It is typical of some medical experiments, leading to measures regarded as the coordinates of points in the plane, that imprecise data can occur. In spite of it we still would like to derive a formula of the function that interpolates these points. We thus test the Newton interpolation method with divided differences when supposing that the entries will be fuzzy numbers in the L-R form. The equation describing the fuzzy function, which goes through the points, can be used as a prognosis in the case of other points that have only one coordinate known.
One of the most important features of fuzzy set theory is its potential for the modeling of natural language expressions. Most works done on this topic focus on some parts of natural language, mostly those that correspond to the so-called “evaluating linguistic expressions”. We build constraints for the mathematical substitutes of these expressions to mark characteristic limits on an ordered scale. We discuss a case of creating the total list of terms of the linguistic variable “symptom presence in diagnosis” replaced by fuzzy sets all emerging from one presence description “seldom”. To accomplish this task we insert a particular parameter in the membership functions of the sets.
In the current paper we mathematically try to support the medical operation decision made for the sake of patients suffering from gastric cancer. We involve the linear model of the simple neural perceptron to distinguish between two decision states determined as “operate” contra “do not operate”. The perceptron input signals are proposed to be given as codes of levels of the most decisive biological markers, considered in surgery decision making. To find the level intervals, tied to the codes, we introduce a procedure of level fuzzification by a family of parametric membership functions.
The German Enigma encoding machine and the contributions of famous cryptologists who broke it, are still topics, which fascinate both scientists and general public. After the monarchy of Kaiser Wilhelm II fell, the Weimar republic came into being, and the idea of equipping the armed forces with machine ciphers already found realization in 1926. The German cipher machine, called Enigma, alarmed the general staffs of neighbouring countries, especially Poland and France. This work intends to describe the efforts of three Polish cryptanalysts who solved the mystery of Enigma during the 30-ties before the beginning of the war. At the end of the paper the cooperation between the Polish cryptologists and Alan Turing – the outstanding English cryptanalyst – is revealed.
In this presentation the author intends to advertise her book titled “Fuzzy and Rough Techniques in Medical Diagnosis and Medication” printed by Springer-verlag in 2007. The volume provides readers with selected fuzzy and rough tools used to medical tasks, especially diagnosing and medication. To build a link between theoretical, mathematical excerpts and practical medical applications, the contents is formed as a sequence of occurrences in which a patient appears to be diagnosed and cured. The fuzzy and rough elements are inserted in the book in the order required by the presentation of medical substance to maintain the logical unity of the book’s essence. In conformity with this pattern the essay presents in turn some necessary elements of fuzzy set theory, the classical fuzzy diagnostic model with extensions, the fuzzy diagnostic model with clinical examinations extended throughout time based on distance theory, methods of drug effectiveness measurements and algorithms selecting the optimal medicine. As the complement, the solution of an approximation problem is suggested to find a curve that surrounds two-dimensional clock-like point sets with the little approximation error. It should be emphasized that all models are also applicable to other fields, especially to technical domains after necessary adaptations. This confirms the existence of the large spectrum of applicable fuzzy and rough methods not only in medicine but also in natural sciences.
Theoretical fuzzy decision-making models mostly developed by Zadeh, Bellman, Jain and Yager can be adopted as useful tools to estimation of the total effectiveness-utility of a drug when appreciating its positive influence on a collection of symptoms characteristic of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as entries of a utility matrix that constitutes the common basic component of all methods. We involve the matrix in a number of computations due to different decision algo-rithms to obtain a sequence of tested medicines in conformity with their abili-ties to soothe the unfavorable impact of symptoms. An adjustment of the large spectrum of applied fuzzy decision-making models to the extraction of the best medicines provides us with some deviations in obtained results but we are thus capable to select this method whose effects closest converge to the physicians’ judgments and expectations.
