A novel cognitive transformation algorithm based on Gaussian cloud model and its application in image segmentation

The representation and processing of uncertain concepts are key issue for both the study of artificial intelligence with uncertainty and human knowledge processing. The intension and extension of a concept can be transformed automatically in the human cognition process, while it is difficult for computers. A Gaussian cloud model (GCM) is used to realize the cognitive transformation between intension and extension of a concept through computer algorithms, including forward Gaussian cloud transformation (FGCT) algorithms and backward Gaussian cloud transformation (BGCT) algorithms. A FGCT algorithm can transform a concept’s intension into extension, and a BGCT algorithm can implement the cognitive transformation from a concept’s extension to intension. In this paper, the authors perform a thorough analysis on the existing BGCT algorithms firstly, and find that these BGCT algorithms have some drawbacks. They cannot obtain the stable intension of a concept sometimes. For this reason, a new backward Gaussian cloud cognitive transformation algorithm based on sample division is proposed. The effectiveness and convergence of the proposed method is analyzed in detail, and some comparison experiments on obtaining the concept’s intension and applications to image segmentation are conducted to evaluate this method. The results show the stability and performance of our method.     

The Karush-Kuhn-Tucker optimality conditions for the optimization problem with fuzzy-valued objective function

The Karush-Kuhn-Tucker (KKT) conditions for an optimization problem with fuzzy-valued objective function are derived in this paper. A solution concept of this optimization problem is proposed by considering an ordering relation on the class of all fuzzy numbers. The solution concept proposed in this paper will follow from the similar solution concept, called non-dominated solution, in the multiobjective programming problem. In order to consider the differentiation of a fuzzy-valued function, we use the Hausdorff metric to define the distance between two fuzzy numbers and the Hukuhara difference to define the difference of two fuzzy numbers. Under these settings, the KKT optimality conditions are elicited naturally by introducing the Lagrange function multipliers.     

Generating optimal path by level set approach for a mobile robot moving in static/dynamic environments

According to the analogy between the mobile robot navigation path and the heat transferring path under steady state, the robot path planning problem during navigation is converted into identify the heat transferring path that minimizes the thermal compliance across the analysis domain. A new path planning approach which combines the concept of growth simulation and level set based heat conduction topology optimization framework is adopted to determine the heat transferring path. By introducing the concept of growth simulation, the proposed approach could calculate a few steps of the navigation path, which is of great significance for online reactive navigation. The proposed approach could avoid local minima and search for the optimal growth orientation freely without constraints from background mesh since the inherent characteristics of heat conduction and the level set approach, respectively. A new reactive navigation algorithm based on the proposed path planning approach and the concept of temporarily safe path is proposed to navigate the mobile robot from the start point to the goal point in unknown dynamic environment with static and dynamic obstacles. Diverse simulation cases are carried to illustrate the effectiveness of the reactive navigation algorithm.     

On the (in)stability of quasi‐static paths of smooth systems: definitions and sufficient conditions

A concept of stability of quasi‐static paths is discussed in this paper that takes into account the existence of fast (dynamic) and slow (quasi‐static) time scales in the evolution of many mechanical systems. The proposed concept is essentially a continuity property with respect to the smallness of the initial perturbations (as in Lyapunov stability) and the smallness of the quasi‐static loading rate (that plays the role of the small parameter in singular perturbation problems). A related concept of attractiveness is also proposed. Several examples illustrate the relevance of the definitions. Sufficient conditions for attractiveness or for instability of quasi‐static paths of smooth systems are proved. Copyright © 2005 John Wiley & Sons, Ltd.     

A class of bivariate distributions including the bivariate logistic

A univariate logistic distribution can be specified by considering a suitable form for the odds in favor of a failure against survival. This concept is extended to the bivariate case and a class of distributions, indexed by a parameter of association, having given marginals is proposed. Some properties of the proposed class of distributions are studied.     

Track initiation of bearings-only tracking based on ant navigation concept

A novel heuristic track initiation method is developed for the bearing-only multi-sensor–multi-target tracking system, in which each target is assumed to move with a straight line. The key idea of the proposed method is derived from the ant navigation concept in its foraging life, which differs from the traditional ant colony optimization algorithm, and it utilizes the concept of path integration and visual landmarks in ants’ navigation toolkit to find the exact positions of each target. Numerous numerical simulations are conducted and the effectiveness of the proposed track initiation method is verified according to the probability of correct track initiation.     

