08-12-2012, 05:51 PM
FUZZY LOGIC –Mathematical Logic Science
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Mathematics is shifting its boundaries, describing the nature of physics and styling the art of human thinking. It prevails both in astrology as well as pure science. To this current date, there has been wonderful progress in mathematics in the names of Algebra, Geometry, Set theory, Probability and Bayes Network, Calculus, Engineering Science, Neural Network, Artificial Intelligence, Automata Theory and many others. As the hierarchy of math develops, and as the researches continue to describe new complex situations, the models change priority and popularity in between these paradigms. With rising complexity, Fuzzy logic has been an emerging model in mathematics. Fuzzy logic, however, is not as fuzzy as the name sounds. It is a new mathematical approach to solve fuzzy nature of science.
Fuzzy science gets its name to describe the general yet 'not set with boundaries' values and norms of this cultural world. It tries to solve riddles involving natural world of unclear meanings like long, small, wide, far etc. These words make different meanings with different subjects. Fuzzy science so makes an approach to make our equipments, devices and our design understand the pattern in the way we people learn. For example, if a blind man asks "What makes a wife beautiful", many people answer it differently and yet when somebody remarks about your wife being beautiful at a party house, all your friends will agree in that. Fuzzy science tries to solve a problem in the way your friends want to agree with that statement.
The path of fuzzy science however has undertaken nameless obstacles and the struggle it faces is many. It has nearly encountered all the possible disasters a theory might stand with. It's because of its nature of redefining the established world of mathematical network with its models. For instance, Aristotle, another name for logic, whose theories of Law of Contradiction (A cannot be both B and not B) and Law of Excluded Middle (A has to be B or not B), mostly sought with respect and wonder in West are actually the flouts to Fuzzy Set. It goes over Arago factor (between 1810 and 1825, French physicists largely forsook particle theory and embraced waves, even though particle theory had achieved increasing successes. When Augustin Fresnel proved diffraction with wave theory, it added its politics of truth. Today we regard light as intermediate: particlelike and wavelike.), sets out to solve Probability problems in simpler steps and makes computer an outstanding gamer. At first it was used by minds who tried to shape a problem to different model. As time progressed, logicists required a more solid platform to work on its pattern again and again. So a new model emerged in the name "Fuzzy Logic" and any designs attributed to its science were collected over it.
The Origin of Fuzzy Set
Sets are basic builders of computer science and most importantly they are the premises of logics, where new relation and membership emerge to make a beautiful web of expressions. These expressions enhance today's decisive power in computing, an efficient control system and the humanoid performance. Fuzzy takes these sets in relatively different approach. While conventional attributes of sets try to divide a universal set to crisp true or false values, which new programming techniques name it logistic regression, fuzzy assigns the membership values to all elements in all classifications. Let's wonder on fruit. When asked "Is apple or olive a fruit", we will answer both. But now asked how much is olive a fruit and how much is apple a fruit, we come with arbitrary values like .4 for olive and 1 for apple. We were right during first and second questions. When asked to different person, they may come for different values and yet they are right. However the more informative approach is the second approach and it evaluates our understanding about the world. It's the fuzziness of nature where fuzzy logic comes to play.
A fuzzy issue
There are issues about defining language to machines in the way human understands his world. Conventional Set theory sets out a major hindrance when defining patterns human brought with ease. There was a debate on how can a grain produce no sound at all and a mussel of grains can still produce a big sound. Cantor's Theory (Complement of a set, Union of Set, Intersection of Set, Subset of a set) about set resolves the dilemmas as fiat: A certain number of grains constitute a heap and that minus one is not a heap. If a heap has vague boundaries as people often do, the assumptions of set theory drains away. Charles Dogson suggests drawing a line somewhere and pretending that to be heap. This gave some trouble to scholars as definition itself was failing. This could be solved by the continuum membership rule i.e. fuzzy logic once we see that how much an individual does considers a heap to be. This gave a statistical fuzzy approach to solving matters.
