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NC-Cross Entropy Based MADM Strategy in Neutrosophic Cubic Set Environment

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  • Surapati Pramanik

    (Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, P.O.-Narayanpur, District–North 24 Parganas, Bhatpara 743126, West Bengal, India)

  • Shyamal Dalapati

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.-Botanic Garden, Howrah 711103, West Bengal, India)

  • Shariful Alam

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.-Botanic Garden, Howrah 711103, West Bengal, India)

  • Florentin Smarandache

    (Department of Mathematics & Science, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA)

  • Tapan Kumar Roy

    (Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.-Botanic Garden, Howrah 711103, West Bengal, India)

Abstract

The objective of the paper is to introduce a new cross entropy measure in a neutrosophic cubic set (NCS) environment, which we call NC-cross entropy measure. We prove its basic properties. We also propose weighted NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision-making (MADM) strategy based on a weighted NC-cross entropy measure. To show the feasibility and applicability of the proposed multi attribute decision-making strategy, we solve an illustrative example of the multi attribute decision-making problem.

Suggested Citation

  • Surapati Pramanik & Shyamal Dalapati & Shariful Alam & Florentin Smarandache & Tapan Kumar Roy, 2018. "NC-Cross Entropy Based MADM Strategy in Neutrosophic Cubic Set Environment," Mathematics, MDPI, vol. 6(5), pages 1-26, April.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:5:p:67-:d:143864
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    References listed on IDEAS

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    1. Edmundas Kazimieras Zavadskas & Romualdas Baušys & Marius Lazauskas, 2015. "Sustainable Assessment of Alternative Sites for the Construction of a Waste Incineration Plant by Applying WASPAS Method with Single-Valued Neutrosophic Set," Sustainability, MDPI, vol. 7(12), pages 1-14, December.
    2. H. D. Cheng & Yanhui Guo & Yingtao Zhang, 2011. "A Novel Image Segmentation Approach Based On Neutrosophic Set And Improved Fuzzy C-Means Algorithm," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 155-171.
    3. Zhang-peng Tian & Hong-yu Zhang & Jing Wang & Jian-qiang Wang & Xiao-hong Chen, 2016. "Multi-criteria decision-making method based on a cross-entropy with interval neutrosophic sets," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(15), pages 3598-3608, November.
    4. Athar Kharal, 2014. "A Neutrosophic Multi-Criteria Decision Making Method," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 10(02), pages 143-162.
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    Cited by:

    1. Xiaozhuan Gao & Yong Deng, 2019. "The generalization negation of probability distribution and its application in target recognition based on sensor fusion," International Journal of Distributed Sensor Networks, , vol. 15(5), pages 15501477198, May.
    2. Muhammad Gulistan & Mutaz Mohammad & Faruk Karaaslan & Seifedine Kadry & Salma Khan & Hafiz Abdul Wahab, 2019. "Neutrosophic cubic Heronian mean operators with applications in multiple attribute group decision-making using cosine similarity functions," International Journal of Distributed Sensor Networks, , vol. 15(9), pages 15501477198, September.

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