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## Fifty years of fuzzy research: A bibliometric analysis and a long-term comparative overview

Metrics details. The concept of risk has pervaded medical literature in the last decades and has become a familiar topic, and the concept of probability, linked to binary logic approach, is commonly applied in epidemiology and clinical medicine.

The application of probability theory to groups of individuals is quite straightforward but can pose communication challenges at individual level. Few articles by the way have tried to focus the concept of "risk" at the individual subject level rather than at population level. The author has reviewed the conceptual framework which has led to the use of probability theory in the medical field in a time when the principal causes of death were represented by acute disease often of infective origin.

In the present scenario, in which chronic degenerative disease dominate and there are smooth transitions between health and disease the use of fuzzy logic rather than binary logic would be more appropriate. The use of fuzzy logic in which more than two possible truth-value assignments are allowed overcomes the trap of probability theory when dealing with uncertain outcomes, thereby making the meaning of a certain prognostic statement easier to understand by the patient.

At individual subject level the recourse to the term plausibility , related to fuzzy logic, would help the physician to communicate to the patient more efficiently in comparison with the term probability , related to binary logic. This would represent an evident advantage for the transfer of medical evidences to individual subjects.

Peer Review reports. The concept of risk has pervaded medical literature in the last decades and has become a familiar topic. Few articles by the way have tried to focus the concept of "risk" at the individual subject level rather than at population level [ 1 ]. The concept of medical risk for the single individual from a mathematical point of view opens an interesting philosophical debate on the appropriate use of the term probability.

As I will try to explain, the recourse to the term plausibility , related to fuzzy logic, would help the physician to communicate to the patient more efficiently in comparison with the term probability , related to binary logic.

The dictionaries tell us that risk is "the possibility of loss or injury". This definition is familiar to most of us when we think of the possibility of being involved in a crash when driving a car or when flying in a plane.

In medicine like in many other contexts the assessment of a particular risk related to the occurrence of a harmful event is generally performed by means of probability theory. Medical science has borrowed this approach from other disciplines, like astronomy, fine arts, gambling, and insurance, which contributed most to the development of the mathematics of probability already back in the 17 th century.

Still today, for well defined random events, the probability distribution can easily be determined employing methods originally developed by Blaise Pascal [ 2 ]. One should not be surprised by this fact, since the development of the modern science of medicine took place when the prevalent causes of death were infectious diseases which typically follow an epidemic behavior.

It is evident that when dealing with pathogen transmission a certain degree of randomness clearly exists, and this justifies the recourse to probability theory. Over the last fifty years, at least in western countries, the overall health scenario has dramatically changed, and cardiovascular diseases, cancer, and degenerative diseases have gradually dominated the health scenario, overtaking infectious diseases as the principal cause of death.

These chronic conditions behave as complex systems dominated by gradual onset over time and multivariate causes changing over time. More specifically, events occurring in association with these diseases definitively have an explanation, and are seldom, almost never, truly random. The problem, if any, lies in the complexity of this explanation which sometimes exceeds our present understanding, forcing us to use sophisticated modeling.

The use of probability theory to assess the risk of undergoing a "cardio-vascular event" for example would mean that the event takes place as a "all or nothing" phenomenon, while it is generally not. An "all or nothing" phenomenon implies that the condition of the subject exposed to the risk of the event does not change in relation to the actual occurrence of the event.

For example, if the event consists in being hit by a tile falling from a roof whilst walking along a street, we wouldn't expect particular transition phases preceding the unfortunate event, at least at the level of the victim of the event. In clinical settings on the contrary, very often, even if the event takes place suddenly, resembling a falling tile, it can be considered as the natural final outcome of an unstable and evolving condition which predisposes by its nature the subject to the event.

In order to better explain this concept we can consider the case of a cerebro-vascular event in relation to the presence of a carotid stenosis. We know that local lesion parameters morphology, degree of stenosis , hemodynamic factors collateral compensation and systemic factors clinical symptoms, accompanying diseases, risk factor control have been taken into account to develop a model able to determine the likelihood of the occurrence of an event.

To simplify the reasoning, we can assume that it is just the degree of stenosis which actually influences and ultimately determines the development of the event.

The patient in this example would make a transition along different degrees of event "plausibility", by evolving with their asymptomatic carotid disease, while the subject walking along the street would remain continuously in a "all or nothing" situation.

