Vector aggregation operator and score function to solve multi-criteria decision making problem in neutrosophic environme
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ORIGINAL ARTICLE
Vector aggregation operator and score function to solve multi‑criteria decision making problem in neutrosophic environment Kanika Mandal1 · Kajla Basu1 Received: 28 May 2016 / Accepted: 17 April 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018
Abstract In our real world there exist uncertain, imprecise, incomplete, and inconsistent information. Those kinds of information can be suitably handled by neutrosophic fuzzy set as it is the generalization of classic set, fuzzy set and intuitionistic fuzzy set. The uncertain, imprecise, incomplete and inconsistent information provided by several sources need to be aggregated to come to a conclusion. Aggregation and fusion of information are basic concerns for all kinds of knowledge based systems. The main purpose of this paper is to aggregate neutrosophic fuzzy information by introducing a new aggregation operator in vector approach. The new approach is simple based on basic vector operations and reliable as it will always give a meaningful result. Also a new vector score function has been defined to compare the neutrosophic fuzzy numbers and explained through geometrical interpretation. The newly proposed vector score function always gives different values for any two different neutrosophic numbers. Further, a multiple-criteria decision-making method is established on the basis of the proposed operator and newly defined score function. Keywords Neutrosophic set · Vector aggregation operator · Vector score function · Decision making in vector approach
1 Introduction Decision making is the process of making a choice from the alternatives based on the values and preferences of decision makers (DMs). All the managerial functions such as planning, organizing, directing and controlling are governed by the process of decision making. The key issues of decision making problem is to find out the proper way to aggregate uncertain, imprecise, incomplete and inconsistent information related to each alternaive and rank the alternatives in a proper and justified manner. DMs have to take decisions based on uncertain and imprecise data. To address the uncertainties, fuzzy set (FS) theory has been successfully used in various decision making problems [1–6]. Liu et al. [7] conducted a bibliometric analysis on fuzzy decision-related research to find out some underlying patterns and dynamics. FS, an extension of
* Kanika Mandal [email protected]; [email protected] Kajla Basu [email protected] 1
Department of Mathematics, NIT, Durgapur 713209, India
ordinary or crisp set, was introduced by Zadeh [8]. FS only considers the membership degree but can not address the non membership degree of an element to the set. Regarding this issue, Atanasov [9] introduced the concept of intuitionistic fuzzy set (IFS ) in 1986 as an extension of FS considering membership and non membership degrees of an element to the set. Various multi-criteria decision making methods in IFS [10–16] have been proposed and developed in the past years. Yu et al. [17] discussed the
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