Given a non-associative unital ring R, a monoid G and a set π of additive maps R→R, we introduce the Ore monoid ring R[π;G], and, in a special case, the differential monoid ring. We show that these structures generalize, in a natural way, not only the classical Ore extensions and differential polynomial rings, but also the constructions, introduced by Cojuhari, defined by so-called D-structures π. Moreover, for commutative monoids, we give necessary and sufficient conditions for differential monoid rings to be simple. We use this in a special case to obtain new and shorter proofs of classical simplicity results for differential polynomial rings in several variables previously obtained by Voskoglou and Malm by other means. We also give examples of new Ore-like structures defined by finite commutative monoids. © 2019 Elsevier Inc.
The use of ubiquitous network has made real time tracking of objects, animals and human beings easy through the use of radio frequency identification system (RFID). Localization techniques in RFID rely on accurate estimation of the read range between the reader and the tags. The tags consist of a small chip and a printed antenna which receives from and transmits information to the reader. The range information about the distance between the tag and the reader is obtained from the received signal strength indication (RSSI). Accuracy of the read range using RSSI can be very complicated especially in complicated propagation environment due to the nature and features of the environment. There are different kinds of localisation systems and they are Global Positioning System (GPS) which can be used for accurate outdoor localization; while technologies like artificial vision, ultrasonic signals, infrared and radio frequency signals can be employed for indoor localization. This project focuses on the location estimation in RFID Non Line-of-Sight (NLOS) environment using Real Time Localization System (RTLS) with passive tags, in carrying out passengers and baggage tracking at the airport. Indoor location radio sensing suffers from reflection, refraction and diffractions due to the nature of the environment. This unfavourable phenomenon called multipath leads to delay in the arrival of signal and the strength of signal received by receiving antenna within the propagation channel which in turns affects the RSSI, yielding inaccurate location estimation. RTLS based on time difference of arrival and error compensation technique and extended Kalman filter technique were employed in a NLOS environment to determine the location of tag. The better method for location estimation in a NLOS between the Kalman filtering and extended Kalman filtering is investigated. According to simulation results, the extended Kalman filtering technique is more suitable to be applied to RTLS.
Autostereoscopic multi view displays require multiple views of a scene to provide motion parallax. When an observer changes viewing angle different stereoscopic pairs are perceived. This allows new perspectives of the scene to be seen giving a more realistic 3D experience. However, capturing arbitrary number of views is at best cumbersome, and in some occasions impossible. Conventional stereo video (CSV) operates on two video signals captured using two cameras at two different perspectives. Generation and transmission of two views is more feasible than that of multiple views. It would be more efficient if multiple views required by an autostereoscopic display can be synthesized from these sparse set of views. This paper addresses the conversion of stereoscopic video to multiview video using the video effect morphing. Different morphing algorithms are implemented and evaluated. Contrary to traditional conversion methods, these algorithms disregard the physical depth explicitly and instead generate intermediate views using sparse sets of correspondence features and image morphing. A novel morphing algorithm is also presented that uses scale invariant feature transform (SIFT) and segmentation to construct robust correspondences features and qualitative intermediate views. All algorithms are evaluated on a subjective and objective basis and the comparison results are presented.
We describe the dimension of the space of possible linear endomorphisms that turn skew-symmetric three-dimensional algebras into Hom-Lie algebras. We find a correspondence between the rank of a matrix containing the structure constants of the bilinear product and the dimension of the space of Hom-Lie structures. Examples from classical complex Lie algebras are given to demonstrate this correspondence.
