Consistency Fuzzy Sets and a Cosine Similarity Measure in Fuzzy Multiset Setting and Application to Medical Diagnosis

The main purpose of this study is to construct a base for a new fuzzy set concept that is called consistency fuzzy set (CFS) which expresses the multidimensional uncertain data quite successfully. Our motive is to reduce the complexity and difficulty caused by the information contained in the truth sequence in a fuzzy multiset (FMS) and to present the data of the truth sequence in a more understandable and compact manner. Therefore, this paper introduces the concept of CFS that is characterized with a truth function defined on a universal set 0,1 2 . The first component of the truth pair of a CFS is the average value of the truth sequence of a FMS and the second component is the consistency degree, that is, the fuzzy complement of the standard deviation of the truth sequence of the same FMS. The main contribution of a CFS is the reflection of both the level of the average of the data that can be expressed with the different sequence lengths and the degree of the reasonable information in data via consistency degree. To develop this new concept, this paper also presents a correlation coefficient and a cosine similarity measure between CFSs. Furthermore, the proposed correlation coefficient and cosine similarity measure are applied to a multiperiod medical diagnosis problem. Finally, a comparison analysis is given between the obtained results and the existing results in literature to show the efficiency and rationality of the proposed correlation coefficient and cosine similarity measure.

O cristianismo e suas formas de veridicção: ressonâncias foucaultianas

The introduction of christianity as an object of analysis in the work of Michel Foucault marks a new moment in his intelectual course, Where the author commits hinself to the project of a geneology of ethic and forms of subjectivation in the West. The objetive of this paper consists in pointing to the importance os christianity in the formulations that Foucault made startings in the 1970’s, specially on what concerns to his studies on ethic, truth and subjectivity. For that, we analyzed the development of this the me in the intelectual’s work, specially the courses ministraded by Foucault in College de France. Another central point to the discussion were the concepts os exomologesis and exagoreusis, forms of penitence in christianity which points to a shift in how regimes of truth function in the West. The shift in paying penitence as a public performative act to a confession by word can be traced as a point of conection between christian practices and modern subjectivity, in that of which concers to the Productions of forms of interpretation and relation of the subject with itself based on confessional dispositives. Finally we searched, based on foucaultian thought, to make a paralel between the christian penitential dispositive of exagoreusis and different power-knowledge relations of modernity (such as law, psychiatry and psychology) that utilize the confessional alegory as a disciplinary practice and Productions of subjectivity and truth.

The P–T Probability Framework for Semantic Communication, Falsification, Confirmation, and Bayesian Reasoning

Many researchers want to unify probability and logic by defining logical probability or probabilistic logic reasonably. This paper tries to unify statistics and logic so that we can use both statistical probability and logical probability at the same time. For this purpose, this paper proposes the P–T probability framework, which is assembled with Shannon’s statistical probability framework for communication, Kolmogorov’s probability axioms for logical probability, and Zadeh’s membership functions used as truth functions. Two kinds of probabilities are connected by an extended Bayes’ theorem, with which we can convert a likelihood function and a truth function from one to another. Hence, we can train truth functions (in logic) by sampling distributions (in statistics). This probability framework was developed in the author’s long-term studies on semantic information, statistical learning, and color vision. This paper first proposes the P–T probability framework and explains different probabilities in it by its applications to semantic information theory. Then, this framework and the semantic information methods are applied to statistical learning, statistical mechanics, hypothesis evaluation (including falsification), confirmation, and Bayesian reasoning. Theoretical applications illustrate the reasonability and practicability of this framework. This framework is helpful for interpretable AI. To interpret neural networks, we need further study.

