Lógica del lenguaje fuzzy

Go to top

Other languages:

English · Italiano · Français · Deutsch · Español ·

En este capítulo hablaremos de la lógica difusa. Se llama difusa porque se caracteriza por la gradualidad: se puede dar a un objeto una cualidad que puede tener diversos grados de verdad.

En la primera parte de este capítulo se discutirá conceptualmente el significado de la verdad graduada, mientras que en la segunda parte nos adentraremos en el formalismo matemático introduciendo la función de pertenencia Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} es el elemento que nos permite sintetizar matemáticamente los matices de esta lógica del lenguaje. Se ha podido demostrar que con el razonamiento difuso, a diferencia de las lógicas lingüísticas anteriores, los diagnósticos muestran menos incertidumbre. Sin embargo, a pesar de ello, uno sigue sintiendo la necesidad de perfeccionar el método lingüístico y de enriquecerlo con otras "lógicas".

Article by Gianni Frisardi · Riccardo Azzali · Flavio Frisardi

Book Index

Introducción

Hemos llegado hasta aquí porque, como compañeros, muchas veces nos enfrentamos a responsabilidades y decisiones muy difíciles de tomar y entran en juego cuestiones como la conciencia, la inteligencia y la humildad. En tal situación, sin embargo, nos enfrentamos a dos obstáculos igualmente difíciles de manejar: el de un Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} (Base de conocimiento), como discutimos en el capítulo 'Lógica del lenguaje probabilístico', limitado en el tiempo que codificamos en Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_t} y uno Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} limitado en el contexto específico (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} ). Estos dos parámetros de la epistemología caracterizan la era científica en la que vivimos. Además, tanto el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_t} que el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} son variables dependientes de nuestra filogenia y, en particular, de nuestra plasticidad conceptual y actitud ante el cambio.^[1]

«Yo no te entiendo»
(te doy un ejemplo practico)

¿Cuánta investigación se ha producido sobre el tema 'Lógica difusa'?

Pubmed responde con 2862 artículos en los últimos 10 años,^[2]^[3] por lo que podemos decir que el nuestro es actual y está suficientemente actualizado. Sin embargo, si quisiéramos centrar la atención en un tema específico como "Trastornos temporomandibulares", la base de datos responderá con hasta 2235 artículos.^[4] Por lo tanto, si quisiéramos consultar otro tema como 'Dolor orofacial', Pubmed nos brinda 1.986 artículos.^[5] Esto quiere decir que el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_t} para estos tres temas en los últimos 10 años se ha actualizado suficientemente.

Si, ahora, quisiéramos verificar la interconexión entre los temas, notaremos que Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} en los contextos será el siguiente:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c=} 'Trastornos temporomandibulares Y dolor orofacial'Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rightarrow} 9 artículos en los últimos 10 años^[6]
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c=} 'Trastornos temporomandibulares Y Dolor orofacial Y Lógica difusa' 0 artículos en los últimos 10 años^[7]

El ejemplo significa que el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_t} está relativamente actualizado individualmente para los tres temas, mientras que disminuye drásticamente cuando los temas entre contextos se fusionan y específicamente a 9 artículos para el Punto 1 e incluso a 0 artículos para el Punto 2. Entonces, el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_t} es una variable dependiente del tiempo mientras que el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} es una variable cognitiva dependiente de nuestra aptitud para el progreso de la ciencia, como ya se mencionó —entre otras cosas— en el capítulo 'Introducción'.

«casi me convences»
(Espera y verás)

Terminamos el capítulo anterior afirmando que la lógica de un lenguaje clásico y posteriormente la lógica probabilística nos han ayudado mucho en el progreso de la ciencia médica y del diagnóstico pero llevan implícitamente dentro de sí los límites de su propia lógica del lenguaje, lo que limita la visión de el universo biológico. También comprobamos que con la lógica de un lenguaje clásico —por así decirlo, Aristotélico— la sintaxis lógica que de ella se deriva en los diagnósticos de nuestra Mary Poppins limita, de hecho, la conclusión clínica.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \{a \in x \mid \forall \text{x} \; A(\text{x}) \rightarrow {B}(\text{x}) \vdash A( a)\rightarrow B(a) \}} (ver capítulo Lógica del lenguaje clásico),

sostiene que: "todo paciente normal Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \forall\text{x}} que es positivo en el examen radiográfico de la ATM Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mathrm{\mathcal{A}}(\text{x})} tiene TTM Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rightarrow\mathrm{\mathcal{B}}(\text{x})} , como consecuencia directa Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vdash} Mary Poppins es positiva (y además es una paciente "normal") en la radiografía de la ATM Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A(a)} entonces Mary Poppins también está afectada por los TTM Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \rightarrow \mathcal{B}(a)}

