A characterization of uninorms on bounded lattices by means of triangular norms and triangular conorms

ABSTRACT

Uninorms are generalizations of triangular norms and triangular conorms leaving the freedom for the neutral element to be an arbitrary element from a bounded lattice. In this paper, we study uninorms on bounded lattices and investigate their main characteristics. We also introduce the new construction methods for uninorms on bounded lattices with a neutral element based on the fact that the presence of triangular norms and triangular conorms. Furthermore, we assess and exemplify the differences between our constructions and the present approaches.     

Generalized convex combination of triangular norms on bounded lattices

ABSTRACT

In this paper, we introduce the notions of the linear and generalized convex combination (shortly, g-convex combination) for triangular norms on bounded lattices. We investigate the conditions for the g-convex combination to be a triangular norm again. We introduce a triangular norm defined on a bounded lattice of equivalence classes and investigate some basic properties of the introduced triangular norm.     

Solution of an open problem on pseudo-Archimedean t-norms

An open problem on pseudo-Archimedean t-norms, recently posed by B. De Baets and R. Mesiar [B. De Baets, R. Mesiar, Triangular norms on product lattices, Fuzzy Sets and Systems 104 (1) (1999) 61-75], is discussed.     

A bounded harvest strategy for an ecological system in the presence of uncertain disturbances

We examine a bounded harvest strategy for an ecological system with uncertainty appearing in all system parameters. The instantaneous values of those system parameters are not known except for the bounds of their possible variations. The harvest strategy is required to stabilize the ecological system at a prescribed desired level.     

Generalized triangular norm and conorm aggregation operators on ordinal spaces

We describe the basic features of the t-norm operator and then introduce a family of t-norm operators that are defined on an ordinal space. We then do the same for the t-conorms. We note the strong limitation that the requirement of associativity places on the t-norm and t-conorm operators. We particularly note how it limits our ability to model different types of reinforcement. We then define a generalization of the t-conorm aggregation operator, which relaxes the requirement of associativity, we denote these operators as GENOR operators. We show that these operators have the same functionality as the t-conorm. We provide some examples of GENOR operators which allow us to control the reinforcement process. We define a related extension for the t-norm, the GENAND operator and provide some examples.     

On internal and locally internal uninorms on bounded lattices

In this paper, we introduce the definition of an internal uninorm on an arbitrary bounded lattice L. We investigate some properties of these operators and the relationship with locally internal uninorms. We show that an internal uninorm need not always exist on an arbitrary bounded lattice. Furthermore, based on the Zermelo's well-ordering theorem, we propose two construction methods to obtain internal uninorms on a bounded lattice L with some additional constraints.     

Calculational derivation of a counter with bounded response time and bounded power dissipation

Summary A counter is calculationally designed by applying a functional way of programming, in which a machine is conceived as a function from states to behaviours. The design exploits the fine-grained concurrency available in VLSI. It is obtained by applying a series of correctness-preserving transformations on an initial design, which satisfies the functional specification but does not meet the cost/performance requirements. The transformations are purely calculational, i.e. they are based on a few simple axioms. The design is generic in that it describes counters with all possible periods. An attractive property of the design is that all these counters have the same response time as well as the same power dissipation. Joep Kessels is a senior scientist at Philips Research Laboratories. He was involved in projects on applicative programming, distributed processing and local area networks. Currently he is engaged in a project on designing asynchronous VLSI circuits. His main research interests are design methodology and distributed processing.     

Robust exponential convergence of a class of linear delayed systems with bounded controllers and disturbances

This brief paper deals with the problem of robust exponential stabilization of a class of dynamic systems subject to time-varying delays, external disturbances and control saturation. A linear memoryless state feedback controller is synthesized to guarantee that there is a domain of admissible initial conditions from which all solutions of the class of systems considered converge exponentially to a ball with a prespecified convergence rate. The problem is formulated as a two-step optimization problem with matrix inequality constraints to enlarge the size of the ball of admissible initial conditions.     

