MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

TLDR

The intuitionistic fuzzy set, introduced by Atanassov as a generalization of Zadeh’s fuzzy set, provides a framework for handling fuzziness and uncertainty. This study investigates multiple‑attribute decision‑making problems where attribute weights are incomplete and attribute values are expressed as intuitionistic fuzzy numbers. The authors define an intuitionistic fuzzy ideal solution and, using a distance measure, formulate optimization models to derive attribute weights, then develop ranking procedures and extend them to interval‑valued intuitionistic fuzzy information. Illustrative examples demonstrate the effectiveness and practicality of the proposed models and procedures.

Abstract

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.