La limitación del camino lógico seguido nos ha llevado a emprender un camino alternativo, en el que se evita el carácter bivalente o binario de la lógica del lenguaje clásico y se sigue un modelo probabilístico. El colega dentista, de hecho, cambió el vocabulario y prefirió una conclusión como:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P(D| Deg.TMJ \cap TMDs)=0.95}

y es que nuestra Mary Poppins está afectada en un 95% por TTM ya que tiene una degeneración de la articulación temporomandibular avalada por la positividad del dato Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D=\{\delta_1,\dots\delta_4\}} en una muestra poblacional 0. Sin embargo, también encontramos que en el proceso de construcción de la lógica probabilística (Analysandum Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle = \{P(D),a\}} ) que nos permitió formular las mencionadas conclusiones del diagnóstico diferencial y elegir la más plausible, existe un elemento crucial para todo el Analysand Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle = \{\pi,a,KB\}} representado por el término Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} que indica, en concreto, una 'Base de Conocimiento' del contexto sobre la que se construye la lógica del lenguaje probabilístico.

Por lo tanto, llegamos a la conclusión de que tal vez el colega dentista debería haberse dado cuenta de su propia 'incertidumbre subjetiva' (¿afectada por TMD o _nOP?) e 'incertidumbre objetiva' (¿probablemente más afectada por TMD o _nOP?).

¿Por qué hemos llegado a estas conclusiones críticas?

Por una forma ampliamente compartida de representación de la realidad, sustentada en el testimonio de figuras autorizadas que confirman su criticidad. Esto ha dado lugar a una visión de la realidad que, a primera vista, parecería inadecuada para el lenguaje médico; de hecho, expresiones como “alrededor de 2” o “moderadamente” pueden suscitar legítima perplejidad y parecer un retorno anacrónico a conceptos precientíficos. Sin embargo, por el contrario, el uso de números borrosos o afirmaciones permite tratar los datos científicos en contextos en los que no se puede hablar de “probabilidad” sino solo de “posibilidad”.^[8]

«¿Probabilidad o Posibilidad?»

Fuzzy truth

En el ambicioso intento de traducir matemáticamente la racionalidad humana, se pensó a mediados del siglo XX en ampliar el concepto de lógica clásica formulando la lógica difusa. La lógica difusa se refiere a las propiedades que podríamos llamar de “gradualidad”, es decir, que se le pueden atribuir a un objeto con diferentes grados. Algunos ejemplos son las propiedades 'estar enfermo', 'tener dolor', 'ser alto', 'ser joven', etc.

Matemáticamente, la lógica difusa nos permite atribuir a cada proposición un grado de verdad entre Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0} y Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} . El ejemplo más clásico para explicar este concepto es el de la edad: podemos decir que un recién nacido tiene un ‘grado de juventud’ igual a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} , un joven de dieciocho años igual a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0,8} , un sexagenario igual a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0,4} , etcétera

En el contexto de la lógica clásica, por otro lado, las declaraciones:

un niño de diez años es joven
un treintañero es joven

ambos son verdaderos. Sin embargo, en el caso de la lógica clásica (que sólo admite los dos datos verdadero o falso), esto significaría que el infante y el treintañero son igualmente jóvenes. Lo cual obviamente está mal.

La importancia y el encanto de la lógica difusa surgen del hecho de que es capaz de traducir la incertidumbre inherente a algunos datos del lenguaje humano en formalismo matemático, codificando conceptos 'elásticos' (como casi alto, bastante bueno, etc.), en para hacerlos comprensibles y manejables por las computadoras.

Teoría de conjuntos

Como se mencionó en el capítulo anterior, el concepto básico de la lógica difusa es el de multivalencia, es decir, en términos de teoría de conjuntos, de la posibilidad de que un objeto pueda pertenecer a un conjunto aunque sea parcialmente y, por lo tanto, también a varios conjuntos con diferentes grados. . Recordemos desde el principio los elementos básicos de la teoría de los conjuntos ordinarios. Como se verá, en ellos aparecen las expresiones formales de los principios de la lógica aristotélica, recordados en el capítulo anterior.

