Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making
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)
Journal: Mathematics
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• MDPI AG
• ISSN: 2227-7390
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.
Shio Gai Quek, Ganeshsree Selvachandran, Florentin Smarandache, et al. (2020). "Entropy Measures for Plithogenic Sets and Applications in Multi-Attribute Decision Making". Mathematics. https://doi.org/10.3390/math8060965