This thesis concerns healthcare management and specifically addresses the problems of operating room planning and waiting list management. The operating room department is one of the most expensive areas within the healthcare system which necessitates many expensive resources such as staff, equipment and medicine. The planning of operating rooms is a complex task involving many dependencies and conflicting factors and hence careful operating room planning is critical to attain high productivity. One part of the planning process is to determine a Master Surgery Schedule (MSS). An MSS is a cyclic timetable that specifies the allocation of the surgical groups into different blocks of operating room time. Using an optimization-based approach, this thesis investigates whether the MSS can be adapted to better meet the varying surgery demand. Secondly, an extended optimization-based approach, including post-operative beds, is presented in which different policies related to priority rules are simulated to demonstrate their affect on the average waiting time. The problem of meeting the uncertainty in demand of patient arrival, as well as surgery duration, is then incorporated. With a combination of simulation and optimization techniques, different policies in reserving operating room capacity for emergency cases together with a policy to increase staff in stand-by, are demonstrated. The results show that, by adopting a certain policy, the average patient waiting time and surgery cancellations are decreased while operating room utilization is increased. Furthermore, the thesis focuses on how different aspects of surgery pre-conditions affect different performance measures related to operating room planning. The emergency surgery cases are omitted and the studies are delimited to concern the elective healthcare process only. With a proposed simulation model, an experimental tool is offered, in which a number of analyses related to the process of elective surgeries can be conducted. The hypothesis is that, sufficiently good estimates of future surgery demand can be assessed at the referral stage. Based on this assumption, an experiment is conducted to explore how different policies of managing incoming referrals affect patient waiting times. Related to this study, possibility of using data mining techniques to find indicators that can help to estimate future surgery demand is also investigated. Finally, in parallel, an agent-based simulation approach is investigated to address these types of problems. An agent-based approach would probably be relevant to consider when multiple planners are considered. In a survey, a framework for describing applications of agent based simulation is provided.
Relying on organizational innovativeness for long-term growth and profitability can be difficult, time consuming, and expensive. In the context of service delivery of 395 strategic business units (SBU) in Israel's healthcare industry, this paper examines the role of a learning-orientation as a moderator in an integrative model of organizational innovativeness. We find moderation of the impacts of risk-taking, creativity, competitor benchmarking orientation, and environmental opportunities on innovativeness. Moreover, we find the influence on performance pronounced for high learning-oriented SBUs. The paper shows that learning orientation should be considered for understanding effective innovativeness work for competitive service delivery.
In the past decade, cooperative communications has been emerging as a pertinent technology for the current and upcoming generations of mobile communication infrastructure. The indispensable benefits of this technology have motivated numerous studies from both academia and industry on this area. In particular, cooperative communications has been developed as a means of alleviating the effect of fading and hence improve the reliability of wireless communications. The key idea behind this technique is that communication between the source and destination can be assisted by several intermediate nodes, so-called relay nodes. As a result, cooperative communication networks can enhance the reliability of wireless communications where the transmitted signals are severely impaired because of fading. In addition, through relaying transmission, communication range can be extended and transmit power of each radio terminal can be reduced as well. The objective of this thesis is to analyze the system performance of cooperative relay networks integrating advanced radio transmission techniques and using the two major relaying protocols, i.e., decode-and-forward (DF) and amplify-and-forward (AF). In particular, the radio transmission techniques that are considered in this thesis include multiple-input multiple-output (MIMO) systems and orthogonal space-time block coding (OSTBC) transmission, adaptive transmission, beamforming transmission, coded cooperation, and cognitive radio transmission. The thesis is divided into an introduction section and six parts based on peer-reviewed journal articles and conference papers. The introduction provides the readers with some fundamental background on cooperative communications along with several key concepts of cognitive radio systems. In the first part, performance analysis of cooperative single and multiple relay networks using MIMO and OSTBC transmission is presented wherein the diversity gain, coding gain, outage probability, symbol error rate, and channel capacity are assessed. It is shown that integrating MIMO and OSTBC transmission into cooperative relay networks provides full diversity gain. In the second part, the performance benefits of MIMO relay networks with OSTBC and adaptive transmission strategies are investigated. In the third part, the performance improvement with respect to outage probability of coded cooperation applied to opportunistic DF relay networks over conventional cooperative networks is shown. In the fourth part, the effects of delay of channel state information feedback from the destination to the source and co-channel interference on system performance is analyzed for beamforming AF relay networks. In the fifth part, cooperative diversity is investigated in the context of an underlay cognitive AF relay network with beamforming. In the sixth part, finally, the impact of the interference power constraint on the system performance of multi-hop cognitive AF relay networks is investigated.
