**5. Conclusions**

Many studies have applied the MCDM approach to various fields of science and engineering, and their numbers have been increasing over the past years. The fuzzy MCDM model has been applied to supplier selection problems. Although some studies have considered a review of applications of MCDM approaches in this field, little work has focused on this problem in a fuzzy environment. This is a reason why hybrid ANP with fuzzy logic and DEA is proposed in this study.

Initially, we proposed the ANP model combined with a fuzzy set, to evaluate supplier selection criteria and define a priority of each supplier, which are able to be utilized to clarify important criteria that directly affect the profitability of the business. The FANP can be used for ranking suppliers but the number of supplier selections is practically limited because of the number of pairwise comparisons that need to be made, and a disadvantage of the FANP approach is that input data, expressed in linguistic terms, depend on the experience of decision-makers and, thus, involves subjectivity. This is a reason why several DEA models are proposed for ranking suppliers in the final stage. The DEA model can handle hundreds of suppliers with multiple inputs and outputs for the best supplier rating. The FANP-DEA integration model supports a grea<sup>t</sup> deal of corporate decision-making because of the effectiveness and complication of this model, for exactly choosing the most suitable supplier. Finally, this research will provide a potential suppliers list, which has a conditioned response to the enterprises' supply requirements.

The main contribution of this research is to develop complete approaches for supplier evaluation and selection of the rice supply chain as a typical example. This is a useful proposed model on an academic and practical front. The FANP-DEA method not only provides reasonable results but also allows the decision-maker to visualize the impact of different criteria in the final result. Furthermore, this integrated model may offer valuable insights, as well as provide methods for other sectors to select and evaluate suppliers. This model can also be applied to many different industries for future research directions.

For improving these MCDM model, outlier detection and the curse of dimensionality of the DEA model will be considered in future research. Moreover, different methodologies, such as the preference ranking organization method for enrichment of evaluations (PROMETHEE), fuzzy data envelopment analysis (FDEA), etc., can also been combined for different scenarios.

**Author Contributions:** In this research, C.-N.W. contributed to generating the research ideas and designing the theoretical verifications, and reviewed the manuscript; V.T.N. contributed the research ideas, designed the framework, collected data, analyzed the data, and summarized and wrote the manuscript; D.H.D. collected data, analyzed the data, wrote the manuscript; and H.T.D. wrote and formatted the manuscript.

**Conflicts of Interest:** The authors declare no conflict of interest.
