Hesitant interval neutrosophic linguistic set and its application in multiple attribute decision making
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ORIGINAL ARTICLE
Hesitant interval neutrosophic linguistic set and its application in multiple attribute decision making Jun Ye1 Received: 22 December 2015 / Accepted: 14 November 2017 © Springer-Verlag GmbH Germany, part of Springer Nature 2017
Abstract Motivated by the ideas of interval neutrosophic linguistic sets and hesitant fuzzy sets (HFSs), this paper proposes the concept of hesitant interval neutrosophic linguistic sets by combining the three concepts of the HFS, interval neutrosophic set, and linguistic set and defines the operational laws of hesitant interval neutrosophic linguistic elements (HINLEs) and the score, accuracy, and certainty functions for HINLEs. Then, a hesitant interval neutrosophic linguistic weighted average (HINLWA) operator and a hesitant interval neutrosophic linguistic weighted geometric (HINLWG) operator are developed to aggregate the hesitant interval neutrosophic linguistic information. Moreover, some desirable properties of the two operators are investigated. A decision-making method based on the HINLWA and HINLWG operators is developed to handle multiple attribute decision-making problems, in which evaluation values of each alternative with respect to attributes are expressed by the form of HINLEs, under hesitant interval neutrosophic linguistic environment. Finally, an illustrative example about investment alternatives is given to demonstrate the application of the developed method. Keywords Hesitant interval neutrosophic linguistic set · Hesitant interval neutrosophic linguistic element · Score function · Hesitant interval neutrosophic linguistic weighted average (HINLWA) operator · Hesitant interval neutrosophic linguistic weighted geometric (HINLWG) operator · Decision making
1 Introduction In real decision-making problems, the decision information is often incomplete, indeterminate, and inconsistent. Hence, fuzzy decision making is a useful method under various fuzzy environments [5–9]. Since the neutrosophic set proposed by Smarandache [12] can be better to express incomplete, indeterminate, and inconsistent information, some researchers have introduced some subclasses of neutrosophic sets to easily apply in real science and engineering areas. Wang et al. [15, 16] introduced the concepts of an interval neutrosophic set (INS) and a single-valued neutrosophic set (SVNS), which are the subclasses of a neutrosophic set, and provided the set-theoretic operators and various properties of SVNSs and INSs. Then, Ye [18] proposed a correlation coefficient of SVNSs and applied it to multiple attribute * Jun Ye [email protected] 1
Department of Electrical and Information Engineering, Shaoxing University, 508 Huancheng West Road, Shaoxing 312000, Zhejiang, People’s Republic of China
decision-making problems with single-valued neutrosophic information. Ye [19] presented a single-valued neutrosophic cross-entropy measure for single-valued neutrosophic multiple attribute decision-making problems. Liu and Wang [11] presented single-valued neutrosophic normalized weighted Bonferro
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