Fuzzy Theory Presented by Gao Xinbo E.E.Dept. Xidian University
Fuzzy Theory Presented by Gao Xinbo E.E. Dept. Xidian University
OUTLINE ●Motivation ●History ●Fuzzy Sets ·Fuzzy Logic ·Fuzzy System
OUTLINE ⚫ Motivation ⚫ History ⚫ Fuzzy Sets ⚫ Fuzzy Logic ⚫ Fuzzy System
Motivation ●The term "fuzzy logic?”refers to a logic of approximation. Boolean logic assumes that every fact is either entirely true or false. Fuzzy logic allows for varying degrees of truth. Computers can apply this logic to represent vague and imprecise ideas,such as "hot","tall or "balding
Motivation ⚫ The term “fuzzy logic” refers to a logic of approximation. ⚫ Boolean logic assumes that every fact is either entirely true or false. ⚫ Fuzzy logic allows for varying degrees of truth. ⚫ Computers can apply this logic to represent vague and imprecise ideas, such as “hot” , “tall” or “balding
History The precision of mathematics owes its success in large part to the efforts of Aristotle and the philosophers who preceded him. Their efforts led to a concise theory of logic and mathematics. The "Law of the Excluded Middle,"states that every proposition must either be True or False. There were strong and immediate objections.For example,Heraclitus proposed that things could be simultaneously True and not True
History ⚫ The precision of mathematics owes its success in large part to the efforts of Aristotle and the philosophers who preceded him. ⚫ Their efforts led to a concise theory of logic and mathematics. ⚫ The “Law of the Excluded Middle,” states that every proposition must either be True or False. ⚫ There were strong and immediate objections. For example, Heraclitus proposed that things could be simultaneously True and not True
History Plato laid a foundation for what would become fuzzy logic,indicating that there was a third region (beyond True and False)where these opposites“tumbled about.”(非此即彼) The modern philosophers,Hegel,Marx,and Engels,echoed this sentiment. Lukasiewicz proposed a systematic alternative to the bi-valued logic of Aristotle
History ⚫ Plato laid a foundation for what would become fuzzy logic, indicating that there was a third region (beyond True and False) where these opposites “tumbled about.”（非此即彼） ⚫ The modern philosophers, Hegel, Marx, and Engels, echoed this sentiment. ⚫ Lukasiewicz proposed a systematic alternative to the bi-valued logic of Aristotle
History In the early 1900's,Lukasiewicz described a three-valued logic.The third value can be translated as the term“possible,”and he assigned it a numeric value between True and False. Later,he explored four-valued logics,five-valued logics,and declared that in principle there was nothing to prevent the derivation of an infinite- valued logic
History ⚫ In the early 1900’s, Lukasiewicz described a three-valued logic. The third value can be translated as the term “possible,” and he assigned it a numeric value between True and False. ⚫ Later, he explored four-valued logics, five-valued logics, and declared that in principle there was nothing to prevent the derivation of an infinitevalued logic
History Knuth proposed a three-valued logic similar to Lukasiewicz's. He speculated that mathematics would become even more elegant than in traditional bi-valued logic. His insight was to use the integral range [-1,0+1]rather than[0,1,2]
History ⚫ Knuth proposed a three-valued logic similar to Lukasiewicz’s. ⚫ He speculated that mathematics would become even more elegant than in traditional bi-valued logic. ⚫ His insight was to use the integral range [-1, 0 +1] rather than [0, 1, 2]
History Lotfi Zadeh,at the University of California at Berkeley,first presented fuzzy logic in the mid- 1960's. Zadeh developed fuzzy logic as a way of processing data.Instead of requiring a data element to be either a member or non-member of a set,he introduced the idea of partial set membership. In 1974 Mamdani and Assilian used fuzzy logic to regulate a steam engine. In 1985 researchers at Bell laboratories developed the first fuzzy logic chip
History ⚫ Lotfi Zadeh, at the University of California at Berkeley, first presented fuzzy logic in the mid- 1960's. ⚫ Zadeh developed fuzzy logic as a way of processing data. Instead of requiring a data element to be either a member or non-member of a set, he introduced the idea of partial set membership. ⚫ In 1974 Mamdani and Assilian used fuzzy logic to regulate a steam engine. ⚫ In 1985 researchers at Bell laboratories developed the first fuzzy logic chip
The World is vague Natural language employs many vague and imprecise concepts. Translating such statements into more precise language removes some of their semantic value. The statement "Dan has 100,035 hairs on his head" does not explicitly state that he is balding,nor does "Dan's head hair count is 1.6 standard deviations below the mean head hair count for people of his genetic pool". ● Suppose Dan were actually only 1.559999999 standard deviations below the mean?How does one determine his genetic pool?
The World is Vague ⚫ Natural language employs many vague and imprecise concepts. ⚫ Translating such statements into more precise language removes some of their semantic value. The statement “Dan has 100,035 hairs on his head” does not explicitly state that he is balding, nor does “Dan’s head hair count is 1.6 standard deviations below the mean head hair count for people of his genetic pool”. ⚫ Suppose Dan were actually only 1.559999999 standard deviations below the mean? How does one determine his genetic pool?
Precision and Significance A 1500 kg mass is approaching LOOK your head at 45.3mse0. oUT！ Precision Significance
Precision and Significance