This project is a continuation of the last one from 2002 with the supplement, which introduces the space of verbally defined fuzzy numbers in the L-R form. The space has its total order, and the numbers in it have borders from the interval [0, 1]. This gives a possibility of testing the fuzzy norms as the operations on fuzzy numbers from the space. The models discussed earlier can now be solved again by using this new technique.
We expand the classical model of a two-player game by inserting fuzzy sets as payoff values in the game matrix. Players can thus formulate their payoff expectations with words instead of deciding on numerical entries of the matrix. In this way we count on the better verbal communication between players when designing the preliminaries of the game. The players can also assign powers-weights to their strategies to mark importance of all tactics introduced in the game. As a final result we expect to obtain samples of the players’ optimal strategies, which will follow the final results in order to preserve the profit of the game on the neutral level. We also intend to estimate fuzzy probabilities of adapting the optimal strategies to achieve the objective of the game.
Radiation cystitis is a rare disease, appearing as the result of radiation of pelvic tumors. We support mathematically the recognition of the most efficacious treatments, which reduce the impact of symptoms typical of the illness. To permute the therapies in the ordering, commencing with the optimal therapy, we apply the fuzzy decision making model furnished with finite fuzzy sets. These act as measures of the treatment effectiveness-utility. In the solution, we adopt the older operations on fuzzy sets of type 1, which make the model simple to be easily converted into a computer program.
Theoretical fuzzy decision-making models mostly developed by Zadeh, Bellman, Jain, Herrera and Yager can be adopted as useful tools to estimation of the total effectiveness-utility of a treatment when appreciating its distinct influences on a collection of symptoms characteristic of a considered diagnosis. We prove, as a novelty of the classical fuzzy decision making model, the insertion of fuzzy numbers in the α-cut form to a utility matrix. In the current paper we wish to apply the modified fuzzy decision making to extract the most efficacious treatment in radiation cystitis.
By proposing a new approach to fuzzy decision making, we try to support the medical decision, concerning recommendations for the treatment with hyperbaric oxygen (HBO). This treatment can be used for patients, suffering from necrotizing fasciitis. Due to the disease rarity, it sometimes is difficult for a physician to determine, if a single patient needs the treatment with HBO. We thus identify the decision with a linguistic variable, equipped with treatment recommendation levels. The choice of the appropriate level is based on values of clinical symptoms, found in the patient. To extract the optimal recommendation level for the treatment with HBO, we involve fuzzy set techniques in the decision model. In the paper, we mainly concentrate on designs of fuzzy sets, standing for clinical symptoms and recommendation levels. The levels act as the outcomes, dependent on the cumulative input of the patient’s clinical markers. Since the focus is laid on a parametric structure of the outcomes, then we can categorize the model as robust approach to algorithmic modeling of outcomes, being part of eHealth data records.
In the current research, we aim to define a new form of the similarity coefficient to compare the resemblance grade of two Gaussian density functions. We aim to assess the method utility on a theoretical model. The density functions are stated for a biological marker “survival length”, observed in three groups of patients, suffering from a hypothetical disease. The first group consists of patients who are not treated, whereas we recommend 2 possible treatment methods for the second and the third group, respectively. All the “survival length” assumptions of the model (mean values and standard deviations) are made to exclude the equivocal conclusion, regarding a selection of the better treatment. At the first stage, we apply the measure of similarity to populations: survival among untreated patients contra survival among patients after Treatment 1. Another similarity coefficient estimates a relation between populations: survival among untreated patients versus survival among patients after Treatment 2. The lower value of the coefficient points out the more effective treatment. In order to simplify calculations, proposed in the definition of a similarity coefficient, we approximate the Gaussian curve by a specially designed polynomial, known as the p-function.
