Granular computing in zero-divisor graphs of Zn

• DOI: 10.1016/j.kjs.2024.100231
• Publication Date: 2024-04-09T15:42:51Z
• Authors: Hibba Arshad; Imran Javaid; Asfand Fahad
• Keywords: Zero divisor; Reduct

In this article, we study the zero-divisor graphs Γ(Zn) of rings integers modulo n as information systems I(Γ(Zn)) using equivalence classes and rough sets. Equivalence are referred granules partitions indiscernible partitions. We define an indiscernibility relation on vertex set identify different sets attributes that induce same partition. A reduct is a minimal subset which yields partition original attribute set. compute all reducts defined system classify them in to two types including: (i) P prime divisors (ii) consisting P∖pi, powers pi factorization elements form pipj, where pj∈P∖pi. Moreover, give structures cardinalities subsets whose removal than attributes, essential prove either consist or one divisor combined with pi. Further, determine lower upper approximations various properties graphs. also membership function for Γ(Zn). Furthermore, introduce class-based discernibility matrix induced by zero general its entries. entries coincide Based these results, information-granularity measures corresponding notable provide example establish consistency proved results well-known measures. Thus, starting from introducing system, investigate components granular computing utilize our findings granularity measures, contributing deeper understanding via theory.