The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group de
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ORIGINAL ARTICLE
The neutrosophic number generalized weighted power averaging operator and its application in multiple attribute group decision making Peide Liu1 • Xi Liu1
Received: 26 July 2015 / Accepted: 29 January 2016 Ó Springer-Verlag Berlin Heidelberg 2016
Abstract Neutrosophic number (NN) is a useful tool which is used to overcome the difficulty of describing indeterminate evaluation information. The purpose of the study is to propose some power aggregation operators based on neutrosophic number which is used to deal with multiple attributes group decision making problems more effectively. Firstly, the basic concepts and the operational rules and the characteristics of NNs are introduced. Then, some aggregation operators based on neutrosophic numbers are developed, included the neutrosophic number weighted power averaging (NNWPA) operator, the neutrosophic number weighted geometric power averaging (NNWGPA) operator, the generalized neutrosophic number weighted power averaging (GNNWPA) operator. At the same time, the properties of above operators are studied such as idempotency, monotonicity, boundedness and so on. Then, the generalized neutrosophic number weighted power averaging (GNNWPA) operator is applied to solve multiple attribute group decision making (MAGDM) problems. Afterwards, a numerical example is given to demonstrate the effective of the new developed method, and some comparison are conducted to verify the influence of different parameters or to reveal the difference with another method. In the end, the main conclusion of this paper is summarized. Keywords Multiple attribute group decision making (MAGDM) Neutrosophic numbers Power aggregation
& Peide Liu [email protected] 1
School of Management Science and Engineering, Shandong University of Finance and Economics, Jinan 250014, Shandong, China
operator Neutrosophic numbers power aggregation operator
1 Introduction In real decision making, since the fuzziness and complexity of decision making problems, sometimes it is different to express the people’s judgments by crisp numbers in conveying their opinions thoroughly. Zadeh [1] innovatively proposed the fuzzy set (FS) to cope with the fuzzy information. Since the fuzzy set has only the membership degree and has not the non-membership degree, Atanassov [2] made an improvement to overcome this shortcoming, and proposed the intuitionistic fuzzy set (IFS) which is made up with membership degree and non-membership degree. However IFS did not consider the indeterminacymembership degree. Further, Smarandache [3] proposed the neutrosophic set (NS) which added the independent indeterminacy-membership function to the IFS. Obviously, NS is easier to express uncertain information and there are some research results for NS [4–14]. In addition, Smarandache [3, 15] further proposed the neutrosophic numbers (NNs), and it can be divided into determinate part and indeterminate part. The neutrosophic number (NN) is in the form of N ¼ a þ bI. As we can see that a is the determinate part and bI represe
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