms of similarity. Moreover, in some cases, they could not be applied appropriately. In this study, we proposed some novel similarity measures of IFSs constructed by combining the exponential function of membership functions and the negative function of non-membership functions. In this paper, we also proposed a new entropy measure as a stepping stone to calculate the weights of the criteria in the proposed multi-criteria decision making (MCDM) model. The similarity measures used to rank alternatives in the model. Finally, we used this MCDM model to evaluate the quality of software projects.

Perishable products are commonly seen in inventory management. By allowing shortages and backlogging, the impact on the cost from the decay of the products can be balanced out. In a recent paper published in Computers and Industrial Engineering [P.L. Abad, Optimal lot size for a perishable good under conditions of finite production and partial backordering and lost sale, Comput. Ind. Eng. 38 (2000) 457-465] considered a problem in such context. However, his algorithm was incomplete due to flaws in his solution procedure. The purpose of this note is to explore the same production inventory models with a mixture of partial backordering and lost sales for deteriorated items. We find the criteria for the optimal solution for different cases and derive a formulated minimum value. By theoretical analysis, we develop a few lemmas to reveal parameter effects and optimal solution procedure. The solutions are illustrated by solving the same examples from Abad's paper to illustrate the accuracy and completeness of our procedure.

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