Radiation cystitis is in general rarely occurring, which makes it very difficult to study in a large group of clinical trials. Most available data about radiation cystitis treatment come from a small number of descriptive studies or from expert opinions. As clinical data are considered to have low quality then physicians, who are still facing patients with a disease hugely influencing quality of life, mostly base on their own experience. We thus want to test fuzzy decision-making model, regarded as a valuable tool, to help in selecting a patient-tailored treatment in radiation cystitis. Theoretical fuzzy decision-making models, possessing the utility matrix filled with distinct utilities of pairs (decision, object-state), give rise to own trials of successfully accomplished applications concerning the item of medication. After interpreting pairs (decision, object-state) as (therapy, symptom), we intend to prove decision-making based on the Choquet integral to extract the optimal treatment in radiation cystitis.
In the current paper we mathematically try to support the decision concerning the treatment with hyperbaric oxygen for patients, suffering from necrotizing fasciitis. To accomplish the task, we involve the fuzzified model of a quasi-perceptron, which is our modification of the classical artificial simple neuron. By means of the fuzzification of input signals and output decision levels, we wish to distinguish between decisions “treatment without recommended hyperbaric oxygen” versus “treatment with hyperbaric oxygen”. The number of decision levels can be arbitrary in order to extend the decision scale.
In the current paper we mathematically try to support the decision concerning the treatment with hyperbaric oxygen for patients, suffering from necrotizing fasciitis. To accomplish the task, we involve the fuzzified model of a quasi-perceptron, which is our modification of the classical artificial simple neuron. By means of the fuzzification of input signals and output decision levels, we wish to distinguish between decisions "treatment without recommended hyperbaric oxygen" versus "treatment with hyperbaric oxygen". The number of decision levels can be arbitrary in order to extend the decision scale.
Computation intelligence paradigms including artificial neural networks, fuzzy systems, evolutionary computing techniques, intelligent agents and so on provide a basis for human like reasoning in medical systems. Approximate reasoning is one of the most effective fuzzy systems. The compositional rule of inference founded on the logical law modus ponens is furnished with a true conclusion, provided that the premises of the rule are true as well. Even though there exist different approaches to an implication, being the crucial part of the rule, we modify the early implication proposed in our practical model concerning a medical application. The approximate reasoning system presented in this work considers evaluation of a risk in the situation when physicians weigh necessity of the operation on a patient. The patient’s clinical symptom levels, pathologically heightened, indicate the presence of a disease possible to recover by surgery. We wish to evaluate the extension of the operation danger by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.
The concepts of the Choquet and Sugeno integrals, based on a fuzzy measure, can be adopted as useful tools in estimation of the total effectiveness of a drug when appreciating its positive influence on a collection of symptoms typical of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as measures in the Choquet and Sugeno problem formu-lations. After comparing the quantities of total effectiveness among medicines, expressed as the values of the Choquet or Sugeno integrals, we accomplish the selection of the most efficacious drug.
Theoretical fuzzy decision-making models mostly developed by Zadeh, Bellman, Jain and Yager can be adopted as useful tools to estimation of the total effectiveness-utility of a drug when appreciating its positive influence on a collection of symptoms characteristic of a considered diagnosis. The expected effectiveness of the medicine is evaluated by a physician as a verbal expression for each distinct symptom. By converting the words at first to fuzzy sets and then numbers we can regard the effectiveness structures as entries of a utility matrix that constitutes the common basic component of all methods. We involve the matrix in a number of computations due to different decision algorithms to obtain a sequence of tested medicines in conformity with their abilities to soothe the unfavorable impact of symptoms. An adjustment of the large spectrum of applied fuzzy decision-making models to the extraction of the best medicines provides us with some deviations in obtained results but we are thus capable to select this method whose effects closest converge to the physicians’ judgments and expectations. In the current paper we apply fuzzy decision making algorithms to rank medicines in multifocal toxoplasmosis.
