A complete ranking method for interval-valued intuitionistic fuzzy numbers and its applications to multicriteria decisio
- PDF / 273,048 Bytes
- 8 Pages / 595.276 x 790.866 pts Page_size
- 36 Downloads / 191 Views
METHODOLOGIES AND APPLICATION
A complete ranking method for interval-valued intuitionistic fuzzy numbers and its applications to multicriteria decision making Weiwei Huang1 · Fangwei Zhang2 · Shihe Xu3
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this study, a complete ranking method for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced by using a score function and three types of entropy functions. This work is motivated by the work of Lakshmana Gomathi Nayagam et al. (Soft Comput 21, 7077–7082, 2017) in which a novel non-hesitant score function for the theory of interval-valued intuitionistic fuzzy sets was introduced. The authors claimed that the proposed non-hesitant score function could overcome the shortcomings of some familiar methods. By using some examples, they pointed out that the non-hesitant score function is better compared with Sahin’s and Zhang et al.’s approaches. It is pointed out that although in some specific cases, the cited method overcomes the shortcomings of several of the existing methods mentioned, it also created new defects that can be solved by other methods. The main aim of this study is to give a complete ranking method for IVIFNs which can rank any two arbitrary IVIFNs. At last, two examples to demonstrate the effectiveness of the proposed method are provided. Keywords Interval-valued intuitionistic fuzzy numbers · Entropy function · Score function
1 Introduction Zadeh (1965) introduced the concept of fuzzy sets (FSs) (Zadeh 1965) which have been firmly established as a fruitful area of research, as well as of a tool for the evaluation of different objects and processes in nature and society. In recent years, some authors have introduced the extensions of the FSs, such as the terms “type-1 fuzzy sets” (T1FSs) ,“interval type-2 fuzzy sets” (IT2FSs), “generalized type-2 fuzzy sets” (GT2FSs) (see, e.g., Atanassov 2017; Castillo and Melin 2008; Castillo et al. 2014; Gonzalez et al. 2017; Ponce-Cruz et al. 2016 and references therein). Atanassov Communicated by V. Loia.
B B
Fangwei Zhang [email protected] Shihe Xu [email protected]
1
School of Education, Zhaoqing University, Zhaoqing 526061, Guangdong, People’s Republic of China
2
College of Transport and Communications, Shanghai Maritime University, Shanghai 201306, People’s Republic of China
3
School of Mathematics and Statistics, Zhaoqing University, Zhaoqing 526061, Guangdong, People’s Republic of China
(1986) proposed the intuitionistic fuzzy sets (IFSs). In the theories of IFSs, the relationship between an element and a set is described by two numbers which represent, respectively, the membership degree and non-membership degree of the element to its corresponding set. A comparison between type1 fuzzy sets (T1FSs) and intuitionistic fuzzy sets (IFSs) is made by Atanassov (2017), and some applications of IFSs were made (e.g., Shannon et al. 2006; Sotirov et al. 2018). Atanassov and Gargov (1989) proposed the concept of interval-valued intuitionistic fuzzy sets (IVIFSs) t
Data Loading...
