Neutrosophic Linguistic Labels

Neutrosophic trapezoidal functions can be extended to neutrosophic pentagonal (or more general) polygonal functions. Mostly general we can extend even to just any functions: T(x), I(x), F(x): [a, b] → [0, 1], but we need to get some applications in order to justify this extension.

Neutrosophic Linguistic Labels

To Said Broumi I have set that the linguistic set has to be organized increasingly, upon the importance (or other attribute) of the labels. So, {High, Medium, Low} has to be rewritten {Low, Medium, High}, where one has Low < Medium < High. Therefore one can compute min/max easily. One can also compute additions, subtractions, multiplication of labels (I have done within the information fusion), but these are more complex. Said Broumi Each linguistic may be a membership value. Florentin Smarandache When we go to linguistic, the components T, I, F instead of numbers simply get linguistic labels. For example,

x(high, low, low) belongs to the linguistic neutrosophic set A, which means that, with respect to the set A, the membership degree of x is "high", the indeterminate-membership degree of x is "low", and the false-membership degree of x is "low". For a linguistic complex neutrosophic set B, an element y( (high, low), (low, medium), (medium, low) ) belongs to B in the following way:  the degree of membership of y is "high" but the quality (phase) of this membership is "low",  the degree of indeterminate-membership of y is "low" but the quality of it is "medium",  and the degree of false-membership degree of y is "medium" but the quality of it is "low". The extension is done from 'numbers' to 'labels' straightforwardly (simply), for single-valued labels {not interval of labels, not subsets of labels}. For single-values:  the linguistic neutrosophic set is the same as the numerical neutrosophic set, but instead of numbers we put labels. For example, instead of T = 0.8, we put for example T = high; similarly for I and F;