Generalized ordered weighted averaging operators based methods for MADM in intuitionistic fuzzy set setting

Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.

The Counting Problem of an Order N-group of Set

In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.

SOME EQUAL DIVISIONS ON ORDERED TREE SET

We say a divisien (S = SA or SB, g) is equal if it divides set S into two subsets SA and SB satisfying f (SA) = f (SB), where f is som attribute function on these sets and SA or SB need not be empty. In the present paper, we have obtained some equal divisions on set of ordered tree with n modes: two equal divisions on tree set; two equal divisions on node set; two divisions on leaf set, one is equal, another one is ''asymptotically'' equal. We conclude that, ordered tree set is on its good behavior in equal dividing.

Results of Associated Implication Algebra on a Partial Ordered Set

Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.

The Fractal Structures of the Sample Path of a General Subordinator and the Random Re-orderings of the Cantor Set

In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.

REAIZATION OF THE NEIGHBORING LOGIC SYMMETRY FOR BOOLEAN ORDERED SET

By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results are intuitional and realizable for computer.

Higher-order Optimality Conditions for Henig Effcient Solution in Set-valued Optimization under Cone-convexlike Maps

This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.

The Ellipsoidal Invariant Set of Fractional Order Systems Subject to Actuator Saturation:The Convex Combination Form

The domain of attraction of a class of fractional order systems subject to saturating actuators is investigated in this paper. We show the domain of attraction is the convex hull of a set of ellipsoids. In this paper, the Lyapunov direct approach and fractional order inequality are applied to estimating the domain of attraction for fractional order systems subject to actuator saturation. We demonstrate that the convex hull of ellipsoids can be made invariant for saturating actuators if each ellipsoid with a bounded control of the saturating actuators is invariant. The estimation on the contractively invariant ellipsoid and construction of the continuous feedback law are derived in terms of linear matrix inequalities (LMIs). Two numerical examples illustrate the effectiveness of the developed method. © 2014 Chinese Association of Automation.

The Normal Meromorphic Functions Family Concerning Higher Order Derivative and Shared Set by One-Way

Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

Effects of Second-Order Sum-and Difference-Frequency Wave Forces on the Motion Response of a Tension-Leg Platform Considering the Set-down Motion

This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.

Continuity of Solution Mappings for Parametric Set Optimization Problems under Partial Order Relations

This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.

基于Roughset的有序信息表的排序问题研究

针对有序信息表的排序问题,提出了总体排序的过程框架。将有序信息表转化为二进制信息表,运用粗糙集理论对信息表进行简化,在对属性值标准化的基础上构造有序信息表中实体的排序度量函数,根据度量函数值的大小进行排序。实例表明该过程框架在误差允许范围内是有效可行的。

利用到达定义集计算流依赖和def-order依赖

针对生成程序系统依赖图时语句顶点之间的流依赖和def-order依赖计算问题,给出了定义清晰的路径以及到达定义集的概念,描述了利用到达定义集进行计算的方法步骤,有助于确立语句之间的流依赖和def-order依赖关系。

On the Monotone Iterative Method for Set Valued Equation

This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.

Solution with Singularity of Order One for Singular Integral Equation with Hilbert Kernal

The basic sets of solutions in classH(orH *) for the characteristic equation and its adjoint equation with Hilbert kernel are given respectively. Thus the expressions of solutions and its solvable conditions are simplified. On this basis the solutions and the solvable conditions in classH 1 * as well as the generalized Noether theorem for the complete equation are obtained. Key words Hilbert kernel - solution with singularity of order one - basic set of solutions - Noether theorem - characteristic equation and its adjoint equation CLC number O 175.5 Foundation item: Supported by the National Natural Science Foundation of China (19971064) and Ziqiang Invention Foundation of Wuhan University (201990336)Biography: Zhong Shou-guo(1941-), male, Professor, research direction: singular integral equations and their applications.

Risk analysis and assessment for make-to-order manufacturing

Based on the characteristics of make-to-order manufacturing, risks in enterprises are analyzed, which are encountered when receiving orders. Dividing the whole process into three stages, this paper provides a qualitative explanation of the risky factors, failure rate, risk level and changes of each stage, and then provides a mathematic model of quantitative analysis by using fuzzy sets and an analytical hierarchy process. In the light of the relationship among the three stages, a formula for calculating risk levels of orders is worked out. Meanwhile, both economic and non-economic losses due to an order failure are considered in the assessment system. An actual case is analyzed using the described method. Suggestions for risk prevention or loss reduction are given.

EKELAND’S VARIATIONAL PRINCIPLE AND CARISTI’S COINCIDENCE THEOREM FOR SET-VALUED MAPPINGS IN PROBABILISTIC METRIC SPACES

By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.

Lower Approximation Reduction in Ordered Information System with Fuzzy Decision

Attribute reduction is one of the most important problems in rough set theory. This paper introduces the concept of lower approximation reduction in ordered information systems with fuzzy decision. Moreover, the judgment theorem and discernable matrix are obtained, in which case an approach to attribute reduction in ordered information system with fuzzy decision is constructed. As an application of lower approximation reduction, some examples are applied to examine the validity of works obtained in our works..

Some Fixed Point Results of Ciric-Type Contraction Mappings on Ordered <i>G</i>-Partial Metric Spaces

We introduce the concept of generalized quasi-contraction mappings in G-partial metric spaces and prove some fixed point results in ordered G-partial metric spaces. The results generalize and extend some recent results in literature.