Linguistic reasoning based on generalized modus ponens with linguistic modifiers and hedge moving rules

Abstract

Approximate reasoning is based on generalized modus ponens (GMP). Its principle is that from an observation different but approximately equal to the rule premise, we can deduce a fact approximately equal to the rule conclusion. However, the deduced fact is not obtained with an arbitrary way. In this paper, we propose a new rule of GMP in linguistic many-valued logic framework with using hedge moving rules for linguistic reasoning.

Generalized Modus Tollens with Linguistic Modifiers for Inverse Approximate Reasoning

“…In this section, some concepts, properties of the monotonous hedge algebra, hedge inverse mapping that have been researched in [3][4][5][8][9][10] are presented.…”

“…In many-valued logic, the aggregation functions of Lukasiewicz are often used. In this context and with N truth degrees, they are difined by [9][10][11]15]:…”

“…In [9,10], we studied new generalized modus ponens with linguistic modifiers for If…Then rules in linguistic many valued-logic and its application for forward approximate reasoning.…”

“…Studied in [10][11][12][13][14][15] are new generalized modus ponens based on linguistic modifiers for approximate reasoning with linguistic modifiers, but the computation and application are complicated. In [9,10], we studied new generalized modus ponens with linguistic modifiers for If…Then rules in linguistic many valued-logic and its application for forward approximate reasoning.…”