Fuzzy Multiple Criteria Hierarchical Group Decision-Making Based on Interval Type-2 Fuzzy Sets

Abstract

In this paper, we present a new method for handling fuzzy multiple criteria hierarchical group decision-making problems based on arithmetic operations and fuzzy preference relations of interval type-2 fuzzy sets. Because the time complexity of the proposed method is O( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nk</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> is the number of criteria and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> is the number of decision-makers, it is more efficient than Wu and Mendel's method, whose time complexity is O( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">mnk</i> ), where <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> is the number of α-cuts, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> is the number of criteria and <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> is the number of decision-makers. Moreover, the proposed method can overcome another drawback of Wu and Mendel's method, i.e., it can handle evaluating values represented by nonnormal interval type-2 fuzzy sets. The proposed method provides us with a useful way to handle fuzzy multiple criteria hierarchical group decision-making problems.