Decision making based on linguistic interval-valued intuitionistic neutrosophic Dombi fuzzy hybrid weighted geometric op
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Decision making based on linguistic interval-valued intuitionistic neutrosophic Dombi fuzzy hybrid weighted geometric operator Aliya Fahmi1 • Fazli Amin2 • Sidra Niaz2
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, we proposed the notion of a linguistic interval-valued intuitionistic neutrosophic fuzzy number. We define some score and accuracy functions of LIVINFNs are defined with a brief study of related properties. Moreover, we propose the geometric forms of LIVINDFWG, LIVINDFOWG, and LIVINDFHWG operator, which is called the geometric operators. Then, we present its characteristics and some special cases. Moreover, we put forward two new MADM approaches founded on the developed LIVINDFWG and LIVINDFOWG operators. Finally, a representative example is provided to verify the effectiveness and superiority of the proposed method by comparing it with other several existing representative MAGDM methods. Keywords Linguistic term LIVINDFWG operator LIVINDFOWG operator LIVINDFHWG operator MCDM
1 Introduction The decision-making problems of real life do not provide enough information to make the decision. Smarandache (1998) gave the idea of the neutrosophic set which is a much better concept to express that kind of information. In 1965 Zadeh (1965) defined the concept of membership function between 0 and 1: Atanassov (1989) proposed the concept of the fuzzy set to intuitionistic fuzzy set (IFS). It is a more generalized form of fuzzy set. The spectacular property of an IFS is that it assigns membership degree and nonmembership degree to every element. The appropriate use of IFSs is that it is used in the field of decision making. Atanassov (1994) proposed the concept of interval-value intuitionistic fuzzy (IVIF) set. Smarandache (1998) defined a neutrosophic set for undefined information. Gau and Buehrer (1993) introduced the conventional fuzzy c-means clustering (FCM) algorithm with justified number of clusters. Chen and Ten (1994) defined the score function which
Communicated by A. Di Nola. & Aliya Fahmi [email protected] 1
School of Mathematics, Department of Management Sciences, The University of Faisalabad, Faisalabad, Pakistan
2
Department of Mathematics, Hazara University Mansehra, Mansehra, Pakistan
deals with the multiple attribute decision making (MACD) problems based on uncertain values (Atanassov 1999) or equal to IF number, as figure out by Deschrijver and Kerre (2007). Moreover, Hong and Choi (2000) proposed an accuracy function to describe additional differentiation powers. Li (2005) proposed some techniques for solving the MADM problems in which the attributes values and attribute weights are intuitionistic fuzzy numbers. By using the multiplication operation of Atanassove (1999) and power operation by De et al. (2000) on IFSs Xu and Yager (2006) proposed some geometric operators, like IFWG operator, IFOWG operator, and IFHG operator. Moreover, Xu (2007) introduced IFOW averaging operator, IFH a
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