基于二型直觉模糊信息的多属性决策方法

模糊数直觉模糊集是直觉模糊集和区间数直觉模糊集的拓展,本文提出了二型直觉模糊数概念,对基于二型直觉模糊信息的多属性决策进行了研究.以结构元理论为基础,给出了二型直觉模糊数的距离公式,然后定义了二型直觉模糊正、负理想点,进而给出了一种基于二型直觉模糊数的多属性决策的步骤.最后通过实例来证明其有效性.     

L-fuzzy N-收敛空间

本文给出L-fuzzy N-收敛空间的定义,讨论L-fuzzy N-收敛空间范畴(L-fuzzyN-收敛空间和它们之间的连续映射构成的范畴)的若干范畴的性质,并且证明它的一个子范畴同构与L-fuzzy拓扑空间范畴.     

The Leading Ideal of a Complete Intersection of Height Two,Part III

Let (S, 𝔫) be an s-dimensional regular local ring with s > 2, and let I = (f, g) be an ideal in S generated by a regular sequence f, g of length two. As in [2 Goto , S. , Heinzer , W. , Kim , M.-K. ( 2006 ). The leading ideal of a complete intersection of height two . J. Algebra 298 : 238 – 247 . [Google Scholar], 3 Goto , S. , Heinzer , W. , Kim , M.-K. ( 2007 ). The leading ideal of a complete intersection of height two, II . J. Algebra 312 : 709 – 732 . [Google Scholar]], we examine the leading form ideal I* of I in the associated graded ring G: = gr_𝔫(S). Let μ _G (I*) = n ≥ 3, and let {ξ₁, ξ₂,…, ξ _n } be a minimal homogeneous system of generators of I* such that ξ₁ = f* and ξ₂ = g*, and c _i : = deg ξ _i  ≤ deg ξ _i+1: = c _i+1 for each i ≤ n ? 1. For m ≤ n, we say that K _m : = (ξ₁,…, ξ _m )G is an ideal generated by part of a minimal homogeneous generating set of I*. Let D _i : = GCD(ξ₁,…, ξ _i ) and d _i  = deg D _i for i with 1 ≤ i ≤ m. Let K _m be perfect with ht _G K _m  = 2. We prove that the following are equivalent: 1. deg ξ _i+1 = deg ξ _i  + (d _i?1 ? d _i ) +1, for all i with 3 ≤ i ≤ m ? 1;

2. deg ξ _i+1 ≤ deg ξ _i  + (d _i?1 ? d _i ) +1, for all i with 3 ≤ i ≤ m ? 1.

Furthermore, if these equivalent conditions hold, then K _m  = I*. Moreover, if e(G/K _m ) = e(G/I*), we prove that K _m  = I*. We illustrate with several examples in the cases where K _m is or is not perfect.     

FBN Modules

For M ∈ R-Mod and τ ∈M-tors, we define the concept of fully τ-bounded module as a generalization of the concept of fully τ-bounded ring. We prove that for a τ-noetherian module M with local τ _M -Gabriel correspondence, which is a progenerator of σ[M] and with τ is FIS-invariant, then M is fully τ-bounded. Also, we show that if M is τ-noetherian and fully τ-bounded, then M has local τ _M -Gabriel correspondence.     

The Structure of Finite Local Principal Ideal Rings

A ring R is called a principal ideal ring (PIR), if each ideal of R is a principal ideal. A local ring (R, 𝔪) is an artinian PIR if and only if its maximal ideal 𝔪 is principal and has finite nilpotency index. In this article, we determine the structure of a finite local PIR.     

Inverse Problems of Boundary Value Problems for Annular Vibrating Membranes with Piecewise Smooth Positive Functions in the Boundary Conditions

The asymptotic expansions of the trace of the heat kernel for small positive t, where λ_ν are the eigenvalues of the negative Laplacian in Rⁿ (n=2 or 3), are studied for a general annular bounded domain Ω with a smooth inner boundary ?Ω₁ and a smooth outer boundary ?Ω₂ where a finite number of piecewise smooth Dirichlet, Neumann and Robin boundary conditions on the components Γ _j (j=1,…,m) of ?Ω₁ and on the components of ?Ω₂ are considered such that and and where the coefficients in the Robin boundary conditions are piecewise smooth positive functions. Some applications of Θ (t) for an ideal gas enclosed in the general annular bounded domain Ω are given.     

THREE NOTES ON NICE EXTENSION DOMAINS

The first note shows that the integral closure L′ of certain localities L over a local domain R are unmixed and analytically unramified, even when it is not assumed that R has these properties. The second note considers a separably generated extension domain B of a regular domain A, and a sufficient condition is given for a prime ideal p in A to be unramified with respect to B (that is, p B is an intersection of prime ideals and B/P is separably generated over A/p for all P ∈ Ass (B/p B)). Then, assuming that p satisfies this condition, a sufficient condition is given in order that all but finitely many q ∈ S = {q ∈ Spec(A), p ? q and height(q/p) = 1} are unramified with respect to B, and a form of the converse is also considered. The third note shows that if R′ is the integral closure of a semi-local domain R, then I(R) = ∩{R′ _p′ ;p′ ∈ Spec(R′) and altitude(R′/p′) = altitude(R′) ? 1} is a quasi-semi-local Krull domain such that: (a) height(N ^*) = altitude(R) for each maximal ideal N ^* in I(R); and, (b) I(R) is an H-domain (that is, altitude(I(R)/p ^*) = altitude(I(R)) ? 1 for all height one p ^* ∈ Spec(I(R))). Also, K = ∩{R _p ; p ∈ Spec(R) and altitude(R/p) = altitude(R) ? 1} is a quasi-semi-local H-domain such that height (N) = altitude(R) for all maximal ideals N in K.     

Fuzzy real valued lacunary I-convergent sequences

In this article, we introduce the concept of lacunary I-convergent sequence of fuzzy real numbers and study some basic properties.     

A note on strong matrix summability via ideals

Following the line of recent works of Das et al. (2011) [15] and Savas and Das (2011) [19] we apply the notion of ideals to strong matrix summability, and in this note, we introduce the notion of strong A^I-summability with respect to an Orlicz function. We make certain investigations on the classes of sequences arising out of this new summability method.     

相容半连续Domain

引入了相容半连续Domain、相容强连续Domain的概念,给出了一系列性质,讨论了相容半连续Domain、相容强连续Domain与相容连续Domain间的关系.引入了相容半Scott拓扑,并讨论了其相关性质.