Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions called ponen (FMP) and it intuitionistic (IFMP) when are generalized to propositions. In this paper, we aim investigate reasoning methods for with mixture fuzzy/intuitionistic information. For mixed types GMP, present two solve problems based on the triple I method (TIM). One transform problem in...

Fuzzy Decision Tree is becoming increasingly significant as it is applied to areas of different platforms in real life. This paper gives an overview of the applications of fuzzy decision tree in heterogeneous fields. It is being actively used in fields as varied as intrusion detection, flexible querying (modus ponens), analysis of cognitive process (Human Computer Interaction), for user authent...

Initially, the idea of approximate reasoning using generalized modus ponens and a fuzzy implication is recalled. Next, a fuzzy system based on logical interpretation of if–then rules and with parametric conclusions is presented. Then, it is shown that global and local -insensitive learning of the above fuzzy system may be presented as the learning of a support vector regression machine with a s...

In this article Russell’s paradox and Cantor’s resolved successfully using intuitionistic logic with restricted modus ponens rule.

Considering the instability of nonlinear dynamics, the deductive inference rule Modus ponens itself is not enough to guarantee the validness of reasoning sequence in the real physical world, and from similar cause cannot gain similar result. Some kind of stability hypothesis should be added in order to draw meaningful conclusion. So the uncertainty of deductive inference appears the same as tha...

Based on the fully implicational idea, we investigate the interval-valued fuzzy reasoning with multiantecedent rules. First, we construct a class of interval-valued fuzzy implications by means of a type of implications and a parameter on the unit interval, then use them to establish three kinds of fully implicational reasoning methods for the interval-valued fuzzy reasoning with multi-anteceden...

The aim of this paper is to prove that the following two mathematical concepts are equivalent: 1) Fuzzy Preorders which are compatible with an "AND" operation and 2) Fuzzy Consequence Operators (FCO) [8] verifying a finiteness property with respect to that "AND" operation. The role proposed to fuzzy consequences operators is to be a general notion for obtaining approximate consequences from app...

The abstract is: Qualitative research is just as able as quantitative research to follow certain fundamental principles of logic in general and scientific reasoning in particular. Two such principles are the logic of modus ponens and the logic of modus tollens. In this essay, we frame different research approaches – positivist research, interpretive research, action research, and design researc...