The studies of Internet Protocol data give rise to the creation of polygons consisting of finite numbers of points tied together. Since the polygons are not formalized by some mathematical expressions, we suggest creating continuous functions, which approximate them thoroughly in spite of their irregular shapes. To warrant a high accuracy of approximating, otherwise impossible to obtain when using standard curves, we test a continuous function, which is composed of joined truncated pi-class functions with seven parameters. By operating with the functions representing polygons having unusual shapes, we attempt a classification of Internet traffic data, based on datagram sizes. We adopt rough sets to assign the members to an investigated Internet class even if their origin sometimes is unknown.
The studies of data, which result in sampled information in the form of finite fuzzy sets, give rise to the creation of polygons consisting of finite numbers of points tied together. Since the polygons are not formalized by some mathematical expressions, it would be desirable to find continuous functions approximating them rather thoroughly in spite of their irregular shapes. An approximation by the standard curves is sometimes too rough to be a reliable source of a further analysis of the polygons. To improve the accuracy of approximating we test a continuous function, which is composed of joined pi-class functions with seven parameters. The function, called by us “the sampled, truncated pi”, is very sensitive for each little deviation in the polygon’s shape, which allows us to classify it exactly without large errors usually accompanying a process of standard approximation.
We expand the classical model of a two-player game to select the best strategies, whose action is expected to maintain the values of a certain variable on the neutral level. By inserting fuzzy sets as payoff values in the game matrix we facilitate the procedure of formulations of payoff expectations by players. Instead of making difficult decisions about the choice of accurate numerical entries of the matrix the players are able to use words, which should simplify a communication between them when designing the preliminaries of the game. The players also have the possibility of making a ranking of their favorite strategies.
We expand the classical model of a two-player game by inserting of fuzzy sets as payoff values in the game matrix. Players can thus formulate their payoff expectations with words instead of deciding on numerical entries of the matrix. In this way we count on the better verbal communication between players when designing the preliminaries of the game. As a final result we expect to obtain samples of the players optimal strategies, which will preserve the profit of the game on the neutral level.
The evaluation of Resort Management System (RMS) quality is an item of many trials. We propose applying a complex system of two control algorithms to provide a final estimation of RMS. This distinct quality value will be dependent on some individual appreciations assigned by customers to basic services. We also discuss some improvements concerning the fuzzification parts of controllers.
The series Studies in Computational Intelligence (SCI) publishes new developments and advances in the various areas of computational intelligence – quickly and with a high quality. The intent is to cover the theory, applications, and design methods of computational intelligence, as embedded in the fields of engineering, computer science, physics and life science, as well as the methodologies behind them. The series contains monographs, lecture notes and edited volumes in com putational intelligence spanning the areas of neural networks, connectionist systems, genetic algorithms, evolutionary computation, artificial intelligence, cellular automata, self-organizing systems, soft computing, fuzzy systems and hybrid intelligent systems. Critical to both contributors and readers are the short publication time and world-wide distribution – this permits a rapid and broad dissemina tion of research results. springer.com Intelligent paradigms are increasing finding their ways in the design and development of decision support systems. This book presents a sample of recent research results from key researchers. The contributions include: • Introduction to intelligent systems in decision making • A new method of ranking intuitionistic fuzzy alternatives • Fuzzy rule base model identification by bacterial memetic algorithms • Discovering associations with uncertainty from large databases • Dempster-Shafer structures, monotonic set measures and decision making • Interpretable decision-making models • A General methodology for managerial decision making • Supporting decision making via verbalization of data analysis results using linguistic data summaries • Computational intelligence in medical decisions making This book is directed to the researchers, graduate students, professors, decision makers and to those who are interested to investigate intelligent paradigms in decision making.
The work is particularly addressed to some beginners in performing operations on continuous fuzzy numbers. We discuss three different approaches to operations on fuzzy numbers to make comparisons of results in the aspect of their advantages and disadvantages. By demonstrating different possibilities of making calculations on fuzzy numbers we intend to help users in the proper selection of such operators that are adapted to their tasks in the most adequate way.
