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Fuzzy Logic with Engineering Appl 2e
Fuzzy logic refers to a large subject dealing with a set of methods to characterize and quantify uncertainty in engineering systems that arise from ambiguity, imprecision, fuzziness, and lack of knowledge. Fuzzy logic is a reasoning system based on a foundation of fuzzy set theory, itself an extension of classical set theory, where set membership can be partial as opposed to all or none, as in the binary features of classical logic. Fuzzy logic is a relatively new discipline in which major advances have been made over the last decade or so with regard to theory and applications. Following on from the successful first edition, this fully updated new edition is therefore very timely and much anticipated. Concentration on the topics of fuzzy logic combined with an abundance of worked examples, chapter problems and commercial case studies is designed to help motivate a mainstream engineering audience, and the book is further strengthened by the inclusion of an online solutions manual as well as dedicated software codes. Senior undergraduate and postgraduate students in most engineering disciplines, academics and practicing engineers, plus some working in economics, control theory, operational research etc, will all find this a valuable addition to their bookshelves.
- GenresMathematics
652 pages, Paperback
First published August 4, 2004
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February 8, 2023While fuzzy systems are shown to be universal approximators to algebraic functions, it is not this attribute that actually makes them valuable to us in understanding new or evolving problems. Rather, the primary benefit of fuzzy systems theory is to approximate system behavior where analytic functions or numerical relations do not exist.
fuzzy systems, as they are posed now, can be described as shallow models in the sense that they are primarily used in deductive reasoning. This is the kind of reasoning where we infer the specific from the general. In contrast to this is the kind of reasoning that is inductive, where we infer the general from the particular;
How do humans reason in situations that are complicated or ill-defined? we are superb at seeing or recognizing or matching patterns– behaviors that confer obvious evolutionary benefits. In problems of complication then, we look for patterns; and we simplify the problem by using these to construct temporary internal models or hypotheses or schemata to work with. We carry out localized deductions based on our current hypotheses and we act on these deductions. Then, as feedback from the environment comes in, we may strengthen or weaken our beliefs in our current hypotheses, discarding some when they cease to perform, and replacing them as needed with new ones. In other words, where we cannot fully reason or lack full definition of the problem, we use simple models to fill the gaps in our understanding; such behavior is inductive.
When students graduate, it seems that their biggest fear upon entering the real world is ‘‘forgetting the correct formula.’’ These formulas typically describe a deterministic process, one where there is no uncertainty in the physics of the process (i.e., the right formula) and there is no uncertainty in the parameters of the process (i.e., the coefficients are known with impunity).
For example, suppose you are teaching your child to bake cookies and you want to give instructions about when to take the cookies out of the oven. You could say to take them out when the temperature inside the cookie dough reaches 375◦F, or you could advise your child to take them out when the tops of the cookies turn light brown. Which instruction would you give? Most likely, you would use the second of the two instructions. The first instruction is too precise to implement practically; in this case precision is not useful. The vague term light brown is useful in this context and can be acted upon even by a child. We all use vague terms, imprecise information, and other fuzzy data just as easily as we deal with situations governed by chance
The centroids of each of the diagrams in Fig. 1.4
my ‘‘mission to Canada.’’
for 100 cities there are 100 × 99×98×97×···×2×1, or about 10200, possible routes to consider!
The statement ‘‘I shall return soon’’ is vague, whereas the statement ‘‘I shall return in a few minutes’’ is fuzzy; the former is not known to be associated with any unit of time (seconds, hours, days), and the latter is associated with an uncertainty that is at least known to be on the order of minutes. The phrase, ‘‘I shall return within 2 minutes of 6pm’’ involves an uncertainty which has a quantifiable imprecision; probability theory could address this form.
an abstract algebra (one dealing with groups, fields, and rings) and a linear algebra (one dealing with vector spaces, state vectors, and transition matrices) and the structure of a fuzzy system, which is comprised of an implication between actions and conclusions (antecedents and consequents).
For example, suppose we need a controller to bring an aircraft out of a vertical dive. Conventional controllers cannot handle this scenario as they are restricted to linear ranges of variables; a dive situation is highly nonlinear. In this case, we could use a fuzzy controller, which is adept at handling nonlinear situations albeit in an imprecise fashion, to bring the plane out of the dive into a more linear range, then hand off the control of the aircraft to a conventional, linear, highly accurate controller.
