P. Balasubramaniam and R. Uthayakumar (Eds.): ICMMSC 2012, CCIS 283, pp. 333–342, 2012. © Springer-Verlag Berlin Heidelberg 2012 A Search for the Correlation Coefficient of Triangular and Trapezoidal Intuitionistic Fuzzy Sets for Multiple Attribute Group Decision Making John Robinson P. and Henry Amirtharaj E.C. PG and Research Department of Mathematics, Bishop Heber College Tiruchirappalli – 620 017, Tamil Nadu, India robijohnsharon@gmail.com, henry_23@rediff.com Abstract. This paper introduces a new technique for defining the correlation coefficient of triangular and trapezoidal intuitionistic fuzzy sets for solving Multi-attribute Group Decision Making (MAGDM) problems. In situations where the information or the data is of the form of triangular or trapezoidal intuitionistic fuzzy numbers, some arithmetic aggregation operators, namely the trapezoidal intuitionistic fuzzy ordered weighted averaging (TzIFOWA) operator and the trapezoidal intuitionistic fuzzy hybrid aggregation (TzIFHA) operator are utilized. A new model is developed to solve the MAGDM problems using a new type of correlation coefficient defined for trapezoidal intuitionistic fuzzy sets based on the trapezoidal intuitionistic fuzzy weighted arithmetic averaging (TzIFWAA) operator and the TzIFHA operator. Keywords: Multiple Attribute Group Decision Making, Correlation of Triangular Intuitionistic Fuzzy Number, Trapezoidal Intuitionistic Fuzzy Ordered Weighted Averaging Operator, Trapezoidal Intuitionistic Fuzzy Hybrid Aggregation Operator. 1 Introduction Out of several higher-order fuzzy sets, Intuitionistic Fuzzy Set (IFS) was first introduced by Atanassov [1], [2] had been found to be compatible to deal with vagueness. With best of our knowledge, Burillo [3], [4] proposed the definition of intuitionistic fuzzy number (IFN) and studied the perturbations of IFN and the first properties of the correlation [4] between these numbers. Triangular IFS is a special case of IFSs, with two characterizations, namely the triangular fuzzy characterization and the intuitionistic fuzzy characterization [11], [13]. A MAGDM problem is to find a desirable solution from a finite number of feasible alternatives assessed on multiple attributes, both quantitative and qualitative ([9], [14] and [15]). In order to choose a desirable solution, the decision maker often provides his/her preference information which takes the form of numerical values, such as exact values, interval number values and fuzzy numbers [5]. Hence, MAGDM problems under a intuitionistic fuzzy or a triangular intuitionistic fuzzy environment is an interesting area of study for