Approximate reasoning with linguistic modifiers

Linguistic modifiers, which slightly change the qualification of linguistic variables, pervade natural languages and their mathematical treatment is very important in some fields of artificial intelligence and related research such as knowledge representation and understanding natural languages. As early as 1972, Zadeh gave a fuzzy set-theoretic interpretation of some linguistic modifiers. Afterward, Bouchon and Bouchon-Meunier and Yao investigated various aspects such as stability of linguistic modifiers and proposed some new descriptions of linguistic modifiers. In this article, we are going to analyze systematically the influence of some usual linguistic modifiers, such as scalar products, normalization, BouchonŽ . Meunier modifiers, perturbation, and weakening or reinforcement power, in Ž . the process of approximate fuzzy reasoning. More exactly, we want to clarify the difference between the conclusions of fuzzy modus ponens in which linguistic modifiers appear and do not appear in premises.