In the latter case one would use the frequency of being hit on the head by a falling tile in a general population to describe the risk to which this subject is exposed, for example 1: As it is known, standard logic applies only to concepts that are completely true having degree of truth 1.

Traditionally, logical calculi are bivalent that is, there are only two possible truth values for any proposition, true and false which generally correspond to our intuitive notions of truth and falsity. But bivalence is only one possible range of truth values that may be assigned, and other logical systems have been developed with variations on bivalence, or with more than two possible truth-value assignments. In the classical bivalence scheme, true and false are determinate values: a proposition is either true or false exclusively , and if the proposition does not have one of those values, by definition it must have the other.

Fuzzy logic is a generalization of standard logic, in which a concept can possess a degree of truth anywhere between 0. Fuzzy logic was originally intended to be used for reasoning about inherently vague concepts, such as 'height. For example, we might say that 'President Berlusconi is tall,' with a degree of truth of 0. At this stage it is important to point out the distinction between fuzzy systems and probability. Both operate over the same numeric range, and at first glance both have similar values: 0.

By contrast, fuzzy terminology supposes that Mandela is "more or less" old, and in the specific example the "fuzzy degree" of membership corresponds to the value of 0.

It is important to reiterate that at mathematical level, fuzzy values can be easily misunderstood to be probabilities, and that one can believe that fuzzy logic is a fancy way to handle probabilities.

A fundamental difference is that while the sum of probabilities of two disjoint sets must always be equal to one requirement of additivity , fuzzy measures can be either super or subadditive.

In other words sets that are fuzzy, or multivalent, break the Aristotelian law of the excluded middle and can belong only partially to a fuzzy set sub-additive or also belong to more than one set super-additive. Probability measures whether something will occur or not.

Fuzziness measures the degree to which some condition exists or something occurs [ 4 ]. For the readers interested to deepen the topic of the differences between probability and fuzzy theory the essay written by George Klir represents an essential reference [ 5 ].

Although traditional statistics systems based on binary logic have been used successfully as diagnostic decision aids in different fields of medicine, it is now more and more evident that their obliged recourse to probability theory to represent uncertainty in the medical context may be inappropriate in many circumstances and partly responsible for their limitations in certain applications.

In recent years interesting proposals for the application of fuzzy logic in medical science have appeared in the literature, and in this regards a special mention has to be made to the contributions coming from the group of Helgason, aiming for example to better individualize diagnostic process[ 6 ] or prescribing and dosing of particular medications at the bedside[ 7 , 8 ].

An interesting concept among others emerging from these papers is that fuzzy measures are better able to capture variables interactions in the individual subjects in comparison with standard statistical measures [ 9 ]. Other authors have also proposed the use of fuzzy logic to concepts to population biology with emphasis in epidemiological problems like causal studies, epidemic models and designing of vaccination strategies [ 10 ], showing that the applications of fuzzy sets in epidemiology is a very promising area of research.

In the cardiovascular field of medicine this could make a substantial difference. In the case of a probabilistic approach we would have to inform the patient that given their present clinical condition, i. The use of fuzzy logic could allow to escape the probability theory trap in order to deal with a certain degree of uncertainty, thereby making the meaning of a certain prognostic statement easier to understand by the patient. This would represent an evident advantage for the transfer of knowledge of diseases to individual subjects.

Hald A: A history of probability and statistics and their applications before Google Scholar. Zadeh LA: Torwards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets Syst.

Klir G: Is there more to uncertainty than some probability theorists might have us believe?. Int J Gen Syst. Helgason CM, Jobe TH: Fuzzy logic and causal reasoning with an 'n' of 1 for diagnosis and treatment of the stroke patient. Expert Rev Neurother. Helgason CM: The application of fuzzy logic to the prescription of antithrombotic agents in the elderly.

Drugs Aging. Curr Treat Options Cardiovasc Med. Artif Intell Med. Download references. Correspondence to Enzo Grossi. Reprints and Permissions. Grossi, E. Medical concepts related to individual risk are better explained with "plausibility" rather than "probability".

Discussion The author has reviewed the conceptual framework which has led to the use of probability theory in the medical field in a time when the principal causes of death were represented by acute disease often of infective origin. Summary At individual subject level the recourse to the term plausibility , related to fuzzy logic, would help the physician to communicate to the patient more efficiently in comparison with the term probability , related to binary logic.

