Communicating between information systems based on including degrees

Communication between information systems is a basic problem in granular computing. In current research, a homomorphism mapping between information systems is required. In this paper, the concept of the general relation mapping between two universes is proposed in order to construct the equivalence relation on one universe according to the given equivalence relation on the other universe based on the including degrees. The main properties of the mapping are studied, and it is proved that attribute reductions in the original system and image system are equivalent to each other under the given conditions. Finally, we also define the concept of fuzzy general relation mapping between two fuzzy information systems and give some properties.     

O-THEORY—A HYBRID UNCERTAINTY THEORY

A hybrid uncertainty theory is developed to bridge the gap between fuzzy set theory and Dempster-Shafer theory. Its basis is the Dempster-Shafer formalism, which is extended to include a complete set of basic operations for manipulating uncertainties in a set-theoretic framework. The new theory, operator-belief theory (OT), retains the probabilistic flavor of Dempster's original point-to-set mappings but includes the potential for defining a wider range of operators like those found in fuzzy set theory.

The basic operations defined for OT in this paper include those for: dominance and order, union, intersection, complement and general mappings. Several sample problems in approximate reasoning are worked out to illustrate the new approach as well as to compare it with the other theories currently being used. A general method or extending the theory by using fuzzy set theory as a guide is suggested.     

FUZZINESS VS. PROBABILITY

Fuzziness is explored as an alternative to randomness for describing uncertainty. The new sets-as-points geometric view of fuzzy sets is developed. This view identifies a fuzzy set with a point in a unit hypercube and a nonfuzzy set with a vertex of the cube. Paradoxes of two-valued logic and set theory, such as Russell's paradox, correspond to the midpoint of the fuzzy cube. The fundamental questions of fuzzy theory—How fuzzy is a fuzzy set? How much is one fuzzy set a subset of another?—are answered geometrically with the Fuzzy Entropy Theorem, the Fuzzy Subsethood Theorem, and the Entropy-Subsethood Theorem. A new geometric proof of the Subsethood Theorem is given, a corollary of which is that the apparently probabilistic relative frequency n_A /N turns out to be the deterministic subsethood S(X, A), the degree to which the sample space X is contained in its subset A. So the frequency of successful trials is viewed as the degree to which all trials are successful. Recent Bayesian polemics against fuzzy theory are examined in light of the new sets-as-points theorems.     

CONCEPTS OF FUZZY INFORMATION MEASURES ON CONTINUOUS DOMAINS

Measures of information based on fuzzy sets (possibility distributions) had been defined only for finite domains of discourse. This paper presents a method of defining such information functions on a continuous universe of discourse—a domain which is a measurable space of measure 1. The method is based on the concept of “rearangement” of a function, used in lieu of sorting discrete possibility values. For technical reasons, it is preferred to express information value as information distance to the most “uninformed” (constant possibility 1) distribution. The final form of the information for possibility distribution f is

The paper then discusses related information distances and approximations using discrete information functions.     

Continuity and completeness of lattice-valued possibilistic measures

Properties such as continuity from above and from below and various kinds of completeness are analysed when investigating set functions, in particular probabilistic and possibilistic measures and the relations of these properties to properties such as (σ)-additivity of probability measures or (complete) maxitivity of possibilistic measures are proved. In this work, the notions of continuity from above and from below are introduced for non-numerical possibilistic measures, taking their values in a complete lattice and at least for some relations valid for real-valued possibilistic measures of their analogies for lattice-valued possibilistic measures are stated and proved.     

面向可能性数据库的异构双极信息查询策略研究

在日常交流中,人们常常会对同一事物同时使用正面的描述和负面的描述来表达其愿望和不满,由于不要求正、负面的描述必须相互对称,此类信息因而被称为异构双极(Heterogeneous bipolarity)信息.传统信息系统中的模糊查询方法,不能很好地处理用户查询需求中所含有的异构双极信息.本文基于可能性数据库,在限定的条件下,以在模糊查询选择操作的基本查询条件中,能够处理异构双极信息为目标,将Vague集用于异构双极信息的建模,并给出了在基本查询条件中含有异构双极信息的情况下,查询结果相关可能性测度和必要性测度的计算公式,同时还通过实例讨论了该方法的语义、特点及其与基于可能性理论方法的一致性.     

一种二进制可分辨矩阵修正方法及其求核

传统的二进制可分辨矩阵不适用于不相容决策表,而改进的二进制可分辨矩阵虽然适用于不相容决策表,但需要先进行等价类的计算.为了解决因决策表存在不相容性造成构建二进制可分辨矩阵要计算等价类的问题,提出一种二进制可分辨矩阵修正方法.首先对传统二进制可分辨矩阵进行分析,根据矩阵中各行的取值情况,得到修正论域;然后利用其对矩阵进行局部修正,得新的二进制可分辨矩阵,避免了等价类的计算,并证明了新二进制可分辨矩阵与改进的二进制可分辨矩阵是等价的;其次给出了基于新二进制可分辨矩阵的求核方法,并证明了所求核与基于正区域的核是等价的;最后通过实例证明了此方法的正确性.     

基于灰色关联分析的改进GAC模型轮廓检测方法

针对传统的基本测地线活动轮廓( GAC)模型在检测噪声干扰、弱边界及凹陷边界目标的轮廓时提取效果不佳的问题,文中提出一种基于灰色关联分析的改进GAC模型轮廓检测方法。该方法利用灰色关联度代替梯度信息来构建停止函数。与传统的梯度信息相比,灰色关联系数对于具有模糊的边界信息的图像信息表示更为准确,从而更好地提取弱边界目标轮廓。初步实验结果表明,文中方法在提取弱边界目标轮廓时效果优于基于传统GAC模型和传统的LBF模型的轮廓检测方法。