Fuzzy Algorithm
The procedures specification to solve a problem is an algorithm. Algorithms are the most important structures of programming. They define the pattern of flow of data (numbers and strings) and designing the computing style in an efficient way. Most of us solve using algorithm defining the boundaries like: if a value lies between number a and number b then do a*b. However this approach can't solve a fuzzy problem. During 1970s Professor Ebrahim Mamdani of London University, developed a fuzzy engine with a little boiler and piston. While the digital control system defined the engine in terms of value boundaries the performance was oscillatory and the result came poor. He learned Professor Lotfi Zadeh's fuzzy articles and gave a trio to devise a fuzzy engine. The algorithm was similar to this:
1. If temperature is little low, then increase it slightly.
2. If temperature is moderately low, then increase it greatly.
3. If temperature is very low, then increase it very greatly.
Diplomatic Fuzzy
It is funny that politics get affected with economics, strategy plays, Foreign Influences, Laws, Racism, Government strength etc. In fact it is a much complex web of these subjects that define the winning position of a political party. Bart Kosko, a professor in USC developed a FCM (Fuzzy Cognitive Map: a map of graph on subjects. They model situations by their classes and the links between them, and ultimately form a web of interlocking causes and their strengths.) on complex political situation in South Africa. The map contained nine variables, such as mining, black tribal unity, and white racist radicalism. It was so appealing FCM with dynamic system that editors denied to publish certain variables. Angered, he put censored in their place. If Kosko were to design FCM of Nepal's political scenario; maybe he could bring out the issues that all political parties would agree and we would have Constitution by now. Such is the prowess of FCM.
As science makes progress, it demands new concepts and ideologies. May be the witty solves a problem but it requires lots of researches and people efforts to give a model a shape. "E = mc2" is a famous rule not by its three letters, a number and an assignment symbol but by the history of Little boy and Fat man during 1940s and, the succoring nuclear power technology in present date. Today requires any enterprise or government institution or educational industries to act on research, economics, engineering and diplomacy.
Every day technology is making progress at an amazing pace. New ideas and concepts are born each day. May be we think that we are back or may others think they are quite ahead of time, but what determines the strength and weakness is the ability to use the knowledge and diligence to outsmart other. While AI was invested with billions of dollars, our market only consisted of 1% of AI products during 1990s. Then fuzzy logic had zero investment and Japanese market had appliances full of fuzzy tags. Nepalese community is quite behind in terms of AI or fuzzy logic. Engineering Institutions aren't quite easy to implement these new ideas to improve the technical status of Electronics and Computer Industry. They demand good amount of research and hard work which, we lack in every ways. We live in a land where changing syllabus means ejecting out topics and even in Science institutions, students yearn for old notes and past photocopies. This tendency needs to be stopped if we want revolution in education. Instead, teachers and professors should be provided with adequate resources (like research fund) and students need to learn to respect role of teachers. Without this balance our system is fuzzy and there is no fuzzy logic to solve it.
[attachment=43134]
Mathematics is shifting its boundaries, describing the nature of physics and styling the art of human thinking. It prevails both in astrology as well as pure science. To this current date, there has been wonderful progress in mathematics in the names of Algebra, Geometry, Set theory, Probability and Bayes Network, Calculus, Engineering Science, Neural Network, Artificial Intelligence, Automata Theory and many others. As the hierarchy of math develops, and as the researches continue to describe new complex situations, the models change priority and popularity in between these paradigms. With rising complexity, Fuzzy logic has been an emerging model in mathematics. Fuzzy logic, however, is not as fuzzy as the name sounds. It is a new mathematical approach to solve fuzzy nature of science.
Fuzzy science gets its name to describe the general yet 'not set with boundaries' values and norms of this cultural world. It tries to solve riddles involving natural world of unclear meanings like long, small, wide, far etc. These words make different meanings with different subjects. Fuzzy science so makes an approach to make our equipments, devices and our design understand the pattern in the way we people learn. For example, if a blind man asks "What makes a wife beautiful", many people answer it differently and yet when somebody remarks about your wife being beautiful at a party house, all your friends will agree in that. Fuzzy science tries to solve a problem in the way your friends want to agree with that statement.
The path of fuzzy science however has undertaken nameless obstacles and the struggle it faces is many. It has nearly encountered all the possible disasters a theory might stand with. It's because of its nature of redefining the established world of mathematical network with its models. For instance, Aristotle, another name for logic, whose theories of Law of Contradiction (A cannot be both B and not B) and Law of Excluded Middle (A has to be B or not B), mostly sought with respect and wonder in West are actually the flouts to Fuzzy Set. It goes over Arago factor (between 1810 and 1825, French physicists largely forsook particle theory and embraced waves, even though particle theory had achieved increasing successes. When Augustin Fresnel proved diffraction with wave theory, it added its politics of truth. Today we regard light as intermediate: particlelike and wavelike.), sets out to solve Probability problems in simpler steps and makes computer an outstanding gamer. At first it was used by minds who tried to shape a problem to different model. As time progressed, logicists required a more solid platform to work on its pattern again and again. So a new model emerged in the name "Fuzzy Logic" and any designs attributed to its science were collected over it.