Cuantificadores

Membresía: representado por el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \in } (pertenece), - por ejemplo, el número 13 pertenece al conjunto de números imparesFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \in } Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 13\in Odd }
No pertenencia: representado por el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \notin } (No pertenece)
Inclusión: Representado por el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \subset} (es contenido), - por ejemplo, el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} completo está contenido dentro del conjunto más grande Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \subset U} (en este caso se dice que Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} es un subconjunto de Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U} )
Cuantificador universal, que se indica con el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \forall} (para cada uno)
Demostración, que se indica con el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mid} (tal que)

Establecer operadores

Dado todo el universo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U} indicamos con Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} su elemento genérico de modo que Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x \in U} ; entonces, consideramos dos subconjuntos Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} y Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} interna a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U} de modo que Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A \subset U} y Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B \subset U}

	Unión: representado por el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cup} , indica la unión de los dos conjuntos Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} y Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (A\cup B)} . Está definido por todos los elementos que pertenecen a Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} y Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B} o ambos: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (A\cup B)=\{\forall x\in U \mid x\in A \land x\in B\}}
	Intersección: representado por el símboloFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \cap} , indica los elementos pertenecientes a ambos conjuntos: Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle (A\cap B)=\{\forall x\in U \mid x\in A \lor x\in B\}}
	Diferencia:representado por el símbolo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -} , Por ejemplo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A-B} muestra todos los elementos de Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} excepto los compartidos con Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle B}
	Complementaria: representado por una barra sobre el nombre de la colección, indica por Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{A}} La complementaria de Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} ,es decir, el conjunto de elementos que pertenecen a todo el universo excepto los de Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} , en fórmulas:Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{A}=U-A}

La teoría de la lógica del lenguaje difuso es una extensión de la teoría clásica de conjuntos en la que, sin embargo, los principios de no contradicción y del tercero excluido no son válidos. Recuérdese que en lógica clásica, dado el conjunto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} y su Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{A}} complementario, el principio de no contradicción establece que si un elemento pertenece al Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} entero no puede a la vez pertenecer también a su Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{A}} complementario; según el principio del tercero excluido, sin embargo, la unión de un Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} entero y su Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{A}} complementario constituye el universo completo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U}

En otras palabras, si algún elemento no pertenece al todo, necesariamente debe pertenecer a su complementario.

Conjunto difuso Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} y función de pertenencia Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)}

Elegimos, como formalismo, representar un conjunto borroso con la 'tilde': Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} Un conjunto borroso es un conjunto donde los elementos tienen un 'grado' de pertenencia (de acuerdo con la lógica borrosa): algunos pueden incluirse en el conjunto en 100%, otros en porcentajes menores.

Para representar matemáticamente este grado de pertenencia se encuentra la función Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} denominada 'Función de pertenencia'. La función Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} es una función continua definida en el intervalo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle [0;1]} donde es:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_ {\tilde {A}}(x) = 1\rightarrow } si Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} está totalmente contenido en Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} (estos puntos se llaman 'núcleo', indican valores predicados plausibles).
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_ {\tilde {A}}(x) = 0\rightarrow } si Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} no está contenido en Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A}
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1 \;\rightarrow } si Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} está parcialmente contenido en Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle A} (estos puntos se llaman 'soporte', indican los posibles valores predicados).

La representación gráfica de la función Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {\tilde {A}}}(x)} puede ser variado; desde los de líneas lineales (triangulares, trapezoidales) hasta los que tienen forma de campana o 'S' (sigmoidales) como se muestra en la Figura 1, que contiene todo el concepto gráfico de la función de pertenencia....^[9]^[10]

Figure 1: Types of graphs for the membership function.

El conjunto soporte de un conjunto borroso se define como la zona en la que el grado de pertenencia resulta Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1} ; por su parte, el núcleo se define como el ámbito en el que el grado de pertenencia asume el valor Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_ {\tilde {A}}(x) = 1}

El 'Conjunto de soporte' representa los valores del predicado que se consideran posibles, mientras que el 'núcleo' representa los que se consideran más plausibles.

Si Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} representara un conjunto en el sentido ordinario del término o en la lógica del lenguaje clásico descrita anteriormente, su función de pertenencia podría asumir solo los valores Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 1} o Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0} , Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 1 \; \lor \;\mu_{\displaystyle {{A}}}(x)= 0} finalizando en si el elemento Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x} pertenece o no al todo, según se considere. La Figura 2 muestra una representación gráfica del concepto nítido (rígidamente definido) o confuso de membresía, que recuerda claramente las consideraciones de Smuts.^[11]

Volvamos al caso concreto de nuestra Mary Poppins, en el que vemos una discrepancia entre las afirmaciones del dentista y del neurólogo y buscamos una comparación entre la lógica clásica y la lógica difusa:

Figure 2: Representation of the comparison between a classical and fuzzy ensemble.