Association rules are one of the most popular methods of data mining. This technique allows to discover interesting dependences between objects. The thesis concerns on association rules for hierarchy of objects. As a multi–level structure is used DBLP database, which contains bibliographic descriptions of scientific papers conferences and journals in computer science. The main goal of thesis is investigation of interesting patterns of co-authorship with respect to different levels of hierarchy. To reach this goal own extracting method is proposed.
FEM,ALE, ABAQUS
INARFIMA modell föreslås. CLS är FGLS och GMM estimatorer diskuteras. I sin empiriska tillämpning på två aktieserier för AstraZeneca och Ericsson B finner vi att båda serierna har långminne. Intra-dag, hög frekvens, Estimation, Fractional integration, Reaktionstid
In this paper, we review INMA time series of integer-valued model class, and discuss its further development. These models have been developed for analyzing high frequency financial count data. A vivid description of high frequency data in the context of market micro structure is given. The most distinguishing feature that makes the INMA model class different from its continuous variable MA counterpart is that multiplication of variables with real valued parameters no longer remains a viable operation when the result is to be integer-valued. In the estimation of these models, no underlying distributions are assumed. Hence, the discussion of estimations are limited to CL, FGLS and GMM. A further development of estimation procedures for these models have also been reviewed. We suggest that the models could be estimated with Quasi Maximum Likelihood and propose in addition a Generalized Method of Moment of Quasi Maximum Likelihood. We have also discussed how INMA model class can be extended with different underlying distributions for innovations.
This paper introduces Quasi-Maximum Likelihood Estimation for Long Memory Stock Transaction Data of unknown underlying distribution. The moments with conditional heteroscedasticity have been discussed. In a Monte Carlo experiment, it was found that the QML estimator performs as well as CLS and FGLS in terms of eliminating serial correlations, but the estimator can be sensitive to start value. Hence, two-stage QML has been suggested. In empirical estimation on two stock transaction data for Ericsson and AstraZeneca, the 2SQML turns out relatively more efficient than CLS and FGLS. The empirical results suggest that both of the series have long memory properties that imply that the impact of macroeconomic news or rumors in one point of time has a persistence impact on future transactions.
Some researches have already developed fuzzy decision making theoretical algorithms, but there are only a few medical fields of their applications. We thus make a trial of adopting the Yager decision making algorithm to extract the optimal medicine from a collection of drugs that can be given to a patient to cure him of an illness. The choice of the most efficacious remedy is based on clinical symptoms typical of the considered morbid unit.
Fuzzy set theory offers numerous methods that prove helpful in solving medical problems. They have already been successfully used for instance to fix the optimal level of drug action in patients revealing no clinical symptoms after treatment. In many morbid processes, however, although indices of measurable symptoms improve after the course of medication, the symptoms themselves do not retreat entirely. The authors have already proposed different fuzzy techniques involved in the solution of the problem described above. This time the suggestion of comparing three fuzzy decision making models aim at facilitation of the optimal drug choice in the case of symptoms that prevail after treatment.
The paper refers to earlier results obtained by the authors and constitutes their essential complement and extension by introducing to a diagnostic model the assumption that the decision concerning the diagnosis is based on observations of symptoms carried out repeatedly, by stages, which may have effect in a change of these symptoms in increasing time. The model concerns the observations of symptoms at an individual patient at a time interval. The changes of the symptoms give some additional information, sometimes very important in the diagnostic process when the clinical picture of a patient in a certain interval of time differs from that one which has been received from the beginning of the disease. It may occur that the change in the intensity of a symptom decides an acceptance of another diagnosis after some time when the patient does not feel better. The aim is to fix an optimal diagnosis on the basis of clinical symptoms typical of several morbid units with respect to the changes of these symptoms in time. In order to solve such a posed problem the authors apply the method of fuzzy relation equations, which are modelled by means of logical laws and the rules of inference. Moreover, in the final decision concerning the choice of a proper diagnosis, a normalized Euclidean distance is introduced as a measure between a real decision and an ”ideal” decision. A simple example presents the practical action of the method to show its relevance to a possible user.
