Possibility mean, variance and standard deviation of single-valued neutrosophic numbers and its applications to multi-attribute decision-making problems

Ordering single‐valued neutrosophic numbers based on flexibility parameters and its reasonable properties

“…Garai et al 31 ordering is based on the weighted possibility mean of the SVNNs. It is seen that the current method tallies with the existing methods of Deli and Subas, 27 Biswas et al, 28 Garai et al 30 and Garai et al 31 , thus ≻ ͠ ͠ a b. Thus, at all decision level higher than α and lower than γ and ≻ ͠ ͠ β a b , .…”

“…Hence, the current method is robust and logical. Moreover, the results of the SVNNs as well as the corresponding images of current method is equivalent to that of Garai et al 30…”

“…However, this method might sometime fails to rank consistently the SVNNs and their corresponding images as discussed in the numerical examples. In other recent study by Garai et al 30 which is also based on possibility mean, variance and standard deviation fails to rank SVNNs that are symmetric about the y-axis as discussed in the numerical examples. As such their approach might fails to rank consistently the SVNNs and their corresponding images.…”

“…In fact, their approach fails to rank SVNNs that are symmetric about the y-axis. Hence, Garai et al 30,31 approach depict limitations as such this method will not be a good choice in decision making problems. Further, the decision by the current method is equivalent to that of Biswas et al 28 T A B L E = (1, 4, 4, 7), (0, 4, 4, 8), (1,4,4,7) and 〈 〉 ͠ b = (2,4,4,6), (1,4,4,7), (2,4,4,6) .…”

“…Further, Nancy and Garg 26 proposed a ranking approach based on score function. The notions of the values and ambiguities of truth-membership, indeterminacymembership and falsity-membership function was developed for ranking SVNNs by Deli and Subas 27 and Biswas et al, 28 Aal et al 29 A very recent work on ranking SVNNs based on possibility mean, variance and standard deviation and applied to multiattribute decision making problems is developed by Garai et al 30 In another very recent study by Garai et al 31 utilized the weighted possibility means of SVNNs in ordering the SVNNs. However, this method might sometime fails to rank consistently the SVNNs and their corresponding images as discussed in the numerical examples.…”