کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
394069 | 665720 | 2010 | 11 صفحه PDF | دانلود رایگان |
In order to analyze the logical foundation of fuzzy reasoning, this paper first introduces the concept of generalized roots of theories in Łukasiewicz propositional fuzzy logic Łuk, Gödel propositional fuzzy logic Göd, Product propositional fuzzy logic Π, and nilpotent minimum logic NM (the R0-propositional fuzzy logic L∗L∗). Next, it is proved that all consequences of a theory Γ, named D(Γ), are completely determined by its generalized root whenever Γ has a generalized root. Moreover, it is proved that every finite theory Γ has a generalized root, which can be expressed by a specific formula. Finally, we demonstrate the existence of a non-fuzzy version of Fuzzy Modus Ponens (FMP) in Łuk, Göd, Π and NM (L∗)(L∗), and we provide its numerical version as a new algorithm for solving FMP.
Journal: Information Sciences - Volume 180, Issue 23, 1 December 2010, Pages 4661–4671