模糊集合的模糊度的一种表示形式

给出了当论域是有界区间时,模糊度的表示形式的一个定理,利用这个定理可以得到用熵函数和距离函数所表示的模糊度的具体形式.     

模糊关系的模糊度的一般形式

研究了模糊关系的模糊度的一般表示形式问题,得到了关于模糊关系模糊度的一系列定理及公式,丰富了模糊度的内容.     

A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

An adjustable approach to intuitionistic fuzzy soft sets based decision making

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. In this paper we generalize the adjustable approach to fuzzy soft sets based decision making. Concretely, we present an adjustable approach to intuitionistic fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzy soft sets and give some illustrative examples. The properties of level soft sets are presented and discussed. Moreover, we also introduce the weighted intuitionistic fuzzy soft sets and investigate its application to decision making.     

粗糙直觉模糊集的近似表示

在粗糙直觉模糊集的基础上,从新的角度提出了不确定目标概念的近似表示和处理的方法(通过近似模糊集和近似精确集刻画).首先将已有的直觉模糊集相似概念和均值直觉模糊集概念引入到该模型,定义了Pawlak近似空间U/R下的阶梯直觉模糊集、0.5-精确集的概念,然后得到了均值直觉模糊集(0.5-精确集)是所有直觉模糊集中与目标直觉模糊集最接近的直觉模糊集(近似精确集),接着分析了均值直觉模糊集、0.5-精确集分别与目标直觉模糊集的相似度随着知识粒度变化的变化规律.     

药片与模糊集

根据概念原理举例说明模糊集取大取小运算的不完备性,即词不达意的问题.     

B-vex Fuzzy Mappings and Its Application to Fuzzy Optimization Problems

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An argument-based approach to reasoning with clinical knowledge

Better use of biomedical knowledge is an increasingly pressing concern for tackling challenging diseases and for generally improving the quality of healthcare. The quantity of biomedical knowledge is enormous and it is rapidly increasing. Furthermore, in many areas it is incomplete and inconsistent. The development of techniques for representing and reasoning with biomedical knowledge is therefore a timely and potentially valuable goal. In this paper, we focus on an important and common type of biomedical knowledge that has been obtained from clinical trials and studies. We aim for (1) a simple language for representing the results of clinical trials and studies; (2) transparent reasoning with that knowledge that is intuitive and understandable to users; and (3) simple computation mechanisms with this knowledge in order to facilitate the development of viable implementations. Our approach is to propose a logical language that is tailored to the needs of representing and reasoning with the results of clinical trials and studies. Using this logical language, we generate arguments and counterarguments for the relative merits of treatments. In this way, the incompleteness and inconsistency in the knowledge is analysed via argumentation. In addition to motivating and formalising the logical and argumentation aspects of the framework, we provide algorithms and computational complexity results.     

面向复杂产品系统项目评价专家遴选方法研究

专家遴选是复杂产品系统(CoPS)项目科学评价过程中的重要决策问题,科学合理的遴选专家有利于CoPS项目的实现。CoPS项目的多领域知识集成性和项目任务的模糊不确定性,给项目评价的知识属性识别和专家遴选相对“小”领域的科学判断带来较大困难。在面向CoPS项目评价的专家遴选研究问题上,提出了包含技术领域和任务领域的二元知识分类表征方法,构建了基于直觉模糊相似度的专家知识关联度侧度模型,在此基础上建立了包含专家业绩评价和知识关联度的专家遴选多目标决策模型,并给出了一个航天领域电子元器件项目评价的实例。     

A novel approach to multi attribute group decision making based on trapezoidal interval type-2 fuzzy soft sets

Soft set theory, originally proposed by Molodtsov, has become an effective mathematical tool to deal with uncertainty. A type-2 fuzzy set, which is characterized by a fuzzy membership function, can provide us with more degrees of freedom to represent the uncertainty and the vagueness of the real world. Interval type-2 fuzzy sets are the most widely used type-2 fuzzy sets. In this paper, we first introduce the concept of trapezoidal interval type-2 fuzzy numbers and present some arithmetic operations between them. As a special case of interval type-2 fuzzy sets, trapezoidal interval type-2 fuzzy numbers can express linguistic assessments by transforming them into numerical variables objectively. Then, by combining trapezoidal interval type-2 fuzzy sets with soft sets, we propose the notion of trapezoidal interval type-2 fuzzy soft sets. Furthermore, some operations on trapezoidal interval type-2 fuzzy soft sets are defined and their properties are investigated. Finally, by using trapezoidal interval type-2 fuzzy soft sets, we propose a novel approach to multi attribute group decision making under interval type-2 fuzzy environment. A numerical example is given to illustrate the feasibility and effectiveness of the proposed method.     