The influence of user cognition on consumption decision-making from the perspective of bounded rationality

Consumer decision-making is related to the success or failure of enterprises, and products that cater to the cognitive preferences of users have become a focus of current research. Based on the theory of bounded rationality, this paper explores the cognitive process of consumer decision-making. Then, how product shape affects consumption decision-making is analyzed with eye-tracking technology. Finally, the design principle of the product form is further explored. The results demonstrate the following: (1) the perceptual cognition of users has a driving effect on consumption behavior; (2) as a key factor affecting the perceptual cognition of users, product form affects consumer decision-making by influencing the degree of approach motivation; (3) by establishing the mapping relationship between product form elements and user images, the principles of product form design can be more consistent with user image preferences. This study provides useful suggestions for how to increase the purchase behavior of users from the perspective of bounded rationality.     

问题有解与状态空间图的核为有界格的等价性理论

作为求解问题的工具,状态空间图具有直观、清晰的特点,在人工智能应用甚广。论文首次分析状态空间图有解的代数特征,提出序状态空间图及核的概念,证明了问题有解与其状态空间图的核为有界格是等价的,并给出两个实例加以说明,另外给出有关核的性质。     

Existence of unmixed solutions of the discrete-time algebraic Riccati equation and a nonstrictly bounded real lemma

The existence of a solution of the discrete-time algebraic Riccati equation is established assuming modulus controllability and positive semidefiniteness on the unit circle of the Popov function. As an application a nonstrictly bounded real lemma is obtained.     

A solution of the optimal turn problem of an axially symmetric spacecraft with bounded and pulse control under arbitrary boundary conditions

Given a constraint on the modulus of the control action in the quaternion statement, the optimal turn problem of a spacecraft regarded as a rigid body with one symmetry axis is considered under arbitrary boundary conditions with respect to its attitude and angular velocity. The functional combining the time and the integral value of the control vector spent to the spacecraft turn is used as the optimality criterion. Changes of variables allow reducing (in terms of dynamic Euler equations) the initial optimal turn problem of an axially symmetric spacecraft to the optimal turn problem of a rigid body with spherical mass distribution. Two ways of solving the optimal control problem are proposed. In the first case, the Pontryagin maximum principle is used to obtain the expressions of the optimal control and the adjoint system of equations. In the second case, the passage to the limit with the upper value of the control action increasing indefinitely is performed to construct an analytical solution to the pulse optimal turn problem of a spacecraft that implements the double-pulse control scheme. The original procedure of finding the numerical solution to the continuous optimal turn problem of a spacecraft with bounded control is described, and the examples of calculations are given. The numerical approbation of the proposed analytical algorithm of solving the pulse optimal turn problem of a spacecraft is given     

Time-varying discrete-time linear systems with bounded rates of variation: Stability analysis and control design

This paper investigates the problems of robust stability analysis and state feedback control design for discrete-time linear systems with time-varying parameters. It is assumed that the time-varying parameters lie inside a polytopic domain and have known bounds on their rate of variation. A convex model is proposed to represent the parameters and their variations as a polytope and linear matrix inequality relaxations that take into account the bounds on the rates of parameter variations are proposed. A feasible solution provides a parameter-dependent Lyapunov function with polynomial dependence on the parameters assuring the robust stability of this class of systems. Extensions to deal with robust control design as well as gain-scheduling by state feedback are also provided in terms of linear matrix inequalities. Numerical examples illustrate the results.     

