IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i6p965-d370688.html
   My bibliography  Save this article

Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making

Author

Listed:
  • Shio Gai Quek

    (Department of Actuarial Science and Applied Statistics, Faculty of Business & Information Science, UCSI University, Jalan Menara Gading, Cheras, Kuala Lumpur 56000, Malaysia)

  • Ganeshsree Selvachandran

    (Department of Actuarial Science and Applied Statistics, Faculty of Business & Information Science, UCSI University, Jalan Menara Gading, Cheras, Kuala Lumpur 56000, Malaysia)

  • Florentin Smarandache

    (Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301, USA)

  • J. Vimala

    (Department of Mathematics, Alagappa University, Karaikudi, Tamil Nadu 630003, India)

  • Son Hoang Le

    (Faculty of Information Technology, Ho Chi Minh City University of Technology (HUTECH), Ho Chi Minh City 700000, Vietnam)

  • Quang-Thinh Bui

    (Institute of Research and Development, Duy Tan University, Da Nang 550000, Vietnam
    Faculty of Electrical Engineering and Computer Science, VŠB-Technical University of Ostrava, 70800 Ostrava-Poruba, Czech Republic)

  • Vassilis C. Gerogiannis

    (Department of Digital Systems, University of Thessaly, GR 41500 Larissa, Greece)

Abstract

Plithogenic set is an extension of the crisp set, fuzzy set, intuitionistic fuzzy set, and neutrosophic sets, whose elements are characterized by one or more attributes, and each attribute can assume many values. Each attribute has a corresponding degree of appurtenance of the element to the set with respect to the given criteria. In order to obtain a better accuracy and for a more exact exclusion (partial order), a contradiction or dissimilarity degree is defined between each attribute value and the dominant attribute value. In this paper, entropy measures for plithogenic sets have been introduced. The requirements for any function to be an entropy measure of plithogenic sets are outlined in the axiomatic definition of the plithogenic entropy using the axiomatic requirements of neutrosophic entropy. Several new formulae for the entropy measure of plithogenic sets are also introduced. The newly introduced entropy measures are then applied to a multi-attribute decision making problem related to the selection of locations.