Fuzzy set theory has used many auxiliary methods into the trials of solutions of some medical problems. One of the attempts was the evaluation of the optimal level of the drug action in the case when the clinical symptoms disappeared completely after the treatment. However, there can occur such a morbid process in which the symptoms prevail after the treatment. The medication improves too high or too low level of the quantitative symptom but it still indicates the presence of the illness. It is not so easy to choose the medicine, which acts best because it can happen that most of them influence the same symptoms, while they do not improve the others. A fuzzy decision making model tries to make easier to find such a drug which affects most of the symptoms in the highest degree. In the next attempt of solving the problem we propose the using of discrete membership functions in the model instead of the continuous ones. It should improve the thoroughness of the method and heighten the reliability of the accepted decision.
Fuzzy Set Theory has used many auxiliary methods in the trials of solutions of some medical problems. One of the attempts was the finding of the optimal level of drug action in the case when the clinical symptoms disappeared completely after the treatment (Gerstenkorn and Rakus, 1994; Rakus, 1991). However, there can occur such a morbid process in which the symptoms do not disappear after the treatment. The medication improves too high or too low level of the quantitative symptom but it still indicates the presence of the disease. It sometimes makes some problems to choose the medicine, which acts best because it can happen that most of them influence the same symptoms while they do not improve the others. A fuzzy decision making model tries to make easier to find such a drug which affects most of the symptoms in the highest degree. To solve this problem we propose an application of discrete values of the membership degrees in the model instead of the continuous ones that were tested in the paper of Rakus-Andersson and Gerstenkorn (1997). It should improve the thoroughness of the method and heighten the reliability of the accepted decision. It is also considered how to choose the best medicine in the circumstances when some decision-makers have different opinions about the priority of the tested drugs.
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. In the current work we form families of constraints which originate from one function. By introducing a parameter in the initial membership function we can model the rest of family functions, whose shapes depend only on a number of functions and the length of a reference set. This procedure fits perfectly for being a segment of computer programs, where the loops providing us with many functions need only the initializations of two data values.
Artikeln presenterar användning av oskarp egenvektor i processen approximeringen av läkemedelsverkan på kliniska symptom. En oskarp relation, introducerad i en ”fuzzy” ekvation med lösningen lika med den oskarpa egenvektorn, innehåller oskarpa nummer som uttrycker läkemedelsinverkan på parsymtom. Dessa nummer, skapade i L-Rformen ersätter verbala beskrivningar av påverkan. Det resultat, som visar läkemedelsnivåer vid varje symtom, fås genom en tolkning av oskarpa nummer i den erhållna egenvektorn.
The paper refers to earlier results obtained by authors and constitutes their essential complement by introducing to a diagnostic model the assumption that a decision concerning the diagnosis is based on observations of symptoms in some stages at an individual patient. To fix the optimal diagnosis we introduce the normalized Euclidean distance between fuzzy sets representing the ideal decision and a possible real decision stated by studying clinical symptoms.
The compositional rule of inference, grounded on the modus ponens law, is one of the most effective fuzzy systems. We modify the classical version of the Zadeh rule to propose an original model, which concerns determining an operation chance for gastric cancer patients. The operation prognosis will be dependent on values of biological markers indicating the progress of the disease.
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 by Zadeh 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.