FOTOGRAFIA E PÓS-FOTOGRAFIA: do controle ao descontrole

Entre as funções originárias da fotografia está a documental. A foto dá testemunho da verdade. Barthes, em 1980, chegou a encontrar na essência da fotografia o “isso-foi”. Na foto se manifestaria necessariamente a verdade de uma realidade do passado. Ora, o dito popular – uma imagem vale mais que mil palavras! – até há pouco parecia incontestável (hoje desconfiamos mais de uma foto do que há 30 anos atrás). Fotografia documental, medical, policial, foto de identidade, identificação, controle, de tal maneira que aquele dito popular se inscreve em uma série que nos leva a outra frase de nosso cotidiano, de formulação mais recente: sorria, você está sendo filmado! A essa função-verdade da fotografia, ligada ao controle, eu gostaria de opor uma outra: uma pós-função, uma função pós-verdade, no sentido de uma metaverdade, de um para além da verdade fotográfica. – Isso não é verdade! Não é isso o que eu vi! Não pode ser! – essas exclamações podem expressar duas coisas diferentes: seja a denegação da verdade, seja o afloramento na foto de um virtual imagético, de um inconsciente visual. O que me interessa aqui é a segunda alternativa: a de que, numa imagem fotográfica, faça irrupção algo que não tenha sido conscientemente fotografado. PALAVRAS-CHAVE: Controle; virtual; incosciente. ABSTRACT Among the originary functions of photography there is the documental function. The photograph testifies to the truth. Barthes, in 1980, came to find the essence of photography in the “that-has-been”. A photograph would necessarily manifest the truth of a past reality. This explains why the popular saying – a picture is worth a thousand words! – until recently seemed incontestable (today we suspect more of a photo than 30 years ago). Documental photography, medical, identity photography, identification, control, in such a way that that popular saying is inscribed in a series that leads us to another sentence of our daily, in a more recent formulation: smile, you are being filmed! To this truth-function of photography, linked to control, I would like to oppose another: a post-function, a post-truth function, in the sense of a meta-truth, one beyond the photographic truth. – This is not true! That's not what I saw! It can not be! – these exclamations can express two different things: either the denial of truth, or the outcropping in the photograph of an imagetic virtual, of a visual unconscious. What interests me here is the second alternative: that in a photographic image something erupts that has not been consciously photographed. KEYWORDS: Control; virtual; unconcious. RESUMEN Entre las funciones originarias de la fotografía está la documental. La foto es testigo de la verdad. Barthes, en 1980, llegó a ubicar la esencia de la fotografía en el “esto-ha-sido”. En la foto necesariamente se manifesta la verdad de una realidad del pasado. El dicho popular – una imagen vale más que mil palabras! – hasta hace poco parecía incontestable (hoy día sospechamos más de una foto que hace 30 años). La fotografía documental, medical, policial, foto de identidad, identificación, control, de modo que aquel dicho popular se inscribe en una serie que nos lleva a otra frase de nuestra vida cotidiana, de formulación más reciente: sonría, usted está siendo filmado! A esta función-verdad de la fotografía, conectada al control, me gustaría oponer una otra: una posfunción, una función posverdad , en el sentido de una metaverdad, de un más allá de la verdad fotográfica. – ¡Eso no es verdad! Eso no es lo que vi! ¡No puede ser! – estas exclamaciones pueden expresar dos cosas diferentes: o bien la negación de la verdad, o bien el afloramiento en la foto de una imagen virtual, un inconsciente visual. Lo que me interesa aquí es la segunda alternativa: que en una imagen fotográfica haga irrupción algo que no ha sido conscientemente fotografiado. PALABRAS CLAVE: Control; virtual; inconsciente.

EXISTENTIAL GRAPHS AS AN INSTRUMENT OF LOGICAL ANALYSIS: PART I. ALPHA

Peirce considered the principal business of logic to be the analysis of reasoning. He argued that the diagrammatic system of Existential Graphs, which he had invented in 1896, carries the logical analysis of reasoning to the furthest point possible. The present paper investigates the analytic virtues of the Alpha part of the system, which corresponds to the sentential calculus. We examine Peirce’s proposal that the relation of illation is the primitive relation of logic and defend the view that this idea constitutes the fundamental motive of philosophy of notation both in algebraic and graphical logic. We explain how in his algebras and graphs Peirce arrived at a unifying notation for logical constants that represent both truth-function and scope. Finally, we show that Shin’s argument for multiple readings of Alpha graphs is circular.

La forma del Tractatus e la falsa percezione di un disegno di Wittgenstein

The tree of the Tractatus, a true cognitive map, puts every argument at its place into the general plan of the work. If we read the book by succeeding stages of analysis, we can realise that the controversial section 5.6, about the ego and limits of lan- guage and world, is the factual outcome of commentary 5.1-5.6 on "truth-function". The way in which "logic fills the world" leads to the suggestion that "solipsism coincides with pure realism" (path 5.61-5.64); the elimination of an empirical "I" results in the abolition of all a priori forms of our experience - and of any a priori, indeed, outside logics (5.631-5.634); nor does the form of the visual field suggest the need of an observing eye (5.6331). In its last part, the article shows the original drawing of 5.6331 diagram and demonstrates how it was badly read and worse edited and reproduced. Because of its central role in usual readings of the whole section, this implies a substantial review of most of the traditional exegeses.

Generalization Bounds for Certain Class of Ranking Algorithm

The quality of ranking determines the success or failure of information retrieval and the goal of ranking is to learn a real-valued ranking function that induces a ranking or ordering over an instance space. We focus on a ranking setting which uses truth function to label each pair of instances and the ranking preferences are given randomly from some distributions on the set of possible undirected edge sets of a graph. The contribution of this paper is the given generalization bounds for such ranking algorithm via strong and weak stability. Such stabilities have lower demand than uniform stability and fit for more real applications.