Suggested Citation

  • Shio Gai Quek & Ganeshsree Selvachandran & Florentin Smarandache & J. Vimala & Son Hoang Le & Quang-Thinh Bui & Vassilis C. Gerogiannis, 2020. "Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:965-:d:370688
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/6/965/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/6/965/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    2. Miin-Shen Yang & Zahid Hussain, 2018. "Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making," Complexity, Hindawi, vol. 2018, pages 1-14, November.
    3. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    4. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    6. Tongke Fan & Jing Xu, 2020. "Image Classification of Crop Diseases and Pests Based on Deep Learning and Fuzzy System," International Journal of Data Warehousing and Mining (IJDWM), IGI Global, vol. 16(2), pages 34-47, April.
    7. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    8. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    10. Guiwu Wei, 2016. "Picture fuzzy cross-entropy for multiple attribute decision making problems," Journal of Business Economics and Management, Taylor & Francis Journals, vol. 17(4), pages 491-502, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Fujita, Takaaki, 2024. "Expanding Horizons of Plithogenic SuperHyperStructures: Applications in Decision-Making, Control, and Neuro Systems," SocArXiv xqrd6_v1, Center for Open Science.
    2. Fujita, Takaaki, 2024. "Expanding Horizons of Plithogenic SuperHyperStructures: Applications in Decision-Making, Control, and Neuro Systems," SocArXiv xqrd6, Center for Open Science.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kritana Prueksakorn & Cheng-Xu Piao & Hyunchul Ha & Taehyeung Kim, 2015. "Computational and Experimental Investigation for an Optimal Design of Industrial Windows to Allow Natural Ventilation during Wind-Driven Rain," Sustainability, MDPI, vol. 7(8), pages 1-22, August.
    2. Hualin Xie & Jinlang Zou & Hailing Jiang & Ning Zhang & Yongrok Choi, 2014. "Spatiotemporal Pattern and Driving Forces of Arable Land-Use Intensity in China: Toward Sustainable Land Management Using Emergy Analysis," Sustainability, MDPI, vol. 6(6), pages 1-17, May.
    3. Stephan E. Maurer & Andrei V. Potlogea, 2021. "Male‐biased Demand Shocks and Women's Labour Force Participation: Evidence from Large Oil Field Discoveries," Economica, London School of Economics and Political Science, vol. 88(349), pages 167-188, January.
    4. Tie Hua Zhou & Ling Wang & Keun Ho Ryu, 2015. "Supporting Keyword Search for Image Retrieval with Integration of Probabilistic Annotation," Sustainability, MDPI, vol. 7(5), pages 1-18, May.
    5. T. Karski, 2019. "Opinions and Controversies in Problem of The So-Called Idiopathic Scoliosis. Information About Etiology, New Classification and New Therapy," Biomedical Journal of Scientific & Technical Research, Biomedical Research Network+, LLC, vol. 12(5), pages 9612-9616, January.
    6. Wesley Mendes-da-Silva, 2020. "What Makes an Article be More Cited?," RAC - Revista de Administração Contemporânea (Journal of Contemporary Administration), ANPAD - Associação Nacional de Pós-Graduação e Pesquisa em Administração, vol. 24(6), pages 507-513.
    7. Wisdom Akpalu & Mintewab Bezabih, 2015. "Tenure Insecurity, Climate Variability and Renting out Decisions among Female Small-Holder Farmers in Ethiopia," Sustainability, MDPI, vol. 7(6), pages 1-16, June.
    8. Wei Chen & Shu-Yu Liu & Chih-Han Chen & Yi-Shan Lee, 2011. "Bounded Memory, Inertia, Sampling and Weighting Model for Market Entry Games," Games, MDPI, vol. 2(1), pages 1-13, March.
    9. David Harborth & Sebastian Pape, 2020. "Empirically Investigating Extraneous Influences on the “APCO” Model—Childhood Brand Nostalgia and the Positivity Bias," Future Internet, MDPI, vol. 12(12), pages 1-16, December.
    10. Taeyeoun Roh & Yujin Jeong & Byungun Yoon, 2017. "Developing a Methodology of Structuring and Layering Technological Information in Patent Documents through Natural Language Processing," Sustainability, MDPI, vol. 9(11), pages 1-19, November.
    11. He-Yau Kang & Amy H. I. Lee & Tzu-Ting Huang, 2016. "Project Management for a Wind Turbine Construction by Applying Fuzzy Multiple Objective Linear Programming Models," Energies, MDPI, vol. 9(12), pages 1-15, December.
    12. A. B. Atkinson & Stephen P. Jenkins, 2020. "A Different Perspective on the Evolution of UK Income Inequality," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(2), pages 253-266, June.
    13. Haiyan Xu & Yanhui Ding & Jing Sun & Kun Zhao & Yuanjian Chen, 2019. "Dynamic Group Recommendation Based on the Attention Mechanism," Future Internet, MDPI, vol. 11(9), pages 1-15, September.
    14. Adina Letiţia Negruşa & Valentin Toader & Aurelian Sofică & Mihaela Filofteia Tutunea & Rozalia Veronica Rus, 2015. "Exploring Gamification Techniques and Applications for Sustainable Tourism," Sustainability, MDPI, vol. 7(8), pages 1-30, August.
    15. Ahmad N. Alkenani & Mohammad Ashraf & Ghulam Mohammad, 2020. "Quantum Codes from Constacyclic Codes over the Ring F q [ u 1 , u 2 ]/? u 1 2 - u 1 , u 2 2 - u 2 , u 1 u 2 - u 2 u 1 ?," Mathematics, MDPI, vol. 8(5), pages 1-11, May.
    16. Shang-Yuan Chen & Jui-Ting Huang, 2012. "A Smart Green Building: An Environmental Health Control Design," Energies, MDPI, vol. 5(5), pages 1-16, May.
    17. Yanhong Feng & Xu Yu & Gai-Ge Wang, 2019. "A Novel Monarch Butterfly Optimization with Global Position Updating Operator for Large-Scale 0-1 Knapsack Problems," Mathematics, MDPI, vol. 7(11), pages 1-31, November.
    18. Xiaoshu Cao & Feiwen Liang & Huiling Chen & Yongwei Liu, 2017. "Circuity Characteristics of Urban Travel Based on GPS Data: A Case Study of Guangzhou," Sustainability, MDPI, vol. 9(11), pages 1-21, November.
    19. S. B. Reshetnikov & M. R. Skirdov, 2017. "Analysis of methodological approaches to determination and assessment of the human capital," Russian Journal of Industrial Economics, MISIS, vol. 10(1).
    20. Mi Jung Son & Jin Han Park & Ka Hyun Ko, 2019. "Some Hesitant Fuzzy Hamacher Power-Aggregation Operators for Multiple-Attribute Decision-Making," Mathematics, MDPI, vol. 7(7), pages 1-33, July.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:6:p:965-:d:370688. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.