For example, in the game of tic-tac-toe there are only a few moves for the entire game; we can deduce our next move from the previous move, and our knowledge of the game. It is this kind of reasoning that we also called shallow reasoning
It is historically interesting that the word statistics is derived from the now obsolete term statist, which means an expert in statesmanship. Statistics were the numerical facts that statists used to describe the operations of states.
Uncertain information can take on many different forms. There is uncertainty that arises because of complexity; for example, the complexity in the reliability network of a nuclear reactor. There is uncertainty that arises from ignorance,fromvarious classesof randomness,fromthe inability to perform adequate measurements, from lack of knowledge, or from vagueness, like the fuzziness inherent in our natural language.
fuzzy systems, as they are posed now, can be described as shallow models in the sense that they are primarily used in deductive reasoning. This is the kind of reasoning where we infer the specific from the general. In contrast to this is the kind of reasoning that is inductive, where we infer the general from the particular;
How do humans reason in situations that are complicated or ill-defined? we are superb at seeing or recognizing or matching patterns– behaviors that confer obvious evolutionary benefits. In problems of complication then, we look for patterns; and we simplify the problem by using these to construct temporary internal models or hypotheses or schemata to work with. We carry out localized deductions based on our current hypotheses and we act on these deductions. Then, as feedback from the environment comes in, we may strengthen or weaken our beliefs in our current hypotheses, discarding some when they cease to perform, and replacing them as needed with new ones. In other words, where we cannot fully reason or lack full definition of the problem, we use simple models to fill the gaps in our understanding; such behavior is inductive.
When students graduate, it seems that their biggest fear upon entering the real world is ‘‘forgetting the correct formula.’’ These formulas typically describe a deterministic process, one where there is no uncertainty in the physics of the process (i.e., the right formula) and there is no uncertainty in the parameters of the process (i.e., the coefficients are known with impunity).
For example, suppose you are teaching your child to bake cookies and you want to give instructions about when to take the cookies out of the oven. You could say to take them out when the temperature inside the cookie dough reaches 375◦F, or you could advise your child to take them out when the tops of the cookies turn light brown. Which instruction would you give? Most likely, you would use the second of the two instructions. The first instruction is too precise to implement practically; in this case precision is not useful. The vague term light brown is useful in this context and can be acted upon even by a child. We all use vague terms, imprecise information, and other fuzzy data just as easily as we deal with situations governed by chance
The centroids of each of the diagrams in Fig. 1.4
my ‘‘mission to Canada.’’
for 100 cities there are 100 × 99×98×97×···×2×1, or about 10200, possible routes to consider!
The statement ‘‘I shall return soon’’ is vague, whereas the statement ‘‘I shall return in a few minutes’’ is fuzzy; the former is not known to be associated with any unit of time (seconds, hours, days), and the latter is associated with an uncertainty that is at least known to be on the order of minutes. The phrase, ‘‘I shall return within 2 minutes of 6pm’’ involves an uncertainty which has a quantifiable imprecision; probability theory could address this form.
an abstract algebra (one dealing with groups, fields, and rings) and a linear algebra (one dealing with vector spaces, state vectors, and transition matrices) and the structure of a fuzzy system, which is comprised of an implication between actions and conclusions (antecedents and consequents).
For example, suppose we need a controller to bring an aircraft out of a vertical dive. Conventional controllers cannot handle this scenario as they are restricted to linear ranges of variables; a dive situation is highly nonlinear. In this case, we could use a fuzzy controller, which is adept at handling nonlinear situations albeit in an imprecise fashion, to bring the plane out of the dive into a more linear range, then hand off the control of the aircraft to a conventional, linear, highly accurate controller.
For example, in the game of tic-tac-toe there are only a few moves for the entire game; we can deduce our next move from the previous move, and our knowledge of the game. It is this kind of reasoning that we also called shallow reasoning
It is historically interesting that the word statistics is derived from the now obsolete term statist, which means an expert in statesmanship. Statistics were the numerical facts that statists used to describe the operations of states.
Uncertain information can take on many different forms. There is uncertainty that arises because of complexity; for example, the complexity in the reliability network of a nuclear reactor. There is uncertainty that arises from ignorance,fromvarious classesof randomness,fromthe inability to perform adequate measurements, from lack of knowledge, or from vagueness, like the fuzziness inherent in our natural language.
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