In this article, we present a systemic approach toward a fuzzy logic based formalization of an approximate reasoning methodology in a fuzzy resolution, where we derive a truth value of A from both values of B → A and...In this article, we present a systemic approach toward a fuzzy logic based formalization of an approximate reasoning methodology in a fuzzy resolution, where we derive a truth value of A from both values of B → A and B by some mechanism. For this purpose, we utilize a t-norm fuzzy logic, in which an implication operator is a root of both graduated conjunction and disjunction operators. Furthermore by using an inverse approximate reasoning, we conclude the truth value of A from both values of B → A and B, applying an altogether different mechanism. A current research is utilizing an approximate reasoning methodology, which is based on a similarity relation for a fuzzification, while similarity measure is utilized in fuzzy inference mechanism. This approach is applied to both generalized modus-ponens/modus-tollens syllogisms and is well-illustrated with artificial examples.展开更多
Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the d...Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG^*.展开更多
文摘In this article, we present a systemic approach toward a fuzzy logic based formalization of an approximate reasoning methodology in a fuzzy resolution, where we derive a truth value of A from both values of B → A and B by some mechanism. For this purpose, we utilize a t-norm fuzzy logic, in which an implication operator is a root of both graduated conjunction and disjunction operators. Furthermore by using an inverse approximate reasoning, we conclude the truth value of A from both values of B → A and B, applying an altogether different mechanism. A current research is utilizing an approximate reasoning methodology, which is based on a similarity relation for a fuzzification, while similarity measure is utilized in fuzzy inference mechanism. This approach is applied to both generalized modus-ponens/modus-tollens syllogisms and is well-illustrated with artificial examples.
文摘Cancelled the first axiom L1) or the third axiom L3) of the classical formal logic system we established two kinds of quasi-formal deductive system, LG-R^* and LG^* respectively. In LG-R^* we proved that neither the deduction theorem nor the hypothetical syllogism (HS) rule held but a deduction theorem and an HS rule are obtained in a weak sense. We also proved that both the deduction theorem and the hypothetical syllogism(HS) rule hold in LG^*.
