WNSS


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WNSSWydzial Nauk Spolecznych Stosowanych (Polish: Faculty of Applied Social Sciences)
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The tabular representation of the WNSS (f,[A.sup.w]) v(g,[B.sup.w]) is given below:
Two WNSSs (F, [A.sup.w]) and (G, [B.sup.w]) over the common universe U are said to be equal if (F, [A.sup.w]) is neutrosophic soft subset of (G, [B.sup.w]) and (G, [B.sup.w]) is neutrosophic soft subset of (F, [A.sup.w]).
Let (F, [A.sup.w]) and (G, [B.sup.w]) be two WNSSs over the common universe U.
Example 3.4 Let (F, [A.sup.w]) and (G, [B.sup.w]) be two WNSSs over the common universe U = {[h.sub.1], [h.sub.2], [h.sub.3], [h.sub.4], [h.sub.5]} and their tabular representations are given below:
Example 3.5 Consider the WNSSs (F, [A.sup.w]) and (G, [B.sup.w]) as in example 3.4, then their intersection is given in the following tabular form:
Table 7: The Weighted Neutrosophic Soft Sets (F, [A.sup.w]) [??] (G, [B.sup.w]) U beautiful wooden [h.sub.1] (0.24, 0.12, 0.28) (0.21, 0.09, 0.15) [h.sub.2] (0.20, 0.16, 0.20) (0.18, 0.21, 0.09) [h.sub.3] (0.28, 0.16, 0.12) (0.21, 0.09, 0.15) [h.sub.4] (0.32, 0.16, 0.28) (0.18, 0.09, 0.18) [h.sub.5] (0.24, 0.28, 0.08) (0.21, 0.09, 0.12) U costly moderate [h.sub.1] (0.21, 0.18, 0.18) (0.24, 0.28, 0.36) [h.sub.2] (0.24, 0.12, 0.15) (0.24, 0.31, 0.24) [h.sub.3] (0.21, 0.12, 0.18) (0.20, 0.24, 0.42) [h.sub.4] (0.18, 0.09, 0.15) (0.28, 0.25, 0.36) [h.sub.5] (0.24, 0.15, 0.12) (0.24, 0.24, 0.30) Consider (F, [A.sup.w]), (G, [B.sup.w]) and (K, [C.sup.w]) be three WNSSs over the common universe U.
We can verify the De Morgan's laws in case of union and intersection of two WNSSs.
If (F, [A.sup.w]) and (G, [B.sup.w]) be two WNSSs over the common universe U then '(F, [A.sup.w]) OR (G, [B.sup.w])' denoted by (F, [A.sup.w]) [disjunction] (G, [B.sup.w]) is defined by (F, [A.sup.w]) [disjunction] (g, [B.sup.w]) = (O, [C.sup.w]), where C = A x B and the truth-membership, indeterminacy-membership and falsity-membership of (O, [C.sup.w]) are given as follows: