ترجمه مقاله نقش ضروری ارتباطات 6G با چشم انداز صنعت 4.0
- مبلغ: ۸۶,۰۰۰ تومان
ترجمه مقاله پایداری توسعه شهری، تعدیل ساختار صنعتی و کارایی کاربری زمین
- مبلغ: ۹۱,۰۰۰ تومان
We mention some milestones of the development of fuzzy logic understood as a branch of mathematical (symbolic) logic. Clearly, the story begins by Zadeh’s first paper [40] on fuzzy sets. The term “fuzzy logic” is not used; but Zadeh mentions Kleene three-valued logic (just in passing). Goguen’s 1968–1969 paper [17] speaks on logic of inexact concepts but the term “fuzzy logic” occurs there (on p. 359; is this the first occurrence of the term in the literature?) The paper is very general, introduces algebras called closg, very near to algebras presently called residuated lattices, as algebras of truth functions of connectives for many-valued logics of inexact concepts,As an example he presents the unit real interval [0, 1] with product and its residuum (Goguen implication), thus a particular t-norm algebra (not speaking on t-norms). Zadeh has written several papers on fuzzy logic; an early paper is his “Fuzzy logic and approximate reasoning” [41] from 1975 (reprinted in [30]), where he uses connectives of Łukasiewicz logic min, max, 1 − x, Łukasiewicz implication—but not strong conjunction. Note that what we call Łukasiewicz strong (or bold) conjunction or Łukasiewicz t-norm (the t-norm whose residuum is Łukasiewicz implication) was never explicitly used by Łukasiewicz. The first explicit use of this conjunction in the context of Zadeh’s fuzzy logic appears to be the paper [16] by Giles. 1