基于极大模糊熵原理的模糊推理三I算法

用模糊熵来度量模糊推理结果的模糊程度，并用本文给出的极大模糊熵原理对王国俊先生提出的模糊推理三Ⅰ算法做进一步的解释和改进，提出基于极大模糊熵原理的模糊推理三Ⅰ算法，证明这几种算法在一定条件下是关系再现算法。     

模糊错误逻辑分解转化词与内涵否定词的逻辑关系

在文 [1]的基础上 ,在简单分析现时中错误的传递与转化的实际存在的同时 ,介绍国内外在逻辑研究领域对事物传递与转化规律的研究现状。特别为了探索控制与防范证券风险的技术而主要研究模糊错误逻辑分解转化词与内涵否定词的逻辑关系。     

Reaction Rate of Small Diffusing Molecules on a Cylindrical Membrane

Biomembranes consist of a lipid bi-layer into which proteins are embedded to fulfill numerous tasks in localized regions of the membrane. Often, the proteins have to reach these regions by simple diffusion. Motivated by the observation that IP₃ receptor channels (IP₃R) form clusters on the surface of the endoplasmic reticulum (ER) during ATP-induced calcium release, the reaction rate of small diffusing molecules on a cylindrical membrane is calculated based on the Smoluchowski approach. In this way, the cylindrical topology of the tubular ER is explicitly taken into account. The problem can be reduced to the solution of the diffusion equation on a finite cylindrical surface containing a small absorbing hole. The solution is constructed by matching appropriate ‘inner’ and ‘outer’ asymptotic expansions. The asymptotic results are compared with those from numerical simulations and excellent agreement is obtained. For realistic parameter sets, we find reaction rates in the range of experimentally measured clustering rates of IP₃R. This supports the idea that clusters are formed by a purely diffusion limited process.     

Truth: non-additive measures for the determination of relative density of sands using CPT measurements

In this Note, a fuzzy-integral based approach is developed for aggregating some of the available correlations that are commonly used for determining relative density $D_r$, from cone penetration test (CPT) data, in which non-additive measures are used as fuzzy measures to relate the actual compressibility measured by the friction ratio of sands to the base correlations. The results of the case studied show that fuzzy measures and the fuzzy integral can be utilized for a new approach in geo-technical engineering. To cite this article: C. Tran, C. R. Mecanique 333 (2005).     

Maximal element theorems in product FC-spaces and generalized games

Let I be a finite or infinite index set, X be a topological space and (Yi,{φNi})_i∈I be a family of finitely continuous topological spaces (in short, FC-space). For each i∈I, let be a set-valued mapping. Some existence theorems of maximal elements for the family {Ai}_i∈I are established under noncompact setting of FC-spaces. As applications, some equilibrium existence theorems for generalized games with fuzzy constraint correspondences are proved in noncompact FC-spaces. These theorems improve, unify and generalize many important results in recent literature.     

Limit theorems for sums of random exponentials

We study limiting distributions of exponential sums as t→∞, N→∞, where (X_i) are i.i.d. random variables. Two cases are considered: (A) ess sup X_i = 0 and (B) ess sup X_i = ∞. We assume that the function h(x)= -log P{X_i>x} (case B) or h(x) = -log P {X_i>-1/x} (case A) is regularly varying at ∞ with index 1 < ϱ <∞ (case B) or 0 < ϱ < ∞ (case A). The appropriate growth scale of N relative to t is of the form , where the rate function H₀(t) is a certain asymptotic version of the function (case B) or (case A). We have found two critical points, λ₁<λ₂, below which the Law of Large Numbers and the Central Limit Theorem, respectively, break down. For 0 < λ < λ₂, under the slightly stronger condition of normalized regular variation of h we prove that the limit laws are stable, with characteristic exponent α = α (ϱ, λ) ∈ (0,2) and skewness parameter β ≡ 1.Research supported in part by the DFG grants 436 RUS 113/534 and 436 RUS 113/722.Mathematics Subject Classification (2000): 60G50, 60F05, 60E07     

殷墟考古的统计与模糊方法

以殷墟墓葬分期为实例 ,阐述模糊方法用于考古优势的思考 ,提出确定隶属度的方法 :概率法 ,以及确定权值的方法 :模糊方程法 .将数理统计与模糊数学结合起来 ,给出了墓葬分期的模糊模型 ,应用的效果令人满意     

Maximum flow in a network with fuzzy arc capacities

Our main concern is the maximum flow in a network in which an excess over the beforehand fixed quota of arc capacity is admissible. The problem is represented as a partially fuzzy linear programming task. A theorem equivalent to the Ford and Fulkerson one concerning the classic task of maximum flow is proved in the paper. An algorithm for searching maximum flow assuming integer values of flows on network arcs is presented.     

Multiple criteria decision problems with fuzzy domination structures

The concepts of domination structures and nondominated solutions in multiple criteria decision problems, which were introduced by Yu, enable us to tackle general situations in which there exists information concerning the decision maker's preferences.In many of the multiple criteria decision problems the underlying domination structures are not known precisely but only fuzzily determined. Yu primarily works with the case where the domination structure at each point is a convex cone. As a result, there exists a sharp borderline dividing all solutions into nondominated solutions and the others.This paper fuzzifies the concepts of domination structures and nondominated solutions to allow them to be applied to a larger class of the multiple criteria decision problems mentioned above. Introducing the concepts of fuzzy convex cones and fuzzy polar cones, it is shown how some of the main results obtained by Yu are extended.