Multi-criteria decision support models under fuzzy credibility rough numbers and their application in green supply selection.

As the increasing environmental issues, various companies have take initiatives to produce green products or to select green suppliers which maximize the business performance and minimize the environmental pollution. The real numbers data have imbiguity and uncertainty due to described by classical tools. Therefore, we consider a new type of fuzzy set, fuzzy credibility rough sets. In fuzzy credibility rough set has credibility membership of positive membership and they reduced the imbiguity in data information. In this paper we have defined a new set called fuzzy credibility rough set (FCRS), after that we defined Frank operational laws for FCRS information. Using these operational laws, we defined a series of aggregation operators that is fuzzy credibility Frank rough weigthed averaging aggregation operators, fuzzy credibility Frank rough ordered weigthed averaging aggregation operators, fuzzy credibility Frank rough hybrid weigthed averaging aggregation operators and its basic properties like boundedness, monotonicity and idempotency. As there is no work which is based on Frank norms aggregation operators under FCRS information. So, we defined a series of aggregation operators that can help us to collect the data for various green suppliers management. We developed a new set called fuzzy credibility rough set (FCRS). We developed a new Frank norms operational laws under FCRS information. We developed a series of aggregation operators. We developed and extend various steps of GRA, VIKOR and TOPSIS method under FCRS information. We explained the application of our proposed work to a real life decision making problem (green supplier management). All the proposed work is to applied to real life decision making problems (green supplier management) to find the best optimal result. Firstly we can collect the data from the decision makers using the proposed aggregation operators and then we applied all the steps of developed method to find the solution in case of green supplier management.