July 2020
Intermediate to advanced
384 pages
11h 25m
English
Content preview from A Modern Introduction to Fuzzy Mathematics
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8Fuzzy Computation
Computation is about calculating or enumerating mechanically. Typically, the word mechanically means that one builds a device and sets it in motion in order to perform the desired calculation or enumeration. Many and different real or conceptual devices capable of performing computations have been proposed. Most of them operate in a crisp environment and in a crisp manner. However, there are some devices that profit from the use of vagueness in their overall operation. These devices and the related theory are described in this chapter. The material presented in this chapter is based on [220, 274].
8.1 Automata, Grammars, and Machines
A finite automaton can be seen as a machine equipped with scanning head that can read the contents of sequence of cells, while the head can move in only one direction. At any moment, the machine is in a state. Initially, the scanning head is positioned on the leftmost cell, while a number of symbols are printed on consecutive cells starting with the leftmost cell. Also, the machine enters a default initial state. Each machine is associated with a number of transition rules. A transition rule has the general form 
, where 
and 
are ...
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