It is a privilege for the author to be involved in composing a book chapter in the anthology devoted to the life and scientific occupation of Professor Zdzisław Pawlak. The author made a personal acquaintance with the outstanding scientist Professor Pawlak and still remembers him as a warm and gentle human being. Professor Pawlak’s theory of rough sets was taught to students during the courses in Computational Intelligence established at Blekinge Institute of Technology in Karlskrona, Sweden. In some Master of Science theses, the principles of rough set theory were discussed in the aspects of technical applications. In this context, we can feel that the theory is still alive and very useful. In this work, we recall again the basics of rough sets to apply them to the classification of discrete two dimensional point sets, which form the shapes resembling some letters. These possess very irregular patterns and cannot be approximated by standard curves without committing large errors. Since the approximation of letter-like point sets is required by the latter classification of their shapes then we, due to own model, wish to find a continuous curve which fits best for each distribution of points. To accomplish the thorough approximation of finite point sets, we test parametric s-truncated functions piecewise, which warrants a high accuracy of approximating. By operating on the functions, replacing samples of points obtained during experiments carried out, we are able to adopt the rough set technique to verify decisions about the primary recognitions of the curves’ appearance as letter shapes. Even if the curves are stretched and shaped differently in the plane, we will divide them in classes gathering similar objects. Our investigations have not a character of pure art — on the contrary— their results are utilized in the classifications of internet packet streams or the analysis of wave signals typical of, e.g., medical examinations.
This chapter has a theoretical character and can be studied by some medical staff researchers that seek methods of approximation of very irregular point sets. When the shape of an obtained polygon based on the point set is similar to a chain of bells, then it will be difficult to find a continuous standard curve that should approximate the polygon without making a large approximation error. The studies of some medical 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 that approximate them thoroughly in spite of their irregular shapes. To warrant a high accuracy of approximation, otherwise impossible to obtain when using standard curves, we test a continuous function composed of joined truncated π-functions or joined truncated s-functions. © 2007 Springer.
We should admit that the case of patient P1 in Ex. 3.16 has not been very easy to solve especially when you consider the proper interpretation of PD3. By equipping us with equal values of the membership degrees it has not made it easy enough to make the proper choice of an unknown diagnosis. © 2007 Springer.
In this paper we propose a complex system, involving two control algorithms, to provide a final estimation of Resort Management System (RMS). This distinct RMS quality value depends on some individual appreciations, assigned by customers to basic services. In order to improve the qualities of control actions, we intend to add parametric membership functions of fuzzy sets to the fuzzification part. Another modification considers the newly designed technique of determining some essential estimates in the processing part of control to employ all entry data in the result of final decision.
In the first part of this study we explore continuous fuzzy numbers in the interval- and the alpha-cut forms to detect their similar nature. The conversion from one form to the other is a question of using the appropriate apparatus, which we also provide. Since the fuzzy numbers can reproduce fuzzy events we then will make a trial of extending the concept of fuzzy probability, defined by R. Yager for discrete fuzzy events, on continuous fuzzy events. In order to fulfill the task we utilize conclusions made about fuzzy numbers to propose an initial conception of approximating the Gauss curve by a particularly designed function originated from the pi-class functions. Due to the procedure of the approximation, characterized by an irrelevant cumulative error, we expand fuzzy probabilities of continuous fuzzy events in the form of continuous fuzzy sets. Furthermore, we assume that this sort of probability holds some conditions formulated for probabilities of discrete fuzzy events.
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 collec-tion 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 speech we apply fuzzy decision making algorithms to ranking medicines in multifocal toxoplasmosis.
The classical crisp version of Factor Analysis seldom is used in the case of qualitative factors, which often are presented by codes. It is rather difficult to divide codes in level groups without possessing appropriate criteria. To omit this obstacle, we thus propose a fuzzy application of Factor Analysis, which gives a possibility to investigate the strength of an influence of qualitative factors on a tested qualitative variable. When making a new approach to the analysis of factors, we introduce a space of verbal fuzzy numbers that first are expressed as descriptions coming from a natural language and then designed in L-R form. Since the definition of newly created verbal fuzzy numbers deviates from the general conception of fuzzy numbers, we also will check effects of other operations performed on verbal numbers, which are different from the arithmetic based on the extension principle. The verbal fuzzy numbers represent both the qualitative variable and the qualitative factors in all computations that follow the Factor Analysis algorithm. For the first time we also formulate the Yager probability of an event expanded as the verbal fuzzy number.