The Origin of Fuzzy Set
Sets are basic builders of computer science and most importantly they are the premises of logics, where new relation and membership emerge to make a beautiful web of expressions. These expressions enhance today's decisive power in computing, an efficient control system and the humanoid performance. Fuzzy takes these sets in relatively different approach. While conventional attributes of sets try to divide a universal set to crisp true or false values, which new programming techniques name it logistic regression, fuzzy assigns the membership values to all elements in all classifications. Let's wonder on fruit. When asked "Is apple or olive a fruit", we will answer both. But now asked how much is olive a fruit and how much is apple a fruit, we come with arbitrary values like .4 for olive and 1 for apple. We were right during first and second questions. When asked to different person, they may come for different values and yet they are right. However the more informative approach is the second approach and it evaluates our understanding about the world. It's the fuzziness of nature where fuzzy logic comes to play.
A fuzzy issue
There are issues about defining language to machines in the way human understands his world. Conventional Set theory sets out a major hindrance when defining patterns human brought with ease. There was a debate on how can a grain produce no sound at all and a mussel of grains can still produce a big sound. Cantor's Theory (Complement of a set, Union of Set, Intersection of Set, Subset of a set) about set resolves the dilemmas as fiat: A certain number of grains constitute a heap and that minus one is not a heap. If a heap has vague boundaries as people often do, the assumptions of set theory drains away. Charles Dogson suggests drawing a line somewhere and pretending that to be heap. This gave some trouble to scholars as definition itself was failing. This could be solved by the continuum membership rule i.e. fuzzy logic once we see that how much an individual does considers a heap to be. This gave a statistical fuzzy approach to solving matters.
Fuzzy Algorithm
The procedures specification to solve a problem is an algorithm. Algorithms are the most important structures of programming. They define the pattern of flow of data (numbers and strings) and designing the computing style in an efficient way. Most of us solve using algorithm defining the boundaries like: if a value lies between number a and number b then do a*b. However this approach can't solve a fuzzy problem. During 1970s Professor Ebrahim Mamdani of London University, developed a fuzzy engine with a little boiler and piston. While the digital control system defined the engine in terms of value boundaries the performance was oscillatory and the result came poor. He learned Professor Lotfi Zadeh's fuzzy articles and gave a trio to devise a fuzzy engine. The algorithm was similar to this:
1. If temperature is little low, then increase it slightly.
2. If temperature is moderately low, then increase it greatly.
3. If temperature is very low, then increase it very greatly.
Diplomatic Fuzzy
It is funny that politics get affected with economics, strategy plays, Foreign Influences, Laws, Racism, Government strength etc. In fact it is a much complex web of these subjects that define the winning position of a political party. Bart Kosko, a professor in USC developed a FCM (Fuzzy Cognitive Map: a map of graph on subjects. They model situations by their classes and the links between them, and ultimately form a web of interlocking causes and their strengths.) on complex political situation in South Africa. The map contained nine variables, such as mining, black tribal unity, and white racist radicalism. It was so appealing FCM with dynamic system that editors denied to publish certain variables. Angered, he put censored in their place. If Kosko were to design FCM of Nepal's political scenario; maybe he could bring out the issues that all political parties would agree and we would have Constitution by now. Such is the prowess of FCM.
As science makes progress, it demands new concepts and ideologies. May be the witty solves a problem but it requires lots of researches and people efforts to give a model a shape. "E = mc2" is a famous rule not by its three letters, a number and an assignment symbol but by the history of Little boy and Fat man during 1940s and, the succoring nuclear power technology in present date. Today requires any enterprise or government institution or educational industries to act on research, economics, engineering and diplomacy.
Every day technology is making progress at an amazing pace. New ideas and concepts are born each day. May be we think that we are back or may others think they are quite ahead of time, but what determines the strength and weakness is the ability to use the knowledge and diligence to outsmart other. While AI was invested with billions of dollars, our market only consisted of 1% of AI products during 1990s. Then fuzzy logic had zero investment and Japanese market had appliances full of fuzzy tags. Nepalese community is quite behind in terms of AI or fuzzy logic. Engineering Institutions aren't quite easy to implement these new ideas to improve the technical status of Electronics and Computer Industry. They demand good amount of research and hard work which, we lack in every ways. We live in a land where changing syllabus means ejecting out topics and even in Science institutions, students yearn for old notes and past photocopies. This tendency needs to be stopped if we want revolution in education. Instead, teachers and professors should be provided with adequate resources (like research fund) and students need to learn to respect role of teachers. Without this balance our system is fuzzy and there is no fuzzy logic to solve it.