Muhammad Tariq MehmoodFA19-RMT-044LHR TP 7353Dr. Imran Zulfiqar Cheema2026-03-122021https://repository.cuilahore.edu.pk/handle/123456789/2758Fuzzy set theory and fuzzy logics are examples of fuzzy mathematics. It began in 1965, when Lotfi Asker Zadeh's important work Fuzzy sets was issued. Fuzzy Graph theory is becoming very popular these days, so it is used in many major fields. In this thesis, by means of weighted mean fuzzy transitivity here also I want to define for understanding (weighted mean transitivity) Weighted mean transitivity is defined as: μ(u,v) ≤ λ(σ(u)∨σ(v))+(1-λ)(σ(u)∧σ(v)) u₁,u₂∈ Ri′ where λ is optimized parameter and λ∈[0,1]. Now here we check λ at different values of interval. We discuss the different graph structure at λ=0, 0.5, 1. But here only we discuss λ= 0.5, 1. We calculate the Semi Strong min-product on different structures, degree of a vertex and total degree of a vertex. At the end of thesis we write the application as well as Algorithm.enDr. Imran Zulfiqar Cheemafa19Department of MathematicsMathematicsFuzzy set theoryfuzzy logicsThesis