On MPT-implication functions for Fuzzy Logic

نویسندگان

  • Enric Trillas
  • Claudi Alsina
  • Ana Pradera
  • Luis M. Laita
  • E. Trillas
  • A. Pradera
چکیده

This paper deals with numerical functions able to functionally express operators defined as , and verifying either Modus Ponens or Modus Tollens, or both. The concrete goal of the paper is to search for continuous t-norms and strong-negation functions for which it is either (Modus Ponens), or (Modus Tollens), or both, for all in and a given . Functions are taken among those in the most usual families considered in Fuzzy Logic, namely, Rimplications, S-implications, Q-implications and Mamdani-Larsen implications. En passant, the cases of conditional probability and material conditional’s probability are analyzed. Sobre implicaciones MPT en la Lógica Borrosa Resumen. Los operadores de implicación borrosos se suelen expresar por medio de funciones numéricas de acuerdo con la igualdad . El presente artı́culo estudia la verificación por parte de estas funciones numéricas de las meta-reglas del Modus Ponens y Modus Tollens. En concreto, dada una de estas funciones , el objetivo es determinar qué t-normas continuas y qué funciones de negación fuerte verifican alguna (o ambas) de las desigualdades (Modus Ponens) y (Modus Tollens), para cualesquiera en . Las funciones se toman entre las pertenecientes a las familias más habitualmente utilizadas en Lógica Borrosa, esto es, R-implicaciones, S-implicaciones, Q-implicaciones e implicaciones de Mamdani-Larsen.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

ROBUSTNESS OF THE TRIPLE IMPLICATION INFERENCE METHOD BASED ON THE WEIGHTED LOGIC METRIC

This paper focuses on the robustness problem of full implication triple implication inference method for fuzzy reasoning. First of all, based on strong regular implication, the weighted logic metric for measuring distance between two fuzzy sets is proposed. Besides, under this metric, some robustness results of the triple implication method are obtained, which demonstrates that the triple impli...

متن کامل

Truth Values and Connectives in Some Non-Classical Logics

The question as to whether the propositional logic of Heyting, which was a formalization of Brouwer's intuitionistic logic, is finitely many valued or not, was open for a while (the question was asked by Hahn). Kurt Gödel (1932) introduced an infinite decreasing chain of intermediate logics, which are known nowadays as Gödel logics, for showing that the intuitionistic logic is not finitely (man...

متن کامل

AN ALGEBRAIC STRUCTURE FOR INTUITIONISTIC FUZZY LOGIC

In this paper we extend the notion of  degrees of membership and non-membership of intuitionistic fuzzy sets to lattices and  introduce a residuated lattice with appropriate operations to serve as semantics of intuitionistic fuzzy logic. It would be a step forward to find an algebraic counterpart for intuitionistic fuzzy logic. We give the main properties of the operations defined and prove som...

متن کامل

T-NORMS vs. IMPLICATION FUNCTIONS AS IMPLICATION OPERATORS IN FUZZY CONTROL

A comparative study of the implication functions and t-norms behavior when they are used as implication operators in the fuzzy control inference process is carried out in this paper. In order to do it, the widely studied application of the Inverted Pendulum is considered. Moreover, a comparison methodology of the different fuzzy logic controllers designed is defined with the purpose of get more...

متن کامل

Fuzzy implications based on semicopulas

Recently, two new families of fuzzy implication functions called probabilistic implications and probabilistic S-implications were introduced by Grzegorzewski [6, 7, 9]. They are based on conditional copulas and make a bridge between probability theory and fuzzy logic. In this paper we generalize these two classes and propose a new kind of construction methods for fuzzy implications which are ba...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2004