Background The concept of risk has pervaded medical literature in the last decades and has become a familiar topic. Discussion Plausibility vs probability The use of probability theory to assess the risk of undergoing a "cardio-vascular event" for example would mean that the event takes place as a "all or nothing" phenomenon, while it is generally not.

Fuzzy logic vs probability Fuzzy logic was originally intended to be used for reasoning about inherently vague concepts, such as 'height. Fuzzy logic in science and medicine Although traditional statistics systems based on binary logic have been used successfully as diagnostic decision aids in different fields of medicine, it is now more and more evident that their obliged recourse to probability theory to represent uncertainty in the medical context may be inappropriate in many circumstances and partly responsible for their limitations in certain applications.

But what about prognosis? Could we use fuzzy logic in the presence of occurrence facts? My tentative answer would be "yes". References 1. Additional information Competing interests The author s declare that they have no competing interests.

## Fifty Years of Fuzzy Logic and its Applications

The system can't perform the operation now. Try again later. Citations per year. Duplicate citations. The following articles are merged in Scholar. Their combined citations are counted only for the first article.

## Fifty Years of Fuzzy Logic and its Applications Studies in Fuzziness and Soft Computing

Metrics details. The concept of risk has pervaded medical literature in the last decades and has become a familiar topic, and the concept of probability, linked to binary logic approach, is commonly applied in epidemiology and clinical medicine. The application of probability theory to groups of individuals is quite straightforward but can pose communication challenges at individual level. Few articles by the way have tried to focus the concept of "risk" at the individual subject level rather than at population level.

The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining, and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Skip to main content Skip to table of contents.

### Fifty Years of Fuzzy Logic and its Applications

It seems that you're in Germany. We have a dedicated site for Germany. Editors: Tamir , Dan E. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Is the World Itself Fuzzy? JavaScript is currently disabled, this site works much better if you enable JavaScript in your browser.

- Я… я протестую. Я думаю… - Вы протестуете? - переспросил директор и поставил на стол чашечку с кофе.  - Я протестую.

PDF | This book offers a multifaceted perspective on fuzzy set theory, discussing its developments over the last 50 years. It reports It presents a wealth of real-​world sample applications, from routing problem to robotics, and from agriculture to engineering. May ; Fuzzy Logic in Its 50th Year; pp

#### Background

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Если даже он каким-то образом откроет лифт и спустится на нем вместе со Сьюзан, она попытается вырваться, как только они окажутся на улице. Хейл хорошо знал, что этот лифт делает только одну остановку - на Подземном шоссе, недоступном для простых смертных лабиринте туннелей, по которым скрытно перемешается высокое начальство агентства. Он не имел ни малейшего желания затеряться в подвальных коридорах АНБ с сопротивляющейся изо всех сил заложницей. Это смертельная ловушка. Если даже он выберется на улицу, у него нет оружия.

Хейл бросил взгляд на коммандера и Сьюзан, затем достал из кармана бумажник, извлек из него крохотную каталожную карточку и прочитал то, что было на ней написано. Еще раз убедившись, что Сьюзан и коммандер поглощены беседой, Хейл аккуратно нажал пять клавиш на клавиатуре ее компьютера, и через секунду монитор вернулся к жизни. - Порядок, - усмехнулся. Завладеть персональными кодами компьютеров Третьего узла было проще простого. У всех терминалов были совершенно одинаковые клавиатуры. Как-то вечером Хейл захватил свою клавиатуру домой и вставил в нее чип, регистрирующий все удары по клавишам. На следующее утро, придя пораньше, он подменил чужую клавиатуру на свою, модифицированную, а в конце дня вновь поменял их местами и просмотрел информацию, записанную чипом.

Танкадо использовал ТРАНСТЕКСТ, чтобы запустить вирус в главный банк данных. Стратмор вяло махнул рукой в сторону монитора.

Мой Бог. Это была настоящая красотка. - Спутница? - бессмысленно повторил Беккер.

Она протянула руку, поманив его к .

Он остался в живых. Это было настоящее чудо. Священник готовился начать молитву. Беккер осмотрел свой бок. На рубашке расплывалось красное пятно, хотя кровотечение вроде бы прекратилось.

Прости меня, - умолял. Сьюзан пыталась отстраниться, но он не отпускал. ТРАНСТЕКСТ задрожал, как ракета перед стартом.

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