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Article

Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment

1
Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
2
Department of Mathematics, Government College Women University Faisalabad, Punjab 38000, Pakistan
3
Science Department 705 Gurley Ave., University of New Mexico Mathematics, Gallup, NM 87301, USA
*
Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 1058; https://doi.org/10.3390/sym11081058
Submission received: 25 June 2019 / Revised: 26 July 2019 / Accepted: 1 August 2019 / Published: 17 August 2019

Abstract

With the development of the social economy and enlarged volume of information, the application of multiple-attribute decision-making (MADM) has become increasingly complex, uncertain, and obscure. As a further generalization of hesitant fuzzy set (HFS), simplified neutrosophic hesitant fuzzy set (SNHFS) is an efficient tool to process the vague information and contains the ideas of a single-valued neutrosophic hesitant fuzzy set (SVNHFS) and an interval neutrosophic hesitant fuzzy set (INHFS). In this paper, we propose a decision-making approach based on the maximizing deviation method and TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) to solve the MADM problems, in which the attribute weight information is incomplete, and the decision information is expressed in simplified neutrosophic hesitant fuzzy elements. Firstly, we inaugurate an optimization model on the basis of maximizing deviation method, which is useful to determine the attribute weights. Secondly, using the idea of the TOPSIS, we determine the relative closeness coefficient of each alternative and based on which we rank the considered alternatives to select the optimal one(s). Finally, we use a numerical example to show the detailed implementation procedure and effectiveness of our method in solving MADM problems under simplified neutrosophic hesitant fuzzy environment.
Keywords: simplified neutrosophic hesitant fuzzy set; multi-attribute decision-making; maximizing deviation; TOPSIS simplified neutrosophic hesitant fuzzy set; multi-attribute decision-making; maximizing deviation; TOPSIS

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MDPI and ACS Style

Akram, M.; Naz, S.; Smarandache, F. Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment. Symmetry 2019, 11, 1058. https://doi.org/10.3390/sym11081058

AMA Style

Akram M, Naz S, Smarandache F. Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment. Symmetry. 2019; 11(8):1058. https://doi.org/10.3390/sym11081058

Chicago/Turabian Style

Akram, Muhammad, Sumera Naz, and Florentin Smarandache. 2019. "Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment" Symmetry 11, no. 8: 1058. https://doi.org/10.3390/sym11081058

APA Style

Akram, M., Naz, S., & Smarandache, F. (2019). Generalization of Maximizing Deviation and TOPSIS Method for MADM in Simplified Neutrosophic Hesitant Fuzzy Environment. Symmetry, 11(8), 1058. https://doi.org/10.3390/sym11081058

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