تأثير زمرة ضبابية على مجموعة ضبابية

Abstract EN

According to the concept of fuzzy group and resistant mapping, we define fuzzy set called sym(A) (where A is a fuzzy set) then we prove that sym(A) is a fuzzy group with respect to the operation (.) which defined as follows : " f, g e syin{ A): f.

g : A → A x a f g(x) = f (g(x)) And we define act of fuzzy group G over fuzzy set S in two different ways then we prove that they are equivalent in the following theorem: Let G be a fuzzy group and let S be a fuzzy set then there is a resistant mapping: j : G x S → S (g,s) → j(g,s) = g * s satisfy the following conditions: 1) eG * s = s (g g') * s = g * (g'* s) 2) ms (g *s) ^ ms (s) if and only if there is a resistant group homomorphism : q : G → sym(S) g →ϴ (g) = fg satisfy the condition : " g1 e G, g2 e G , s1 e S, s2 e S: min{ m,m'} = min{ n, n'} m n m' n' ^ mS(fgl(si)) = mS(fg2(s2))