Normalized projection approach to group decision-making with hybrid decision information
- PDF / 2,688,843 Bytes
- 11 Pages / 595.276 x 790.866 pts Page_size
- 31 Downloads / 161 Views
ORIGINAL ARTICLE
Normalized projection approach to group decision‑making with hybrid decision information Chuan Yue1
Received: 14 March 2016 / Accepted: 3 February 2017 © Springer-Verlag Berlin Heidelberg 2017
Abstract Projection is an important measure in decision science, and it is also often used as a tool for various administrators. However, there are some defects in the existing projection models. To solve this significant scientific problem, this paper intends to establish new projection measures between two real vectors and between two interval vectors. First, the hidden flaws of existing projection measures are pertinently shown, and new projection measures in real number and interval settings are established, which satisfy the condition of normalization. Then new projection measures are applied to group decision-making with hybrid decision information, including real numbers and interval data. Finally, an experimental analysis shows the applicability, feasibility, effectiveness and advantages of the proposed methods. Keywords Normalized projection measure · Group decision-making · Interval data · Hybrid decision information
1 Introduction Projection measure can consider not only the distance but also the angle between two decision objects [25]. Projection methods have been successfully applied to many multi-attribute decision-making (MADM) problems [34, 36] and group decision-making (GDM) problems [30, 31]. However, this research finds that the existing projection * Chuan Yue yuechuan‑[email protected] 1
College of Mathematics and Computer Science, Guangdong Ocean University, Zhanjiang 524088, China
formulae are unreasonable in real and interval settings (see Examples 1–4 below). In order to improve them, this paper intends to develop two normalized projection measures, and to apply them to GDM with hybrid decision information, including real numbers and interval data. The GDM [3, 4] is a type of decision-making problems [1, 13], which has been widely developed. For example, Yue [27] developed a geometric approach for ranking interval-valued intuitionistic fuzzy numbers with an application to GDM. Verma [15] introduced a GDM method based on generalized trapezoid fuzzy linguistic prioritized weighted average operator. Dong and Herrera-Viedma [5] proposed a consistency-driven automatic methodology to set interval numerical scales of 2-tuple linguistic term sets and its use in the linguistic GDM with preference relation. Cabrerizo et al. [2] developed a method defined in a heterogeneous context. However, this research finds that the projectionbased decision methods are lacking in GDM problems with hybrid decision information. It is noted that an interesting exception is proposed by Yue and Jia [32]. Unfortunately, sometimes the projection measure proposed by Yue and Jia [32] is also unreasonable (see Examples 2 and 4). To fill this research gap, this work will establish a GDM method with hybrid decision information based on new projection measures. The main motivations of this work are as follows. 1.
Data Loading...
