Stability analysis of fractional order fuzzy cellular neural networks with leakage delay and time varying delays

In this paper we investigated the stability of fractional order fuzzy cellular neural networks with leakage delay and time varying delays. Based on Lyapunov theory and applying bounded techniques of fractional calculation, sufficient criterion are established to guarantee the stability. Hybrid feedback control is applied to derive the proposed results. Finally, numerical examples with simulation results are given to illustrate the effectiveness of the proposed method.     

基于Nie-Tan算法的区间二型模糊集质心计算:改变主变量采样个数

计算区间二型模糊集的质心(也称降型)是区间二型模糊逻辑系统中的一个重要模块。Karnik-Mendel(KM)迭代算法通常被认为是计算区间二型模糊集质心的标准算法。尽管如此,KM算法涉及复杂的计算过程,不利于实时应用。在各种改进类算法中,非迭代的Nie-Tan(NT)算法可节省计算消耗。此外,连续版本NT(CNT,continuous version of NT)算法被证明是计算质心的准确算法。本文比较了离散版本NT算法中求和运算和连续版本NT算法中求积分运算,通过四个计算机仿真例子证实了当适度增加区间二型模糊集主变量采样个数时,NT算法的计算结果可以精确地逼近CNT算法。     

n人可信策略博弈

本文研究模糊支付n人策略博弈,由于支付信息的不完全性,模糊支付可视为模糊变量。基于可信性理论,在不同的决策环境中引入模糊排序方法表征支付者行为。因此,本文定义四种可信均衡,等价于纳什均衡。其次证明了可信均衡存在性定理。除此之外,在现实策略博弈中用算例说明四种可信均衡的现实意义。最后讨论四种可信均衡之间可能存在的关系。     

Ideal and non-ideal behaviour of {1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide + γ-butyrolactone} binary mixtures

Density, electrical conductivity and viscosity of binary liquid mixtures of 1-butyl-1-methylpyrrolydinium bis(trifluoromethylsulfonyl)imide, [bmpyrr][NTf₂], with γ-butyrolactone (GBL) were measured at temperatures from (293.15 to 323.15) K and at atmospheric pressure over the whole composition range. Excess molar volumes have been calculated from the experimental densities and fitted with the Redlich–Kister polynomial equation. These values are positive over the whole range of ionic liquid mole fraction and at all temperatures. In the range between 0.55 and 0.6 [bmpyrr][NTf₂] mole fraction, an ideal behaviour of the ionic liquid mixture with molecular solvent was observed for the first time. Other volumetric properties, such as isobaric thermal expansion coefficients, partial molar volumes and partial molar volumes at infinite dilution have been also calculated, in order to obtain information about interactions between GBL and selected ionic liquid. Positive values of these properties for both components also indicate weaker interactions between GBL and IL compared to the pure components. From the viscosity results, the Angell strength parameter was calculated and found to be 3.24 indicating that [bmpyrr][NTf₂] is a “fragile” liquid. From the volumetric and transport properties obtained, formation of the [bmpyrr]⁺ micellar structures was also discussed. All the results are compared to those obtained for imidazolium-based ionic liquid with GBL.     

Rough path properties for local time of symmetric α stable process

In this paper, we first prove that the local time associated with symmetric $\alpha$-stable processes is of bounded $p$-variation for any $p>\frac{2}{\alpha ?1}$ partly based on Barlow’s estimation of the modulus of the local time of such processes.  The fact that the local time is of bounded $p$-variation for any $p>\frac{2}{\alpha ?1}$ enables us to define the integral of the local time ${\int }_{?\infty }^{\infty }{?}_{?}^{\alpha ?1}f\left(x\right)d_x{L}_t^x$ as a Young integral for less smooth functions being of bounded $q$-variation with $1\le q<\frac{2}{3?\alpha }$. When $q\ge \frac{2}{3?\alpha }$, Young’s integration theory is no longer applicable. However, rough path theory is useful in this case. The main purpose of this paper is to establish a rough path theory for the integration with respect to the local times of symmetric $\alpha$-stable processes for $\frac{2}{3?\alpha }\le q<4$.     

Davey-Stewartson系统粗糙爆破解的极限行为

研究了Davey-Stewartson系统(简记为D-S系统)粗糙爆破解的动力学性质.所谓粗糙爆破解即为正则性为H~s(s1)的爆破解,此时D-S系统粗糙解不再满足能量守恒率.利用I-方法与Profile分解理论,得到了D-S系统粗糙爆破解在H~s(R~2)(其中ss_0,且s_0≤(1+11~(1/2))/5≈0.8633)中的极限行为,包括L~2强极限的不存在性与L~2集中性质以及极限图景.     

Fuzzy logic modifications of the Analytic Hierarchy Process

The Analytic Hierarchy Process (AHP) is a measurement methodology based on pair-wise comparisons that relies on judgment to derive priority scales. During its implementation, one constructs hierarchies, then makes judgments or performs measurements on pairs of elements with respect to a criterion to derive preference scales, which are then synthesized throughout the structure to select the preferred alternative.One of the areas where the AHP finds application is in the subjective phases of risk assessment (RA), where it is used to structure and prioritize diverse risk factors, including the judgments of experts. Since fuzzy logic (FL) has been shown to be an effective tool for accommodating human experts and their communication of linguistic variables, there has been research aimed at modeling the fuzziness in the AHP (FAHP), and recently the focus of some of that modeling has been with respect to RA.The literature discusses more than one FAHP model, which raises the question as to which are the prominent models and what are their characteristics. In response to this question, we examine three of the most influential FAHP models. The article proceeds as follows. It begins with a brief overview of the AHP and its limitations when confronted with a fuzzy environment. This is followed by a discussion of FL modifications of the AHP. A RA-based likelihood score example is used throughout. The article ends with a commentary on the findings.     

Capital allocation for portfolios with non-linear risk aggregation

Existing risk capital allocation methods, such as the Euler rule, work under the explicit assumption that portfolios are formed as linear combinations of random loss/profit variables, with the firm being able to choose the portfolio weights. This assumption is unrealistic in an insurance context, where arbitrary scaling of risks is generally not possible. Here, we model risks as being partially generated by Lévy processes, capturing the non-linear aggregation of risk. The model leads to non-homogeneous fuzzy games, for which the Euler rule is not applicable. For such games, we seek capital allocations that are in the core, that is, do not provide incentives for splitting portfolios. We show that the Euler rule of an auxiliary linearised fuzzy game (non-uniquely) satisfies the core property and, thus, provides a plausible and easily implemented capital allocation. In contrast, the Aumann–Shapley allocation does not generally belong to the core. For the non-homogeneous fuzzy games studied, Tasche’s (1999) criterion of suitability for performance measurement is adapted and it is shown that the proposed allocation method gives appropriate signals for improving the portfolio underwriting profit.     

The valuation of life contingencies: A symmetrical triangular fuzzy approximation

This paper extends the framework for the valuation of life insurance policies and annuities by Andrés-Sánchez and González-Vila (2012, 2014) in two ways. First we allow various uncertain magnitudes to be estimated by means of fuzzy numbers. This applies not only to interest rates but also to the amounts to be paid out by the insurance company. Second, the use of symmetrical triangular fuzzy numbers allows us to obtain expressions for the pricing of life contingencies and their variability that are closely linked to standard financial and actuarial mathematics. Moreover, they are relatively straightforward to compute and understand from a standard actuarial point of view.