Computer Science – Artificial Intelligence
Scientific paper
2006-04-19
IEEE Transactions on Fuzzy Systems, vol. 15(6): 1238-1250, Dec. 2007
Computer Science
Artificial Intelligence
13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy Systems
Scientific paper
Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.
Cao Yongzhi
Chen Guoqing
Ying Mingsheng
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