Existence of inner addition and inner multiplication on Set of Triangular numbers and some inherent properties of Triangular numbers

The set Ptof real parameters for a fuzzy number belonging to a general family of all important parameters are calculated such that a triangular fuzzy number with the same value of the parameter exists for every specified flozzy number. We suggest a method for computing a triangular fuzzy number closest to p/Pt, and review the identity features, scale and translation invariance, additivity and consistency of the approximation operator obtained. Examples of recent findings in this topic and implementation of a flush-number retaining the value for the near triangular approximation. In this paper, we are revisits the topic of TRIANGULAR NUMBERS with new perspective direction to generate them to all integers and proved some of their inherent properties. Also we are defined two types of binary operations inner addition and inner multiplication are satisfied by triangular numbers, which are represented in below. According these binary operations, we are proven is almost Semi Ring under inner addition and inner multiplication. Also we are finding the relation between Triangular numbers with Pascal triangles. And we are proven some of their Inherent Properties. © 2021