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Supplier selection is a fundamental issue of supply chain area that heavily contributes to the overall supply chain performance, and, also, it is a hard problem since supplier selection is typically a multicriteria group decision problem. In many practical situations, there usually exists incomplete and uncertain, and the decision makers cannot easily express their judgments on the candidates with exact and crisp values. Therefore, in this paper an extended technique for order preference by similarity to ideal solution (TOPSIS) method for group decision making with Atanassov's interval-valued intuitionistic fuzzy numbers is proposed to solve the supplier selection problem under incomplete and uncertain information environment. In other researches in this area, the weights of each decision maker and in many of them the weights of criteria are predetermined, but these weights have been calculated in this paper by using the decision matrix of each decision maker. Also, the normalized Hamming distance is proposed to calculate the distance between Atanassov's interval-valued intuitionistic fuzzy numbers. Finally, a numerical example for supplier selection is given to clarify the main results developed in this paper.

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Modern Turnip production methods need significant amount of direct and indirect energy. The optimum use of agricultural input resources results in the increase of efficiency and the decrease of the carbon footprint of turnip production. Data Envelopment Analysis (DEA) approach is a well-known technique utilized to evaluate the efficiency for peer units compared with the best practice frontier, widely used by researches to analyze the performance of agricultural sector. In this regard, a new non-radial DEA-based efficiency model is designed to investigate the efficiency of turnip farms. For this purpose, five inputs and two outputs are considered. The outputs consist turnip yield as a desirable output and greenhouse gas emission as an undesirable output. The new model projects each DMU on the strong efficient frontier. Several important properties are stated and proved which show the capabilities of our proposed model. The new models are applied in evaluating 30 turnip farms in Fars, Iran. This case study demonstrates the efficiency of our proposed models. The target inputs and outputs for these farms are also calculated and the benchmark farm for each DMU is determined. Finally, the reduction of CO 2 emission for each turnip farm is evaluated. Compared with other factors like human labor, diesel fuel, seed and fertilizers, one of the most important findings is that machinery has the highest contribution to the total target energy saving. Besides, the average target emission of turnip production in the region is 7% less than the current emission.

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