Ideal theory of semigroups based on ( 3 , 2 ) -fuzzy sets
M. Vanishree, N. Rajesh, Noorbhasha Rafi, Ravikumar Bandaru · Journal of Mathematics and Computer Science · 2022
In this paper, the notions of \((3,2)\)-fuzzy ideal, \((3,2)\)-fuzzy bi-ideal, \((3,2)\)-fuzzy interior ideal and \((3,2)\)-fuzzy \((1,2)\)-ideal of a semigroup are introduced and investigated their properties. The relation between (\((3,2)\)-fuzzy) ideal, bi-ideal, interior ideal and \((1,2)\)-ideal are given. We characterized \((3,2)\)-fuzzy \((1,2)\)-ideal in terms of \(f^3\)-level \(\alpha\)-cut and \(g^2\)-level \(\alpha\)-cut. A necessary and sufficient condition for a subset of a semigroup to be \((1,2)\)-ideal in terms of \((3,2)\)-fuzzy \((1,2)\)-ideal of a semigroup is given.