On inclusion measures of intuitionistic and interval-valued intuitionistic fuzzy values and their applications to group
- PDF / 483,707 Bytes
- 11 Pages / 595.276 x 790.866 pts Page_size
- 87 Downloads / 254 Views
ORIGINAL ARTICLE
On inclusion measures of intuitionistic and interval-valued intuitionistic fuzzy values and their applications to group decision making Hong-Ying Zhang1 • Shu-Yun Yang1 • Zhi-Wei Yue1
Received: 11 December 2014 / Accepted: 6 August 2015 Springer-Verlag Berlin Heidelberg 2015
Abstract Ranking intuitionistic fuzzy values (IFVs) and interval-valued intuitionistic fuzzy values (IVIFVs) is an important and necessary work in intuitionistic fuzzy group decision making. Since the set of all IFVs is a poset and inclusion measure indicates the degree to which a given element of a poset is contained in another one. This paper studies hybrid monotonic (HM) inclusion measures of IFVs and IVIFVs respectively and discuss their applications to group decision making. Firstly, HM inclusion measure is defined on the posets of all IFVs and IVIFVs respectively. Then HM inclusion measures are studied by constructive approach. Furthermore, the HM inclusion measures are employed to make intuitionistic and interval-valued intuitionistic fuzzy group decisions. Lastly, practical examples are provided to illustrate the developed approaches respectively. Keywords Intuitionistic fuzzy value Interval-valued intuitionistic fuzzy value HM inclusion measure Group decision making
& Hong-Ying Zhang [email protected] Shu-Yun Yang [email protected] Zhi-Wei Yue [email protected] 1
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, Shaanxi, People’s Republic of China
1 Introduction Since fuzzy set theory was proposed by Zadeh [52], there have been a great number of research works in fuzzy fields and the relative fields, including the applications and theoretical generalizations. Intuitionistic fuzzy set (IFS for short), proposed by Atanassov [3], is a generalization of fuzzy set theory which is defined by a membership degree, a non-membership degree and a hesitancy degree. Over the last decades, the IFS theory has been used to a wide range of applications, such as decision making [6, 37, 38, 46], logic programming [7], topology [1, 2, 14, 17, 29, 32], medical diagnosis [15], pattern recognition [26, 28, 31, 39], machine learning and market prediction [28], and so on. Atanassov [4] further introduced the interval-valued intuitionistic fuzzy sets (IVIFSs), as a generalization of IFSs that are more actual. The relations and operations of IVIFSs [8, 13], the correlation coefficients of IVIFSs [11, 21], the topology of IVIFSs [32], and the relationships among the IVIFS, L-fuzzy set, IFS, and interval-valued fuzzy set [16] have been studied. Multi-criteria decision making was first proposed in early 1970s, after which lots of ranking methods and related analyses occurred quickly. Because of the uncertainty in mind, the study in multi-criteria decision making based on IFSs as well as interval-valued fuzzy sets become hot topics. Hong and Choi [20] put forward new methods to solve multi-criteria fuzzy decision-making problems based on vague set theory. Moreover, multi-criteri
Data Loading...
