Fuzzy Logic Abstract This paper gives a general overview of fuzzy logic theory. It describes the concepts of fuzzy sets and operations used in their manipulation, developed by Lofti Zadeh in 1965. The paper gives examples of the fuzzy logic applications, with emphasis on the field of artificial intelligence. Fuzzy Logic "When Theseus returned from slaying the Minotaur, says Plutarch, the Athenians preserved his ship, and as planks rotted, replaced them with new ones. When the first plank was replaced, everyone agreed it was still the same ship. Adding a second plank made no difference either. At some point, the Athenians may have replaced every plank in the ship. Was it a different ship? At what point did it become one?" [1] Questions of the above nature, bothered people acquainted with a classical logic for ages. The Aristotelian concept of the excluded middle, where every logical preposition has to either be completely true or false, does not seem to fulfill expectations of nowadays very technical and logic dependent world. Nevertheless, most computer, control system engineers and many other people involved in modeling and programing behavior still rely on the True/False conditions and differential equations. There were several people who tried to adjust classical logic to accept a broader concept of something being true or false. In the early 1900's, Lukasiewicz presented his three-valued logic, where the third value proposed could be described as "possible", and had a numeric value between True and False [2]. His efforts were followed by Knuth, but none of the notions gained a wide acceptance. It was not until 1965, when Lotfi Zadeh published his works on fuzzy sets and math accompanying them. The theory quickly w... ... middle of paper ... ...trol, Peter Bauer, Stephan Nouak, Roman Winkler, 1996, (http://www.flll.uni-linz.ac.at/fuzzy/fuzzy.html) References: Fuzzy Logic Research and Life, Japanese Technology Evaluation Center, 1995, (http://itri.loyola.edu/kb/c5_s4.htm) Two Responses to Elkan's Paper, Enrique Ruspini, 1993, (http://www-cgi.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/fuzzy/doc/elkan/response.txt) Fuzzy Logic Primer - A Brief Intoduction to Fuzzy Logic, Togai InfraLogic Inc., 1992, (http://www-cgi.cs.cmu.edu/afs/cs/project/ai-repository/ai/areas/fuzzy/doc/intro/primer.tgz) The Seven Noble Truths of Fuzzy Logic, Earl Cox, 1992, (http://freeware.aus.sps.mot.com/freeweb/pub/fuzzy/news5.txt) Building Fuzzy Expert System, William Siler, http://members.aol.com/wsiler/index.html) Logic of the Future, Earl Cox, http://darwin1.ucsd.edu:8000/connect/articles/success/logic.html)
Mill, J. S. (2000). System of Logic Ratiocinative and Inductive. London: Longmans, Green, and Co.
Of the many advancements the Phoenicians made in the ancient world, the most well known and prolific was the development and enhancement of sea travel. Although they did not reach the height of their power at sea until after 1000 B.C.E., over five hundred years after the true beginning of the Phoenician empire circa 1550 B.C.E., it is obvious that the Phoenicians were the true power at sea in the ancient Mediterranean. They were best known for their cargo ships, which were spacious so as to carry more goods at a time, and by 600 B.C.E., the Phoenicians had advanced the classic cargo ship so it no longer had one, but two masts which supported a square sail that was intended to make the steering of the ship easier.
... middle of paper ... ... In Intelligent Data Engineering and Automated Learning–IDEAL 2006 (pp. 1346-1357. Springer Berlin, Heidelberg.
From the beginning to end, the ships had to go through many changes in order to accommodate all of the cargo. The first ships used suffered greatly in the African water because they were wooden. As time passed the ships were modified for the journeys. For example, copper was added to help fight against shipworms. Rediker mentions in the book the details of how the ship is built and he even includes the measurements of the wood used and the supplies needed. Shortly after explaining this, he mentions the beatings some of the crew had to take if they were to mess up any part of the ship.
