Neutrosophic Cubic Einstein Geometric Aggregation Operators with Application to Multi-Criteria Decision Making Method

Neutrosophic cubic sets (NCs) are amore generalized version of neutrosophic sets(Ns) and interval neutrosophic sets (INs). Neutrosophic cubic setsare better placed to express consistent, indeterminate and inconsistent information, which provides a better platform to deal with incomplete, inconsistent and vague data. Aggregation operators play a key role in daily life, and in relation to science and engineering problems. In this paper we defined the algebraic and Einstein sum, multiplication and scalar multiplication, score and accuracy functions. Using these operations we defined geometric aggregation operators and Einstein geometric aggregation operators. First, we defined the algebraic and Einstein operators of addition, multiplication and scalar multiplication. We defined score and accuracy function to compare neutrosophic cubic values. Then we definedthe neutrosophic cubic weighted geometric operator (NCWG), neutrosophic cubic ordered weighted geometric operator (NCOWG), neutrosophic cubic Einstein weighted geometric operator (NCEWG), and neutrosophic cubic Einstein ordered weighted geometric operator (NCEOWG) over neutrosophic cubic sets. A multi-criteria decision making method is developed as an application to these operators. This method is then applied to a daily life problem.

Study on in vitro propagation of Giao co lam (Gynostemma pentaphyllium Thunb.)

Giao co lam (Gynostemma pentaphyllium Thunb.) is a traditional medicine plant and endangered species in Vietnam. The research was carried out to establish the plant propagation for the purpose of conserving and exploiting this endangered medicinal herb. The young leaf and nodes of Giao co lam in vitro were used as explants in the study to evaluate the factors influencing the multiplication. Young leaf explants were excised and cultured in MS medium with TDZ from 0.1 to 1 mg/L. After 10 weeks of culture, new shoots came out from their explants and the MS medium containing TDZ 0,7 mg/L gave the highest shoots (12.89 shoots/explant) with the average percentage of 74.67%. When nodal explants were cultured on MS supplemented with BA at a concentration of 0.3 to 1.5 mg/L and IBA 0.5 mg/L. After 6 weeks of culture, explants on MS medium supplemented with BA 1 mg/L and IBA 0,5 mg/L gave the highest shoots (7.39 shoots/explant) and their average percentage was 83.33%. In comparison to the nodal explant medium in combination with BA (0.5 to 3 mg/L) and NAA 0.2 mg/L for 4 weeks of culture, the best rapid shoot multiplication score was 3.67 times with MS + BA 1.5 mg/L + NAA 0.2 mg/L as compared to MS + BA 1.0 mg/L + IBA 0.5 mg/L. Suitable medium for rooting was MS + 0.5 mg/L IBA with root shoots at 97.33%, average roots at 5.29 roots/shoot after 4 weeks. On organic substrat, 70% coconut fiber and 30% composted cow manure gave the highest survival rate of 91.33%. The plants grew and developed well during the nursery stage.