NC - Cross Entropy Based MADM under 1 Neutrosophic Cubic Set Environment 2

Surapati Pramanik 1*, Shyamal Dalapati 2, Shariful Alam 2, Florentin Smarandache 3 and 3 Tapan Kumar Roy 2 4 1 Department of Mathematics, Nandalal Ghosh B.T. College, Panpur, P.O.-Narayanpur, District–North 24 5 Parganas, Bhatpara 743126, West Bengal, India 6 2 Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, P.O.7 Botanic Garden, Howrah 711103, West Bengal, India; [email protected] (S.D.); 8 [email protected] (S.A.); [email protected] (T.K.R.) 9 3 Department of Mathematics & Science, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, 10 USA; [email protected] 11 * Correspondence: [email protected]; Tel.: +91-9477035544 12 13 Abstract: Neutrosophic cubic set (NCS) is one of the important family members of neutrosophic 14 hybrid sets. Neutrosophic cubic set has more strength than other family members of neutrosophic 15 hybrid sets to express incomplete information due to the presence of interval valued neutrosophic 16 set (IVNS) and single valued neutrosophic set (SVNS) in its structure. Cross entropy measure is one 17 of the best way to calculate the divergence of any variable from the priori one variable. In this paper 18 we first define a new cross entropy measure under NCSs environment which we call NCcross 19 entropy measure. We investigate the basic properties of NC-cross entropy. We also propose weighted 20 NC-cross entropy and investigate its basic properties. We develop a novel multi attribute decision 21 making (MADM) strategy based on weighted NC-cross entropy. To show the feasibility and 22 applicability, we solve a MADM problem using the proposed strategy. 23