Group multi-criteria decision making using intuitionistic multi-fuzzy sets
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RESEARCH
Open Access
Group multi-criteria decision making using intuitionistic multi-fuzzy sets Sujit Das1, Mohuya B Kar2 and Samarjit Kar3* * Correspondence: [email protected] 3 Department of Mathematics, National Institute of Technology, Durgapur, West Bengal 713209, India Full list of author information is available at the end of the article
Abstract In this paper we propose an efficient approach for group multi-criteria decision making (MCDM) based on intuitionistic multi-fuzzy set (IMFS). First we construct intuitionistic multi-fuzzy matrices for decision makers with respect to the criteria (attributes) of the alternatives. Based on intuitionistic multi-fuzzy matrices, we construct the aggregated intuitionistic multi-fuzzy matrix using the proposed intuitionistic multi-fuzzy weighted averaging (IMFWA) operator. Then we use Hamming distance and Euclidean distance measurements in the context of IMFS between the aggregated matrix and the specified sample matrix to reach the optimal decision. This paper also presents score function and accuracy function of IMFS with an application to MCDM. Finally, a real-life case study related to heart disease diagnosis problem is provided to illustrate the advantage of the proposed approach. Keywords: Group MCDM; Intuitionistic multi-fuzzy set; Intuitionistic multi-fuzzy weighted averaging operator; Hamming distance; Euclidean distance; Score function; Accuracy function; Medical diagnosis
Introduction Intuitionistic fuzzy set (IFS) was introduced by Atanassov [1] and can be shown as a generalization and extension of Zadeh's fuzzy set theory [2]. IFS has emerged as an active research area mainly for solving multiple-criteria decision making problems [3-9] and group decision making (GDM) problems [10-12] where the values of local criteria (attributes) of alternatives and/or their weights are intuitionistic fuzzy values (IFVs). Intuitionistic fuzzy set covers such kind of situations where a human being can express the degree of belonging of an element to a set as well as degree of non-belonging of an element to a set. A complete account of the development of multi-set theory has been seen in [13]. As a generalization of multi-set, Yager [14] introduced the concept of multi-fuzzy set (MFS). An element of a MFS can occur more than once with possibly the same or different membership values. MFS theory is an extension of theories of fuzzy sets [2], L-fuzzy sets [15], and intuitionistic fuzzy sets [16]. Group multi-criteria decision making requires certain methods to aggregate the opinions provided by different experts. Yager [17] proposed an interesting and well-grounded approach, namely the ordered weighted averaging (OWA) [17], which enabled aggregation of the variables in terms of their order in the set. © 2013 Das et al.; licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the
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