Neutrosophic Triplet Function

inverse of "a" with respect to the neut(a) and the same algebraic law *: i.e. one has the following: a*neut(a) = neut(a)*a = a

and

a*anti(a) = anti(a)*a = neut(a). An element "a" may have in general more different neutrals neut(a), and more different opposite anti(a). These structures are inspires from our everyday world (from triads). I developed them together with Mumtaz Ali since 2014, but got published barely in 2016.

Neutrosophic Triplet Function

Hur Kul Recently, we must select only one president from many candidatures. Then at present about 30 % of the total electors is movable electors, i.e., neutrals. Thus it is very important for them to select whom. But we think that <A>, <neutA>, <antiA> can select partially another candidate, respectively at voting date. So the final selection is dependent on <A>, <neutA>, <antiA>. Of cause, it is strong dependent to <neutA>. Hence we would like to consider (<A>, <neutA>, <antiA>), <f(<A>, <neutA>, <antiA>) in order to analyze the real world. Your opinion?

Florentin Smarandache We can simply define a neutrosophic triplet function, f( <A>, <neutA>, <antiA> ) = ( f1(<A>), f2(<neutA>), f3(<antiA>) ), alike a classical vector function of three variables. Hur Kul For a group (G, *), can consider the following set <G  {T,I,F}> = {a+bT+cI+dF: a,b,c,d belong to G} ? Florentin Smarandache This is another type of neutrosophic algebraic structures, based on neutrosophic quadruple numbers (numbers of the form ��+����+����+����, where a, b, c, d are real or complex numbers), and called Neutrosophic Quadruple

Algebraic Structures, that I introduced in 2015. Then Dr. Adesina Agboola started to work on this structure too.

I have defined an ABSORBANCE law, or PREVALENCE order on {T, I, F}. If we consider the pessimistic (prudent) order: T < I < F which is the most indicated, then:

TI = IT = I { because "I" is bigger, and thus "I" absorbs T; or the bigger fish eats the smaller fish }. TF = FT = F { similarly, the bigger fish eats the smaller fish }.