This paper deals with the joint verification of the inequalities of Modus Ponens and Modus Tollens in Fuzzy Logic. Although the case of Modus Ponens was partially considered before, the case of Modus Tollens and the joint satisfaction of both inequalities are studied by the first time. The cases of R-implications, Simplications, Q-implications and MamdaniLarsen implications are separatedly cons...

in this paper, a fuzzy version of the analytic form of hahn-banachextension theorem is given. as application, the hahn-banach theorem for$r$-fuzzy bounded linear functionals on $r$-fuzzy normedlinear spaces is obtained.