A Presentation of Quantum Logic Based on an and then Connective

When a physicist performs a quantic measurement, new informationabout the system at hand is gathered. This article studies thelogical properties of how this new information is combined withprevious information. It presents Quantum Logic as a propositionallogic under two connectives: negation and the and then operationthat combines old and new information. The and then connectiveis neither commutative nor associative. Many properties of thislogic are exhibited, and some small elegant subset is shownto imply all the properties considered. No independence or completenessresult is claimed. Classical physical systems are exactly characterizedby the commutativity, the associativity, or the monotonicityof the and then connective. Entailment is defined in this logicand can be proved to be a partial order. In orthomodular lattices,the operation proposed by Finch in [3] satisfies all the propertiesstudied in this article. All properties satisfied by Finch's;operation in modular lattices are valid in Quantum Logic. Itis not known whether all properties of Quantum Logic are satisfiedby Finch's; operation in modular lattices. Non-commutative,non-associative algebraic structures generalizing Boolean algebrasare defined, ideals are characterized and a homomorphism theoremis proved.     

On the convex combination of TD and continuous triangular norms

The problem of when is a triangular norm, where T_D is the drastic product and T is a continuous triangular norm, is studied. It is shown that T_λ cannot be a triangular norm when T is nilpotent. It is also shown that T_λ is a triangular norm if T is strict and its additive generator f satisfies f(λx)=f(x)+f(λ) for all x∈[0,1]. The cases that T=T_M and T is the ordinal sum of continuous Archimedean summands are also discussed. Some left-continuous t-norms which can be combined with each other are given.     

Synthesis of linear and planar arrays with sidelobes of individually arbitrary levels

A procedure is presented to synthesize linear and planar antenna arrays to have individually arbitrary sidelobe levels. This procedure is based on perturbation of the zeros of radiation pattern and is applicable for both sum‐ and difference‐type radiation patterns. Planar antenna arrays are synthesized by transforming synthesized linear arrays to planar arrays. The synthesized planar arrays would have ring type sidelobes. Some examples are brought to verify the effectiveness of the proposed procedure for both linear and planar arrays with sum or difference radiation patterns.     

一种新的信息系统三角模糊自适应评价模型

目前的信息系统评价模型采用通用评价因子来评价不同领域中的系统,不能全面衡量不同信息系统的质量。提出了新的评价模型使用了动态制定不同领域的评价因子,同时提出了一种带有模糊评判调节因子的NTFAHP法,并对模糊综合评价方法进行了改进,将两者相结合,建立了适应现代信息系统的新评价算法。设计了该评价模型的原型系统,利用原型系统实施工程实例的可计算化评价,其实验结果的准确性、可靠性和稳定性有了明显改善和提高。     

新的桶形畸变的点阵样板校正方法

为了校正广角镜头的桶形畸变,提出一种新的桶形畸变数字校正方法。它使用点阵样板校正的方法,根据畸变图和理想图中圆点的位置关系,得出畸变图像素在X轴和Y轴方向上的偏移量曲面,采用三次B插值函数对曲面插值;由曲面插值获取像素点的偏移量,对各像素进行坐标转换得到校正图像;然后对图像进行了双线性插值的灰度重建。仿真结果表明,该方法使图像的坐标位置和灰度都得到很好的校正。     

Approximation of an arbitrary filter and its recursive implementation

Filtering is one of the important techniques in computer vision. It has been widely used in edge detection, image restoration, range image segmentation, etc. However, the efficient implementation of an arbitrary filter has been a challenging problem until now. In this paper, a novel method is proposed to implement an arbitrary filter. Firstly, an efficient recursive structure is proposed to implement any (polynomial) × (exponential)-type (PET) filter. The computational complexity and structure are independent of its filter mask size or its bandwidth. Secondly, a new method is proposed—Lagurre spectrum decomposition method—to obtain the PET approximation of any filters. As an example, the above method is applied to the approximation and implementation of Gaussian filters and experiments have shown that a perfect approximation can be obtained with only third-order Lagurre bases, and therefore only a fourth-order recursive filter is needed to implement Gaussian filters. Finally, the comparison of the present method with the known ones shows that (1) Lagurre polynomial bases are orthogonal with each other, so the filter approximation is simple, (2) the bases are complete and the completeness guarantees the approximation error can be reduced to zero, (3) the method can be used to design both Gaussian and any other filters.