Type-2 single-valued neutrosophic sets and their applications in multi-criteria group decision making based on TOPSIS me
- PDF / 1,066,363 Bytes
- 20 Pages / 595.276 x 790.866 pts Page_size
- 112 Downloads / 178 Views
ORIGINAL RESEARCH
Type-2 single-valued neutrosophic sets and their applications in multicriteria group decision making based on TOPSIS method Faruk Karaaslan1
•
Fatih Hunu1
Received: 8 July 2019 / Accepted: 3 January 2020 Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Type-2 fuzzy set and type-2 intuitionistic fuzzy set are important tools for dealing with problems involving uncertainty and linguistic variables. However, it is sometimes difficult to model problems involving inconsistent data by using these approaches. In this paper, the concept of type-2 single-valued neutrosophic sets is defined in order to cope with this difficulty. Also, some distance measure methods for type-2 single-valued neutrosophic sets based on Hausdorff, Hamming and Euclidean distances are introduced and some properties of them are investigated. Furthermore, a multi-criteria group decision-making method is developed based on TOPSIS approach under the type-2 single-valued neutrosophic environment. Finally, an illustrative example is given in order to show the validity and process of the proposed method. Keywords Single-valued neutrosophic set Type-2 single-valued neutrosophic number Decision making TOPSIS method
1 Introduction The fuzzy set theory was proposed by Zadeh (1965) as a generalization of classical sets. After Zadeh’s work, the fuzzy set theory has engaged attention of researchers and academic studies related to the fuzzy set theory have increased rapidly in various areas such as engineering, economy and social sciences. A fuzzy set is characterized by a membership function. There is a close relation between the concept of linguistic truth and the fuzzy sets whose degrees of membership are specified in linguistic terms such as low, medium, high, very low, not low and not high, etc. On the other hand, a fuzzy set A characterized by a membership function lA involving linguistic variables can be considered as a mapping from discourse universe U to subsets of the interval [0, 1] (Zadeh 1975).To model such situations, the concept of type-2 fuzzy sets was introduced by Zadeh (1975). Operations between two type& Faruk Karaaslan [email protected] Fatih Hunu [email protected] 1
Department of Mathematics, Faculty of Science, C¸ankırı Karatekin University, 18100 C¸ankırı, Turkey
2 fuzzy sets were studied in (Dubois and Pirade 1980; Karnik and Mendel 2001; Mizumoto and Tanaka 1976). In 2002, a new representation for the type-2 fuzzy sets was presented by Mendel and John (2002) and this representation was used to define union, intersection, and complement of the type-2 fuzzy sets without using the Extension Principle. Many researchers have studied on the type-2 fuzzy sets. For example, Hung and Yang (2004) proposed a similarity measure method between two type-2 fuzzy sets and obtained properties of these measures, Yang and Ling (2009) introduced similarity and inclusion measures between type-2 fuzzy sets and discussed their properties, Sing (2014) introduced distance measures between two type-
Data Loading...