On Bivariate Lack of Memory Property and a New Definition

The earlier concept of bivariate lack of memory property has been examined and an alternative concept of bivariate lack of memory property has been presented along with a set of equivalent conditions. In this process, the link relations known in the literature on univariate lack of memory property have been extended to the bivariate set-up. A multivariate extension of the lack of memory property has also been proposed.     

Duality Theory for Optimization Problems with Interval-Valued Objective Functions

A solution concept in optimization problems with interval-valued objective functions, which is essentially similar to the concept of nondominated solution in vector optimization problems, is introduced by imposing a partial ordering on the set of all closed intervals. The interval-valued Lagrangian function and interval-valued Lagrangian dual function are also proposed to formulate the dual problem of the interval-valued optimization problem. Under this setting, weak and strong duality theorems can be obtained.     

An improved training algorithm for feedforward neural network learning based on terminal attractors

In this paper, an improved training algorithm based on the terminal attractor concept for feedforward neural network learning is proposed. A condition to avoid the singularity problem is proposed. The effectiveness of the proposed algorithm is evaluated by various simulation results for a function approximation problem and a stock market index prediction problem. It is shown that the terminal attractor based training algorithm performs consistently in comparison with other existing training algorithms.     

Computational algorithms for hierarchically structured project networks

A new approach to large size network management based on a structured network representation is proposed. Definitions of arc-structured and vertex-structured networks are given and an extension of topological sorting and time computation algorithms is described. A generalization of the concept of vertex-structured networks is discussed.     

On redundancy in multi criteria decision making

The concept of redundancy is accepted in Operations Research and Information Theory. In Linear Programming, a constraint is said to be redundant if the feasible decision space is identical with or without the constraint. In Information Theory, redundancy is used as a measure of the stability against noise in transmission. Analogies with Multi Criteria Decision Making (MCDM) are indicated and it is argued that the redundancy concept should be used as a regular feature in conditioning and analysis of Multi Criteria Programs. Properties of a proposed conflict-based characterisation are stated and some existence results are derived. Redundancy is here intended for interactive methods, when the efficient set is progressively explored. A new redundancy test for the linear case is formulated from the framework. A probabilistic method based on correlation is proposed and tested for the non-linear case. Finally, some general guidelines are given concerning the redundancy problem.     

基于直觉模糊集的多准则模糊决策问题

提出了一种基于直觉模糊集处理模糊决策问题的新方法.该方法用直觉模糊集描述方案关于准则集的满足程度与不满足程度.而且该方法允许决策者给出准则对于模糊集“重要”的隶属度与非隶属度,即准则的权重也由直觉模糊集表示.这种方法为决策者做出最优决策提供了一种方便有效的方法.     

Normalizing and variance stabilizing transformations for intraclass correlations

Summary A concept of normalizing transformations of statistics is constructed on the basis of the rate of convergence to normality. The concept is applied to derive a normalizing transformation of a maximum likelihood estimate of intraclass correlation coefficient in ap-variate normal sample. Numerical comparisons are made to examine whether the proposed transformation is efficient to achieve normality. The relationship between normalization and variance stabilization is also considered. The Institute of Statistical Mathematics     

Saddle Point Optimality Conditions in Fuzzy Optimization Problems

The fuzzy-valued Lagrangian function of fuzzy optimization problem via the concept of fuzzy scalar (inner) product is proposed. A solution concept of fuzzy optimization problem, which is essentially similar to the notion of Pareto solution in multiobjective optimization problems, is introduced by imposing a partial ordering on the set of all fuzzy numbers. Under these settings, the saddle point optimality conditions along with necessary and sufficient conditions for the absence of a duality gap are elicited.     

Factor Model for the Study of Complex Processes

Doklady Mathematics - An original concept of building a factor model based on frames has been proposed. A method has been developed for calculating the values of factors by searching for the...     

On the algebraic solution of fuzzy linear systems based on interval theory

In this paper, fuzzy linear systems involving a crisp square matrix and a fuzzy right-hand side vector are considered. A new approach to solve such systems based on interval theory and the new concept “interval inclusion linear system” is proposed. Also, new necessary and sufficient conditions are derived for obtaining the unique algebraic solution. Numerical examples are given to illustrate the efficiency of the proposed method.     

基于直觉模糊集的突发事件应急预案评估

提出了一种基于直觉模糊集理论的突发事件应急预案评价的新方法.首先,定义了直觉模糊集和两个直觉模糊集之间的距离;然后,建立了应急预案评价指标体系,给出了直觉模糊正理想点和负理想点的概念,提出了基于直觉模糊集和TOPS IS法的应急预案评估方法.最后通过实例说明了该方法的有效性.