1 minute read
Neutrosophic Triplets
Scilogs, V: joining the dots
a sequence of n ≥ 2 degrees of truths, a sequence of n ≥ 2 degrees of indeterminacy, and a sequence of n ≥ 2 degrees of falsehood – using time sequences. Therefore, the degrees of T, I, F of the same element x with respect to the same set A, may change because of various parameters that affect x and A (such as: time, economy, weather, politics, emotions, etc.).
Advertisement
Neutrosophic Triplets
To Kul Hur The Neutrosophic Triplets were introduced for the first time in 2016 by Smarandache and Ali [1]. They are derived from neutrosophy [2], founded in 1998, which is a generalization of dialectics, and it is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophy is also the basis of neutrosophic logic, neutrosophic probability, neutrosophic set, neutrosophic statistics, neutrosophic algebraic structures and so on. Neutrosophy and its neutrosophic derivatives are based on triads of the form (<A>, <neutA>, <antiA>), where <A> is an entity, <antiA> is the opposite of <A>, while <neutA> is the neutral between <A> and <antiA>.
The set of neutrosophic triplets, embedded with a welldefined law * that satisfies some axioms, form the neutrosophic triplet algebraic structures.The first studied one was the neutrosophic triplet group [1]. We introduce another structure, the neutrosophic triplet subgroup, and we study several of its properties. The Neutrosophic Triplet Algebraic Structures follow on the steps of classical algebraic structures, with two distinctions: - the classical unit element is replaced by the neutrosophic elements neut(a)'s; - and the classical inverse element is replaced by the neutrosophic elements anti(a)'s. I tried defining a new neutrosophic triplet equivalence relationship (NTER): aRb iff anti(a)Ranti(b), but I could not get an example that has more than one element in each class. You might try finding one using Cayley's Tables? If we take the subgroupoid of all idempotent elements (a2 = a) of a groupoid, then we have only neutrosophic triplets of the form (a, a, a), then the relationship aRb iff b = neut(a) maybe an equivalence. References:
