Aiming at the previously-proposed entropy-based differently implicational algorithm of fuzzy inference, this study analyzes its continuity. To begin with, for the FMP (fuzzy modus ponens) and FMT (fuzzy modus tollens) problems, the continuous as well as uniformly continuous properties of the entropy-based differently implicational algorithm are demonstrated for the Tchebyshev and Hamming metrics, in which the R-implications derived from left-continuous t-norms are employed. Furthermore, four numerical fuzzy inference examples are provided, and it is found that the entropy-based differently implicational algorithm can obtain more reasonable solution in contrast with the fuzzy entropy full implication algorithm. Finally, in the entropy-based differently implicational algorithm, we point out that the first fuzzy implication reflects the effect of rule base, and that the second fuzzy implication embodies the inference mechanism.
In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the $Q$-relation and the $Q$-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong $Q$-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.
In this note we study some properties concerning certain copies of the classic Banach space $c_{0}$ in the Banach space $\mathcal{L}\left( X,Y\right) $ of all bounded linear operators between a normed space $X$ and a Banach space $Y$ equipped with the norm of the uniform convergence of operators.
We study a wide class of copulas which generalizes well-known families of copulas, such as the semilinear copulas. We also study corresponding results for the case of quasi-copulas.
In [3] the tautology problém for Hájek’s Basic Logic BL is proved to
be co-NP-cornplete by showing that if a formula ϕ is not a tautology of BL then there exists an integer m > 0, polynomially bounded by the length of ϕ, such that ϕ fails to be a tautology in the infinite-valued logic mŁ corresponding to the ordinal sum of m copies of the Łukasiewicz t-norrn. In this paper we state that if ϕ is not a tautology of BL then it already fails to be a tautology of a finite set of finite-valued logics, defined by taking the ordinal sum of m copies of k-valued Łukasiewicz logics, for effectively determined integers m, k > 0 only depending on polynomial-time computable features of ϕ. This result allows the definition of a calculus for mŁ along the lines of [1], [2], while the analysis of the features of functions associated with formulas of mŁ constitutes a step toward the characterization of finitely generated free BL-algebras as algebras of [0, 1]-valued functions.
We give a simple proof that critical values of any Artin L-function attached to a representation ̺ with character χ̺ are stable under twisting by a totally even character χ, up to the dim̺-th power of the Gauss sum related to χ and an element in the field generated by the values of χ̺ and χ over Q. This extends a result of Coates and Lichtenbaum as well as the previous work of Ward., Peng-Jie Wong., and Seznam literatury
We denote by $F_a$ the class of all abelian lattice ordered groups $H$ such that each disjoint subset of $H$ is finite. In this paper we prove that if $G \in F_a$, then the cut completion of $G$ coincides with the Dedekind completion of $G$.