Today, many people associate the word “inception” with the award winning Christopher Nolan film, but what does inception really mean? All dreams aside, inception is the time at which something begins. However, Inception is also the title of a rap composed by artist who goes by the name of Logic. Logic, also known as Sir Robert Bryson Hall II, is a rapper from Maryland. Inception is on Logic’s 2012 mixtape, “Young Sinatra: Undeniable”. I admire much of Logic’s work; however, Inception not only resonates within me emotionally with its sound, but I find that the lyrics echo inspiration and motivation that I can relate to personally.
In the objection to his views I mention that people give “life” to inanimate objects. This life consists of the ownership and history of it which is more important than the physical aspect of the ship. Relating this to the puzzle of Theseus’ ship it is correct to say that the ship remains the same because anyone discussing the ship would say that it Theseus still owns the ship and that it was on the voyage the entire time. In addition, since the wood be placed in the same position as the wood it was replacing if someone looked at the ship before and after they would not be able that the wood had been replaced and would state that it is the same ship. Due to the similar appearance and the important of the history and ownership of the ship it is correct to state that Theseus ship is the same at the beginning and the end of the
(Blackburn, 1999:127). ‘Theseus’ ship’ is used to illustrate this. The ship goes on a long voyage and is in need of constant repair and maintenance. By the end of the voyage, all the components of the ship have been changed.
Gottlieb invented modern quantificational logic, and created the first fully axiomatic system for logic, which was complete in its treatment of propositional and first-order logic, and also represented the first treatment of higher-order logic. In the philosophy of mathematics, he was one of the most vital contributor of logicism, the thesis that mathematical truths are logical truths, and presented influential criticisms of rival views such as psychologism and formalism.
A second assumption is that truth and falsity are mutually exclusive. Quantum logic has disproved this one. There are real world situations that are in both realms, the true and the “not-true”. A particle can “be” in two places at the same time. This fuzzy logic is incompatible with our daily experiences but if there is anything that we have learnt from physics in the last seven decades is that the world is incompatible with our daily experiences.
The case based reasoning system proposed here mimics the human decision making process by learning from previous experience and using the knowledge to solve current problem. This system will utilize previous adverse episodes and their solutions to prevent reoccurrences, and also to detect the oc...
Partridge, Derek and K. M. Hussain. ARTIFICIAL INTELLIGENCE and BUSINESS MANAGMENT. Norwood: Ablex Publishing Corparation, 1992.
There are therefore absolute distinctions between what is true and what is false in such fields where a distinction matters and is significant, but circumstances also arise when truth must be relative to a certainty continuum where one may find a middle ground.
Truth is essentially divided into two main types of truth. There is empirical truth that is what is observed, what can be tangibly learned from observation. For an example we look at, Starbucks makes coffee and other hot beverages. This is a form of empirical truth, which is what is observed. Other than the empirical truth, there is truth. Truth is defined by us, by our beliefs, experiences, observations. This is the problem that there is with the nature of truth, because our experiences, and beliefs may differ from someone else giving them different truth. There are several theories on truth, and they are the Correspondence Theory, the Semantic Theory, the Deflationary Theory, the Coherence Theory, and the Pragmatic Theory. In this paper, we will be focusing on the Correspondence Theory and the Coherence Theory ( insert citation, IEP website).
Mathematical Logic is something that has a very long history behind it. It has been debated on for many centuries. If someone were to divide mathematical logic into groups they would get two major groups. Both groups are very long. One is called “The history of formal deduction” and it goes all the way back to Aristotle and Euclid and other people who lived at that time. The other is “the history of mathematical analysis” which goes back to the times of Archimedes, who was in the same era as Aristotle and Euclid. These to groups or streams were separate for a long time until Newton invented Calculus, which brought Math and logic together.
It was pure joy to learn how the Boolean logic makes computers work. In my undergraduate study I had taken up courses on Software Engineering, Computer Networks, Data Structures, JAVA, Operating Systems, Computer Graphics, Design and Analysis of Algorithms, Database Management, Web Technology and Mobile Application Development. Practical application aspects were introduced to me through laboratories correspond...