Den klassiska versionen av faktoranalys är sällan använd i fall med kvalitativa faktorer. Hindret utgör brist på lämpliga kriterier på nivåer av dessa faktorer. Vi föreslår därför en oskarp version av metoden i vilken kvalitativa faktorer som påverkar den ofta kvalitativa variabeln är uttryckta som först verbala beskrivningar och efteråt vaga tal. Vi kan fortfarande avgöra vilken påverkan faktorerna har på den testade variabeln. Den introducerade "fuzzy" verbala mängd, som har fått sina axiom, hjälper till att lösa den ovanstående frågan.
This 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. A lot of appealing examples are added to facilitate comprehension of theoretical principles for a reader, so that even a beginner in fuzzy set theory can follow calculation steps without implementing computer programs. 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.
The classical fuzzy decision-making model is now tested for qualitative compound states-symptoms to select the most efficacious medicine, acting on all symptoms. Instead of terminating the decision procedure in the way comparing values of total utilities of decisions-treatments, we test the aggregated utility values in utility levels. This activity lets us assign a verbally verified utility to each medicine.
The book presents different algorithms of diagnosing on the base of clinical symptoms. Some modern techniques as computing with words and the use of non-conventional operations on fuzzy membership degrees and fuzzy numbers are proposed as a new approach to the diagnostic problem. A large part of the work is devoted to differentiating the level of the drug action in the case of symptoms, which either disappear or still prevail after the treatment.
In the first part of this study we explore continuous fuzzy numbers in the interval and the α-cut forms to detect their similar nature. The conversion from one form to the other is a question of using the appropriate apparatus, which we also provide. Since the fuzzy numbers can reproduce fuzzy events we then will make a trial of extending the concept of fuzzy probability, defined by R. Yager (1979) for discrete fuzzy events, on continuous fuzzy events. In order to fulfil the task we utilise conclusions made about fuzzy numbers to propose an initial conception of approximating the Gauss curve by a particularly designed function originated from the π-class functions. Due to the procedure of the approximation, characterised by an irrelevant cumulative error, we expand fuzzy probabilities of continuous fuzzy events in the form of continuous fuzzy sets.
From the domain of Computational Intelligence we have selected immunological computation and fuzzy systems to combine them in a new hybrid model. This novel numerical method has been tested on patient data strings to make decisions about the choices of surgery types. The model input clinical data concerns patients who suffer from gastric cancer.
Minimization of regret has been adopted here as a decision making algo-rithm in order to select the best medicine from a collection of drugs considered in the treatment of an individual patient. We assume that symp-toms affected by medicines have a compound qualitative complexion. A model of evaluating the effectiveness of drugs, exerting an influence on qualitative features, is employed to found the utility matrix, which constitutes the input system in decision-making. We thus discuss the method that converts information obtained from a questionnaire to entries of the matrix mentioned. The last technique constitutes a main own contribution in evolving methods of fuzzy calculus.
Some researches have already developed fuzzy decision making theoretical algorithms, but there are only a few medical fields of their applications. We thus make a trial of adopting two decision-making algorithms based on unequal objectives and minimization of regret to extract the optimal medicine from a collection of drugs recommended to a patient. A choice of the most efficacious remedy is based on clinical symptoms typical of the considered morbid unit.
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. One of the premises is formed as the implication, which is represented by different mathematical approaches, but we are especially fond of the results brought by the early implication proposed by Zadeh, which is modified in our practical model concerning a medical application. The approximate reasoning system, grounded on the extended and modified version of Modus Ponens law, will be employed here to predict a chance of survival after the operation for a patient who suffers from cancer. The patient’s symptom levels are the indicators of the disease. If the symptoms do not exceed their critical values there is still a chance to save the patient’s life by trying surgery. We wish to evaluate the verbal prognosis of the surgery by involving specifically designed fuzzy sets in the algorithm of approximate reasoning. Since the chance of successful surgery depends on the interactions of several symptoms then we will name the decision model multi-dimensional.