Figura 2: Imaginemos el Universo de la Ciencia Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle U} en el que existen dos mundos o contextos paralelos, el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} y el Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}=} En el contexto científico, el llamado ‘crisp’, y lo hemos convertido a la lógica del Lenguaje Clásico, en el que el médico dispone de una información científica absoluta Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} con una clara línea divisoria que hemos denominado Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}=} En otro contexto científico llamado ‘lógica difusa’, y en el que existe una unión entre el subconjunto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} en Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} que podemos llegar a decir: unión entre Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c}

Notaremos notablemente las siguientes deducciones:

Lógica Clásica en el Contexto Odontológico Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} en el que sólo será posible un proceso lógico que dé como resultado Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 1 } , o siendo Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 0 } el rango de datos Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle D=\{\delta_1,\dots,\delta_4\}} reducido a conocimientos básicos Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} en el conjunto Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle {A}} . Esto quiere decir que fuera del mundo odontológico existe un void y ese término de la teoría de conjuntos se escribe precisamente Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_{\displaystyle {{A}}}(x)= 0 } y que es sinónimo de un rango alto de:

«Error de diagnóstico diferencial»

Lógica difusa en un contexto dental Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \tilde{A}} en el que se representan más allá de los conocimientos básicos Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} del contexto dental también aquellos parcialmente adquiridos del mundo neurofisiológico Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1} tendrán la prerrogativa de devolver un resultado Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \mu_\tilde{A}(x)= 1 } y un resultado Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 0<\mu_ {\tilde {A}}(x) < 1} debido a conocimientos básicos Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} que en este punto está representado por la unión de Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} contextos dentales y neurológicos. El resultado de esta implementación científico-clínica de la odontología permitiría una
«Reducción del error de diagnóstico diferencial»

Final considerations

Topics that could distract the reader’s attention were, in fact, essential for demonstrating the message. Normally, indeed, when any more or less brilliant mind allows itself to throw a stone into the pond of Science, a shockwave is generated, typical of the period of Kuhn’s extraordinary science, against which most of the members of the international scientific community row. With good faith, we can say that this phenomenon—as regards the topics we are addressing here—is well represented in the premise at the beginning of the chapter.

In these chapters, actually, a fundamental topic for science has been approached: the re-evaluation, the specific weight that has always been given to Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle P-value} , awareness of scientific / clinical contexts Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} , having undertaken a more elastic path of Fuzzy Logic than the Classical one, realizing the extreme importance of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB} and ultimately the union of contexts Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle KB_c} to increase its diagnostic capacity.^[12]^[13]

In the next chapter we will be ready to undertake an equally fascinating path: it will leads us to the context of a System Language logic, and will allow us to deepen our knowledge, no longer in clinical semeiotics only, but in the understanding of system functions (recently it is being evaluated in neuromotor disciplines for Parkinson's disease).^[14]In Masticationpedia, of course, we will report the topic 'System Inference' in the field of the masticatory system as we could read in the next chapter entitled 'System logic'.

Bibliography & references

↑ Takeuchi S, Okuda S, «Knowledge base toward understanding actionable alterations and realizing precision oncology», in Int J Clin Oncol, 2019».
PMID:30542800 - PMCID:PMC6373253
DOI:10.1007/s10147-018-1378-0