We discuss two computational techniques in the current paper. In the first part, we aim at employing FCM (fuzzy c-means) clustering to compute membership degrees of two clusters providing decisions to perform surgery or not for a testing set of 25 gastric cancer patients. The second part handles mathematical modelling of a common function approximating the information obtained from the c-means procedure. After constructing the equation of the function, we can make the decision about the surgery in the form of the surgery degree for an arbitrary gastric cancer patient. A centre, dealing with mathematical techniques concerning surgery prognoses, can quickly decide about surgery for the patient who lives in a remote place. A transmission of information among the centre and some hospitals, interested in adopting the centre services, can facilitate surgery decision-making. This trial can be treated as a contribution in the telemedicine domain.
We explore the classical model of a two-player game to select the best strategies, where action is expected to maintain the values of a certain variable on the neutral level. By inserting fuzzy sets as payoff values in the game matrix, we facilitate the procedure of formulations of payoff expectations by players. Instead of making inconvenient decisions about the choice of accurate numerical entries of the matrix, the players are able to use words, which should simplify communication between them when designing the preliminaries of the game. The players also have the possibility of making a ranking of their favourite strategies. At the next stage of the play, we involve group decision-making in order to aggregate results coming from several paired games, when more than two players contradict each other.
Strict analytic formulas are the tools usually derived for determining the formal relationships between a sample of independent variables and a variable which they affect. If we cannot formalize the function tying the independent and dependent variables then we will utilize some control actions. Apart from crisp versions of control we often adopt their fuzzy variants developed by Mamdani and Assilian or Sugeno. Fuzzy control algorithms are furnished with softer mechanisms, when comparing them to classical control. The algorithms are particularly adaptable to support medical systems, often handling uncertain premises and conclusions. From the medical point of view it would be desirable to prognosticate the survival length for patients suffering from gastric cancer. We thus formulate the objective of the current paper as the utilization of fuzzy control actions for the purpose of making the survival prognoses.
The paper concerns specific problems of color digital picture recognition by use of the concept of fuzzy granulation, and in addition rough information granulation. This idea employs information granules that contain pieces of knowledge about digital pictures such as location of objects as well as their size and color. Each of those attributes is described by means of linguistic values of fuzzy sets, and the shape attribute is also considered with regard to the rough sets. The picture recognition approach is focused on retrieving a picture (or pictures) from a large collection of color digital pictures (images) - based on the linguistic description of a specific object included in the picture to be recognized.
In this paper, a new method of image retrieval is proposed. This concerns retrieving color digital images from a database that contains a specific linguistic description considered within the theory of fuzzy granulation and computing with words. The linguistic description is generated by use of the CIE chromaticity color model. The image retrieval is performed in different way depending on users’ knowledge about the color image. Specific database queries can be formulated for the image retrieval. © Springer International Publishing AG, part of Springer Nature 2018.
In this paper, a new method of image retrieval is proposed. This concerns retrieving color digital images from a database that contains a specific linguistic description considered within the theory of fuzzy granulation and computing with words. The linguistic description is generated by use of the CIE chromaticity color model. The image retrieval is performed in different way depending on users' knowledge about the color image. Specific database queries can be formulated for the image retrieval.
The paper concerns specifc problems of color digital image recognition by use of the concept of fuzzy and rough granulation. This idea employs information granules that contain pieces of knowledge about digital pictures such as color, location, size, and shape of an object to be recognized. The object information granule (OIG) is introduced, and the Granular Pattern Recognition System (GPRS) proposed, in order to solve different tasks formulated with regard to the information granules.
The paper proposes a new method employed in an intelligent pattern recognition system that generates linguistic description of color digital images. The linguistic description is produced based on fuzzy rules and information granules concerning colors as most important among image attributes. With regard to the color, the CIE chromaticity color model is applied, with the concept of fuzzy color areas. The linguistic description uses information about location of color granules in input images. © Springer International Publishing AG 2017.