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. There exist different approaches to an implication, being the crucial part of the rule, but we are especially fond of the results brought by the early implication proposed by Zadeh, which is modified in our practical model concerning a medical application. The approximate reasoning system, grounded on the extended version of Modus Ponens law, will be employed here to predict a chance of positive effects of the operation on a patient who suffers from stomach cancer. The patient’s CRP (C-reactive proteins) symptom level, pathologically heightened, indicates the presence of a disease. When the CRP-value does not exceed a critical border it can be realistic to try surgery to recover the patient from his/her illness due to Do-Kyong Kim. We wish to evaluate the verbal prognosis of the surgery by involving particularly designed fuzzy sets in the algorithm of approximate reasoning.
Rough sets, surrounded by two approximation sets filled with sure and possible members constitute perfect mathematical tools of the classification of some objects. In this work we adopt the rough technique to verify diagnostic decisions concerning a sample of patients whose symptoms are typical of a considered diagnosis. The objective is to extract the patients who surely Suffer from the diagnosis, to indicate the patients who are free from it, and even to make decisions in undefined diagnostic cases. By applying selected logical decision rules, we also discuss a possibility of reducing of symptom sets to their minimal collections preserving the previous results in order to minimize a number of numerical calculations.
Rough sets, surrounded by two approximation sets filled with sure and possible members constitute perfect mathematical tools of the classification of some objects. In this work we adopt the rough technique to verify diagnostic decisions concerning a sample of patients whose symptoms are typical of a considered diagnosis. The objective is to extract the patients who surely suffer from the diagnosis, to indicate the patients who are free from it, and even to make decisions in undefined diagnostic cases. By applying selected logical decision rules, we also discuss a possibility of reducing of symptom sets to their minimal collections preserving the previous results in order to minimize a number of numerical calculations.
Rough sets constitute helpful mathematical tools of the classification of objects belonging to a certain universe when dividing the universe in two collections filled with sure and possible members. In this work we adopt the rough technique to verify diagnostic decisions concerning a sample of patients whose symptoms are typical of a considered diagnosis. The objective is to extract the patients who surely suffer from the diagnosis, to indicate the patients who are free from it, and even to make decisions in undefined diagnostic cases. We also consider a decisive power of reducts being minimal collections of symptoms, which preserve the previous classification results. We use them in order to minimize a number of numerical calculations in the classification process. Finally, by testing influence of symptom intensity levels on the diagnosis indisputable appearance we select these standards, whose either presence or absence in the patients allows us to add complementary remarks making the classification effects even more readable.
Due to the latest research the subject of Computational Intelligence has been divided into five main regions, namely, neural networks, evolutionary algorithms, swarm intelligence, immunological systems and fuzzy systems. Our attention has been attracted by the possibilities of medical applications provided by immunological computation algorithms. Immunological computation systems are based on immune reactions of the living organisms in order to defend the bodies from pathological substances. Especially, the mechanisms of the T-cell reactions to detect strangers have been converted into artificial numerical algorithms. Immunological systems have been developed in scientific books and reports appearing during the two last decades. The basic negative selection algorithm NS was invented by Stefanie Forrest to give rise to some technical applications. We can note such applications of NS as computer virus detection, reduction of noise effect, communication of autonomous agents or identification of time varying systems. Even a trial of connection between a computer and biological systems has been proved by means of immunological computation. Hybrids made between different fields can provide researchers with richer results; therefore associations between immunological systems and neural networks have been developed as well. In the current chapter we propose another hybrid between the NS algorithm and chosen solutions coming from fuzzy systems. This hybrid constitutes the own model of adapting the NS algorithm to the operation decisions “operate” contra “do not operate” in gastric cancer surgery. The choice between two possibilities to treat patients is identified with the partition of a decision region in self and non-self, which is similar to the action of the NS algorithm. The partition is accomplished on the basis of patient data strings/vectors that contain codes of states concerning some essential biological markers. To be able to identify the strings that characterize the “operate” decision we add the own method of computing the patients’ characteristics as real values. The evaluation of the patients’ characteristics is supported by inserting importance weights assigned to powerful biological indices taking place in the operation decision process. To compute the weights of importance the Saaty algorithm is adopted.