This is an Open Access resource!
↑ Fuzzy logic on Pubmed
↑ All statistics collected following visits to the Pubmed site (https://pubmed.ncbi.nlm.nih.gov/). Last checked: December 2020.
↑ Temporomandibular Disorders in Pubmed
↑ Orofacial Pain in Pubmed
↑ Temporomandibular disorders AND Orofacial Pain in Pubmed
↑ "Temporomandibular disorders AND Orofacial Pain AND Fuzzy logic" in Pubmed
↑ Dubois D, Prade H, «Fundamentals of Fuzzy Sets», Kluwer Academic Publishers, 2000, Boston».
↑ Zhang W, Yang J, Fang Y, Chen H, Mao Y, Kumar M, «Analytical fuzzy approach to biological data analysis», in Saudi J Biol Sci, 2017».
PMID:28386181 - PMCID:PMC5372457
DOI:10.1016/j.sjbs.2017.01.027
↑ Lazar P, Jayapathy R, Torrents-Barrena J, Mol B, Mohanalin, Puig D, «Fuzzy-entropy threshold based on a complex wavelet denoising technique to diagnose Alzheimer disease», in Healthc Technol Lett, The Institution of Engineering and Technology, 2016».
PMID:30800318 - PMCID:PMC6371778
DOI:10.1049/htl.2016.0022
↑ •SMUTS J.C. 1926, Holism and Evolution, London: Macmillan.
↑ Mehrdad Farzandipour, Ehsan Nabovati, Soheila Saeedi, Esmaeil Fakharian. Fuzzy decision support systems to diagnose musculoskeletal disorders: A systematic literature review . Comput Methods Programs Biomed. 2018 Sep;163:101-109. doi: 10.1016/j.cmpb.2018.06.002. Epub 2018 Jun 6.
↑ Long Huang, Shaohua Xu, Kun Liu, Ruiping Yang, Lu Wu. A Fuzzy Radial Basis Adaptive Inference Network and Its Application to Time-Varying Signal Classification . Comput Intell Neurosci, 2021 Jun 23;2021:5528291.
doi: 10.1155/2021/5528291.eCollection 2021.
↑ Mehrbakhsh Nilashi, Othman Ibrahim, Ali Ahani. Accuracy Improvement for Predicting Parkinson's Disease Progression. Sci Rep. 2016 Sep 30;6:34181. doi: 10.1038/srep34181.

Masticationpedia is a charity, a not-for-profit organization operating in dentistry medical research,
particularly focusing on the field of the neurophysiology of the masticatory system

[1] Takeuchi S, Okuda S, «Knowledge base toward understanding actionable alterations and realizing precision oncology», in Int J Clin Oncol, 2019».
PMID:30542800 - PMCID:PMC6373253
DOI:10.1007/s10147-018-1378-0

This is an Open Access resource!

[2] Fuzzy logic on Pubmed

[3] All statistics collected following visits to the Pubmed site (https://pubmed.ncbi.nlm.nih.gov/). Last checked: December 2020.

[4] Temporomandibular Disorders in Pubmed

[5] Orofacial Pain in Pubmed

[6] Temporomandibular disorders AND Orofacial Pain in Pubmed

[7] "Temporomandibular disorders AND Orofacial Pain AND Fuzzy logic" in Pubmed

[8] Dubois D, Prade H, «Fundamentals of Fuzzy Sets», Kluwer Academic Publishers, 2000, Boston».

[9] Zhang W, Yang J, Fang Y, Chen H, Mao Y, Kumar M, «Analytical fuzzy approach to biological data analysis», in Saudi J Biol Sci, 2017».
PMID:28386181 - PMCID:PMC5372457
DOI:10.1016/j.sjbs.2017.01.027

[10] Lazar P, Jayapathy R, Torrents-Barrena J, Mol B, Mohanalin, Puig D, «Fuzzy-entropy threshold based on a complex wavelet denoising technique to diagnose Alzheimer disease», in Healthc Technol Lett, The Institution of Engineering and Technology, 2016».
PMID:30800318 - PMCID:PMC6371778
DOI:10.1049/htl.2016.0022

[:0-11] •SMUTS J.C. 1926, Holism and Evolution, London: Macmillan.

[12] Mehrdad Farzandipour, Ehsan Nabovati, Soheila Saeedi, Esmaeil Fakharian. Fuzzy decision support systems to diagnose musculoskeletal disorders: A systematic literature review . Comput Methods Programs Biomed. 2018 Sep;163:101-109. doi: 10.1016/j.cmpb.2018.06.002. Epub 2018 Jun 6.

[13] Long Huang, Shaohua Xu, Kun Liu, Ruiping Yang, Lu Wu. A Fuzzy Radial Basis Adaptive Inference Network and Its Application to Time-Varying Signal Classification . Comput Intell Neurosci, 2021 Jun 23;2021:5528291.
doi: 10.1155/2021/5528291.eCollection 2021.

[14] Mehrbakhsh Nilashi, Othman Ibrahim, Ali Ahani. Accuracy Improvement for Predicting Parkinson's Disease Progression. Sci Rep. 2016 Sep 30;6:34181. doi: 10.1038/srep34181.

[1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

[11]

[12]

[13]

[14]