Multiple-attribute decision making problems based on SVTNH methods
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ORIGINAL RESEARCH
Multiple‑attribute decision making problems based on SVTNH methods Chiranjibe Jana1 · G. Muhiuddin2 · Madhumangal Pal1 Received: 17 May 2019 / Accepted: 29 October 2019 © Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract The neutrosophic set (NS) is a leading tool in modeling of situations involving incomplete, indeterminate and inconsistent information. The single-valued neutrosophic sets (SVNs) is more useful tool than neutrosophic sets in some applications of engineering and scientific problems. In this paper, we study Hamacher operations and operations between single-valued trapezoidal neutrosophic numbers. Then we propose the single-valued trapezoidal neutrosophic Hamacher weighted arithmetic averaging (SVTNHWA) operator, single-valued trapezoidal neutrosophic Hamacher ordered weighted arithmetic averaging (SVTNHOWA) operator, single-valued trapezoidal neutrosophic Hamacher hybrid weighted averaging (SVTNHHWA) operator, single-valued trapezoidal neutrosophic Hamacher weighted geometric averaging (SVTNHWGA) operator and single-valued trapezoidal neutrosophic Hamacher ordered weighted geometric averaging (SVTNHOWGA) operator and single-valued trapezoidal neutrosophic Hamacher hybrid weighted geometric averaging (SVTNHHWGA) operator, and obtain some of their properties. Furthermore, we developed a multiple-attribute decision-making method in single-valued trapezoidal neutrosophic (SVTN) environment based on these operators. Finally, we proposed an application of MADM problem in assessment of potential of software system commercialization. Keywords Single-valued trapezoidal neutrosophic number · Hamacher operation · Arithmetic averaging operator · Geometric averaging operator · MADM method
1 Introduction Multi-attribute decision-making (MADM) problem under different uncertain environments is an interesting research tool having received more and more attention by the researchers in the recent years (Gao et al. 2018; Lu et al. 2019; Wu et al. 2019; Tang and Wei 2019; Garg and Kumar 2018; Zhang et al. 2019; Jana and Pal 2019a, b; Jana et al. 2019b, c). The main aim of this technique is to choose the best alternative among the finite set of alternatives as claimed by the decision makers under the preference values of the alternatives. It has been extensively applied with quantitative or qualitative attribute values and has a board * Chiranjibe Jana [email protected] 1
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia
2
application in management model (Teixeira et al. 2018), economic analysis (Xu 1987), operation research (Xu 1988), analytic management (Levy et al. 2016), etc. As our modern society move forward with the decision-making process, so it always faces imprecise, vague and uncertain facts to take a decision in solving decision-making problems. Neutrosophic set (NS) a tremendous branch of philosophy was p
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