Some collections of two-dimensional points form very irregular shapes, which cannot be approximated by standard curves without making large errors. We approximate the sets of points to introduce formal mathematical expressions giving rise for future predictions for other points, which are not placed in data sets. To accomplish the thorough approximation of finite point sets we test parametric s-truncated functions piecewise, which warrants a high accuracy of approximating. By operating with the functions, which represent samples of points obtained during experiments carried out, and by adopting the rough set technique, we attempt a classification of curves. Even if the curves are stretched and shaped differently we will divide them in classes gathering similar objects. To confirm availability and correctitude of the approximation and the classification proposed, we consider an examination of Internet packet streams, especially a bottleneck distribution based on throughput values.
The project titled: “The Composition of the Book in Fuzzy Logic Adapted to Stationary and Distance Courses for Advanced Students” has been granted by the Swedish Royal Academy of Sciences in 2007 The following contents of the book “Basic Concepts and Applications of Fuzzy Set Theory” is primarily designed as: Contents 1. Introduction 2. Fuzzy sets 3. Fuzzy and linguistic variables 4. Operations on fuzzy sets 5. T and S Norms 6. Fuzzy measures and measures of fuzziness 7. Extension principles 8. Fuzzy numbers and their arithmetic 9. The L-R, interval and alpha-cut representations of fuzzy numbers 10. Fuzzy relations, The compositional rule of inference 11. The eigen sets of a fuzzy relation 12. Fuzzy analysis 13. Possibility theory, Probability of fuzzy events 14. Fuzzy logic and approximate reasoning 15. Fuzzy decision making, 16. Fuzzy control, 17. Imprecise optimization 18. Choquet and Sugeno integrals 19. Rough set theory 20. Discussion of other imprecise theories
I vissa tekniska eller medicinska experiment är data erhållna som vaga mått. Om vi betraktar dessa oskarpa värden som först verbala uttryck, t ex. ”nära fyra” eller ”nästan fyra”, där beskrivningar kommer från en programmerad lista, kan vi efteråt finna deras representation som oskarpa nummer i L-Rform. På dessa nummer testas Dubois-Pradeoperationer i en algoritm av Lagrange polynom, som leder till en fuzzy-funktion. Denna funktion interpolerar punkterna med oskarpa koordinater.
Alla uppgifter blir lösta med hjälp av teorin om oskarpa mängder (Fuzzy Set Theory). I projektet gäller först att approximera medelvärde och varians för stickprov som innehåller oskarpa värden och att skapa en sannolikhetsfördelning enligt Yagers fuzzy definition av sannolikhet. Denna nya fördelning skulle införa en fuzzy mängd istället för ett värde i fördelningen och skulle ersätta den klassiska normalfördelningen. Vidare är det önskvärt att evaluera fuzzy signifikansnivåer som fuzzy nummer och att skapa statistiska tester anpassade till fuzzy data som oskarpa eller verbala uttryck. Det är viktigt att genomföra en statistisk undersökning av en kvalitativ variabel som påvisar faktorernas inverkan på den med hjälp av Faktoranalys, förutsatt att data kommer från en enkät. I flera tillämpningar är det nödvändigt att känna till en fuzzy funktion som approximerar en mängd av punkter med oskarpa koordinater. För att genomföra den sista uppgiften testas olika klassiska numeriska metoder och anpassas till fuzzy omständigheter.
The eigen fuzzy set of a given fuzzy relation often corresponds to an occurrence of invariability in natural sciences. By determining the fuzzy relations as connections between pairs of symptoms we utilize the greatest and the least eigen fuzzy sets in order to find the estimates of the medicine effectiveness levels.