On if-then-else inference rules

In this paper, we start with a short review on “if-then” inference rules by selecting some widely used fuzzy implication operators and summarising their logical properties. Next, we outline Zadeh´s compositional rule of inference which is used in this paper. And then, we focus our attention on the fuzzy conditional proposition “if-then-else” inference rules under the selected fuzzy implication operators. Finally, we investigate the influence of the choice of the fuzzy implication operator on the validity of this -if-then-else” inference scheme as used in fuzzy expert systems. This study, following our previous work, shows that the results of the generalised modus ponens, the generalised modus tollens, the fuzzy syllogism, the generalised method-of-cases and the “if-then-else” inference rule often heavily depend upon the choice of the fuzzy implication operator and the choice of the triangular norm modelling the fuzzy intersection