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,
Vassilis C. Gerogiannis
Affiliations
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
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.