Neural net influenced magdm problem with modified choquet integral aggregation operators and correlation coefficient for triangular fuzzy intuitionistic fuzzy sets

Abstract

With respect to Multiple Attribute Group Decision Making (MAGDM) problems in which attribute values take the form of Triangular Fuzzy Intuitionistic Fuzzy Set (TrFIFS) values, a new decision-making analysis method is developed. First, a novel correlation coefficient for the TrFIFS is proposed and then utilized in the decision-making process for the ranking of the best alternatives. The new correlation coefficient is substantiated by several theorems proved to establish its effectiveness. Then, two TrFIFS Choquet integral aggregation operators are developed and utilized in solving the MAGDM problem. The Triangular  Fuzzy Intuitionistic Fuzzy Improved Choquet Integral Averaging (TrFIFIMCOA) operator for TrFIFS and Triangular  Fuzzy Intuitionistic Fuzzy Improved Choquet Integral Geometric (TrFIFIMCOG) operator for TrFIFS are proposed and some desirable properties are studied. The prominent characteristic of the operators is that they can not only consider the importance of the elements or their ordered positions, but also reflect the correlation among the elements or their ordered positions. Using the proposed two operators, the input vector is produced for Artificial Neural Network (ANN) which is solved to provide an effective solution for MAGDM problem. The newly proposed correlation coefficient and the aggregation operators are effectively utilized to solve real life decision problems. Finally, an illustrative example has been given to show the developed method and comparisons are made with existing methods.