Application of a Near-Optimal Reinforcement Learning Controller to a Robotics Problem in Manufacturing: A Hybrid Approach

Optimization theory provides a framework for determining the best decisions or actions with respect to some mathematical model of a process. This paper focuses on learning to act in a near-optimal manner through reinforcement learning for problems that either have no model or the model is too complex. One approach to solving this class of problems is via approximate dynamic programming. The application of these methods are established primarily for the case of discrete state and action spaces. In this paper we develop efficient methods of learning which act in complex systems with continuous state and action spaces. Monte-Carlo approaches are employed to estimate function values in an iterative, incremental procedure. Derivative-free line search methods are used to obtain a near-optimal action in the continuous action space for a discrete subset of the state space. This near-optimal control policy is then extended to the entire continuous state space via a fuzzy additive model. To compensate for approximation errors, a modified procedure for perturbing the generated control policy is developed. Convergence results under moderate assumptions and stopping criteria are established.     

An Evolutionary Approach to Spatial Fuzzy c-Means Clustering

Fuzzy c-means clustering algorithm (FCM) can provide a non-parametric and unsupervised approach to the cluster analysis of data. Several efforts of fuzzy clustering have been undertaken by Bezdek and other researchers. Earlier studies in this field have reported problems due to the setting of optimum initial condition, cluster validity measure, and high computational load. More recently, the fuzzy clustering has benefited of a synergistic approach with Genetic Algorithms (GA) that play the role of an useful optimization technique that helps to better tolerate some classical drawbacks, such as sensitivity to initialization, noise and outliers, and susceptibility to local minima. We propose a genetic-level clustering methodology able to cluster objects represented by R ^p spaces. The unsupervised cluster algorithm, called SFCM (Spatial Fuzzy c-Means), is based on a fuzzy clustering c-means method that searches the best fuzzy partition of the universe assuming that the evaluation of each object with respect to some features is unknown, but knowing that it belongs to circular regions of R ² space. Next we present a Java implementation of the algorithm, which provides a complete and efficient visual interaction for the setting of the parameters involved into the system. To demonstrate the applications of SFCM, we discuss a case study where it is shown the generality of our model by treating a simple 3-way data fuzzy clustering as example of a multicriteria optimization problem.     

Some ideas to minimize an empirically given fuzzy function

In real world problems, usually, the response variable as well as the adjustable control variables are subject to vagueness and uncertainty. These properties can be taken into account by means of specifying fuzzy sets for the respective values. In the paper the case is considered that the function to be minimized is a fuzzy one and can only be inspected point by point. Then a region is to be found where the values of the response variables are minimum in a given sense. Hence a sequential procedure is sketched for which the observed values will run into such a region.     

A general approach to fuzzy concepts

The paper proposes a flexible way to build concepts within fuzzy logic and set theory. The framework is general enough to capture some important particular cases, with their own independent interpretations, like “antitone” or “isotone” concepts constructed from fuzzy binary relations, but also to allow the two universes (of objects and attributes) to be equipped each with its own truth structure. Perhaps the most important feature of our approach is that we do not commit ourselves to any kind of logical connector, covering thus the case of a possibly non‐commutative conjunction too. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

电测深确定最佳井位的数学模型及其应用

在电测深确定最佳井位过程中 ,本文运用模糊数学和灰色关联度理论建立确定最佳井位的数学模型 ,并通过实例验证了该数学模型的科学性和实用性     

Real-time moving object segmentation in H.264 compressed domain based on approximate reasoning

This paper presents a real-time segmentation algorithm to obtain moving objects from the H.264 compressed domain. The proposed segmentation works with very little information and is based on two features of the H.264 compressed video: motion vectors associated to the macroblocks and decision modes. The algorithm uses fuzzy logic and allows to describe position, velocity and size of the detected regions in a comprehensive way, so the proposed approach works with low level information but manages highly comprehensive linguistic concepts. The performance of the algorithm is improved using dynamic design of fuzzy sets that avoids merge and split problems. Experimental results for several traffic scenes demonstrate the real-time performance and the encouraging results in diverse situations.     

Generalized hesitant fuzzy synergetic weighted distance measures and their application to multiple criteria decision-making

The purpose of this paper is to present a generalized hesitant fuzzy synergetic weighted distance (GHFSWD) measure, which is based on the generalized hesitant fuzzy weighted distance (GHFWD) measure and the generalized hesitant fuzzy ordered weighted distance (GHFOWD) measure proposed by Xu and Xia [Z. Xu, M. Xia, Distance and similarity measures for hesitant fuzzy sets, Inf. Sci. 181 (2011) 2128–2138.], and investigate its some desirable properties and special cases. The GHFSWD measure not only generalizes both the GHFWD and GHFOWD measures as well as the common hesitant fuzzy distance measures, but also reflects the importance degrees of both the given individual distances and their ordered positions. Then, based on the defined notions of positive ideal hesitant fuzzy set and negative ideal hesitant fuzzy set, we utilize the proposed GHFSWD measure to develop a method for multiple criteria decision making with hesitant fuzzy information. The method is flexible because it allows decision makers to provide preference with hesitancy and determine different decision results by choosing different decision strategies. Finally, a numerical example is provided to illustrate the feasibility and practicality of the proposed method.