x 6∈S cxf(x) 2 < ε. Of course g has finite support since g(x) = 0 for x 6∈ S. u t Exercise 2. (*) Recall that the operator norm of an operator T : U → W is define ||T || = supu 6=0 {||Tu||/||u||}. Show the following: • The transition matrix P is a self-adjoint operator from L(V ) into itself. • The operator norm of P is at most 1. • ||P|| ≤ ||P ||. • ||P || = ||P ||. Solution (exercise 2). Sinc...

in this paper, we study the finitely many constraints of fuzzy relation inequalities problem and optimize the linear objective function on this region which is defined with fuzzy max-lukasiewicz operator. in fact lukasiewicz t-norm is one of the four basic t-norms. a new simplification technique is given to accelerate the resolution of the problem by removing the components having no effect on ...