CT: Many concepts of problem solving theory are better understood in an abstract algebraic framework which also applies in automata theory. Because many systems of practical interest fall outside the scope of linear theory, it is desirable to enlarge as much as possible the class of systems for which a complete structure theory is available. The fuzzy system approach is presented as a basis for the design of systems far superior in artificial intelligence to those we can conceive today. The concepts of controllability, observability and minimality are developed, and conditions for the realization of an input‐output map by such a system are given. Several problems, all directly or indirectly related to fuzzification, arise in considering this broader class of systems.
S: http://www.emeraldinsight.com/doi/abs/10.1108/eb005367 (last access: 29 December 2014)
N: 1. fuzzy (adj): 1610s, “soft, spongy,” from fuzz + –y. Compare Low German fussig “weak, loose, spongy,” Dutch voos “spongy.” From 1713 as “covered with fuzz;” 1778 as “blurred;” and 1937 as “imprecise,” with reference to thought, etc. Related: Fuzzily; fuzziness.
system (n): 1610s, “the whole creation, the universe,” from Late Latin systema “an arrangement, system,” from Greek systema “organized whole, a whole compounded of parts,” from stem of synistanai “to place together, organize, form in order,” from syn- “together” + root of histanai “cause to stand” from PIE root sta- “to stand” (see stet).
Meaning “set of correlated principles, facts, ideas, etc.” first recorded 1630s. Meaning “animal body as an organized whole, sum of the vital processes in an organism” is recorded from 1680s; hence figurative phrase to get (something) out of one’s system (1900). Computer sense of “group of related programs” is recorded from 1963. All systems go (1962) is from U.S. space program. The system “prevailing social order” is from 1806.
2. Fuzzy systems is an alternative to traditional notions of set membership and logic that has its origins in ancient Greek philosophy, and applications at the leading edge of Artificial Intelligence. Yet, despite its long-standing origins, it is a relatively new field, and as such leaves much room for development. This paper will present the foundations of fuzzy systems, along with some of the more noteworthy objections to its use, with examples drawn from current research in the field of Artificial Intelligence. Ultimately, it will be demonstrated that the use of fuzzy systems makes a viable addition to the field of Artificial Intelligence, and perhaps more generally to formal mathematics as a whole.
S: 1. OED – http://www.etymonline.com/index.php?allowed_in_frame=0&search=fuzzy&searchmode=none; http://www.etymonline.com/index.php?allowed_in_frame=0&search=system&searchmode=none (last access: 29 December 2014). 2. http://www.austinlinks.com/Fuzzy/tutorial.html (last access: 29 December 2014).