New Operations on n-Intuitionistic Polygonal Fuzzy Numbers.

Recently, intuitionistic fuzzy sets and numbers are widely interesting in the literature, and many types of Intuitionistic Fuzzy Numbers (IFN's) are studied and applied to different mathematical and real life problems. In this paper, an algorithm to approximate general IFN's by the n-Intuitionistic Polygonal Fuzzy Number (n-IPFN) is introduced. The approximation facilitates the calculations due to its linearity, not to mention its realisticity and flexibility. After that, a new method to rank IFN's is introduced and applied to the n-IPFN. Based on that, convenient arithmetic operations for n-IPFN's that preserve the ranking values are proposed and shown to satisfy the most important properties. As a result, defining a ranking equivalence relation gave a strong algebraic structure that is isomorphic to the real numbers set. Finally, some definitions are proposed for dealing with matrices, functions, equalities and inequalities with n-IPFN's. [ABSTRACT FROM AUTHOR]