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The Level Cardinality of Fuzzy Module Under ℤ-Module Homomorphism on ℤn into ℤm Where gcd(n, m) Is Product of Primes
Manju Varghese, Shery Fernandez
29 - 35
10.3233/FAIA231003
Research Article
Frontiers in Artificial Intelligence and Applications
Volume 378: Fuzzy Systems and Data Mining IX
Abstract

The homomorphic image of a fuzzy module of an R-module is a fuzzy module [1]. In one of our papers [2] we have proved that if f : ℤn → ℤm is a ℤ-module homomorphism with gcd(n, m) = p, a prime and λ is any fuzzy module on ℤn with any level cardinality then the fuzzy module f(λ) on ℤm has level cardinality atmost 3. In this paper, we are considering the fuzzy module homomorphism between the ℤ-modules ℤn and ℤm where n,m ∈ ℤ+ with gcd(n, m) = pq, where p and q are primes and trying to find the level cardinality of the fuzzy module f(λ) on ℤm when λ is a fuzzy module on ℤn.

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