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

Shio Gai Quek, Ganeshsree Selvachandran, Florentin Smarandache, J. Vimala, Son Hoang Le, Quang-Thinh Bui and Vassilis C. Gerogiannis
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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
Vassilis C. Gerogiannis: Department of Digital Systems, University of Thessaly, GR 41500 Larissa, Greece

Mathematics, 2020, vol. 8, issue 6, 1-17

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.

Keywords: neutrosophic set; plithogenic set; fuzzy set; entropy; similarity measure; information measure (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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