The paper describes new algorithms proposed for the granular pattern recognition system that retrieves an image from a collection of color digital pictures based on the knowledge contained in the object information granule (OIG). The algorithms use the granulation approach that employs fuzzy and rough granules. The information granules present knowledge concerning attributes of the object to be recognized. Different problems are considered depending on the full or partial knowledge where attributes are "color", "location", "size", and "shape".
This paper presents different aspects of parallelization of a problem of processing color digital images in order to generate linguistic description of their content. A parallel architecture of an intelligent image recognition system is proposed. Fuzzy classifcation and inference is performed in parallel, based on the CIE chromaticity color model and granulation approach. In addition, the parallelization concerns, e.g., processing a large collection of images or parts of a single image.
Dynamic signature verification is a very interesting biometric issue. It is difficult to realize because signatures of the user are characterized by relatively high intra-class and low inter-class variability. However, this method of an identity verification is commonly socially acceptable.
It is a big advantage of the dynamic signature biometric attribute. In this paper, we propose a new hybrid algorithm for the dynamic signature verification based on global and regional approach. We present the simulation results of the proposed method for BioSecure DS2 database, distributed by the BioSecure Association.
Like data analysis, pattern recognition and data mining, fuzzy clustering also has been applied widely, and successful applications have been reported. In this paper we aim to employ the technique of fuzzy c-means (FCM) cluster to prognosticate the operation possibility on gastric cancer patients. Our purpose is to partition some clinical data in two fuzzy clusters. One of them considers patients who have a chance for successful surgery whereas the other cluster contains the patients without a view for surgery. Each patient is given by characteristic biological markers. The initial values of membership degrees taking place in the partition matrix are usually determined randomly. In this work we will use particularly designed membership functions to calculate the degrees of membership.
The chapter is composed of two parts. In the first part we aim at employing fuzzy c-means (FCM) clustering to prognosticate membership degrees pointing out possibilities for operation and none operation for a set of 25 gastric cancer patients characterized by values of decisive biological markers. The second part handles the technique of mathematical modelling of a common membership function approximating the information collected from the given set of patients. When constructing the equation of the function we are able to determine the operation and none operation diagnosis for an arbitrary gastric cancer patient.
Strict analytic formulas are the tools derived for determining the formal relationships between a sample of independent variables and a variable which they affect. If we cannot formalize the function tying the independent and dependent variables then we will utilize fuzzy control actions. The algorithm is particularly adaptable to support the problem of prognosticating the survival length for gastric cancer patients. We thus formulate the objective of the current paper as the utilization of fuzzy control action for the purpose of making the survival prognoses.
Abstract—In this paper, two models, one is called the probabilistic model and the other is known as the model of 2-tuple fuzzy linguistic representations, are applied to solve multi-expert decision making issues (MEDM). A MEDM problem is considered, in which a group of physicians are independently asked about assessing the effectiveness of a set of treatment therapies for a prostate cancer patient. The objective of this paper is to find the most common judgment by means of these two models. Moreover, fuzzy linguistic terms are used to express the experts’ opinions and s-parametric membership functions are designed to depict the fuzzy linguistic terms.
Apart from the probabilistic model and the model of 2-tuple linguistic representations, a new extension of the fuzzy set, known as the hesitant fuzzy linguistic term set can be seen as the third representative of linguistic approaches. In this paper, we focus on multi-expert decision-making problems, in which a group of physicians are independently asked for assessing the effectiveness of a set of treatment therapies. Our goal is to rank the effectiveness of treatment modalities from the most recommended to the contraindicated. Two individual prostate cancer patients have been taken into account in the practical studies. For the first patient, the probabilistic model and the model of 2-tuple linguistic representations have been adopted to accomplish the medical application. Whereas, for the second patient, the approach of hesitant fuzzy linguistic term set has been used to make the medication prognoses. Moreover, the continuous fuzzy numbers in the Left-Right representations are used to mathematically express the experts’ judgments and s-parametric membership functions are designed to represent the fuzzy linguistic terms.