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