Universal triple I fuzzy reasoning algorithm of function model based on quotient space

Aiming at the deficiencies of analysis capacity from different levels and fuzzy treating method in product function modeling of conceptual design,the theory of quotient space and universal triple I fuzzy reasoning method are introduced,and then the function modeling algorithm based on the universal triple I fuzzy reasoning method is proposed.Firstly,the product function granular model based on the quotient space theory is built,with its function granular representation and computing rules defined at the same time.Secondly,in order to quickly achieve function granular model from function requirement,the function modeling method based on universal triple I fuzzy reasoning is put forward.Within the fuzzy reasoning of universal triple I method,the small-distance-activating method is proposed as the kernel of fuzzy reasoning;how to change function requirements to fuzzy ones,fuzzy computing methods,and strategy of fuzzy reasoning are respectively investigated as well;the function modeling algorithm based on the universal triple I fuzzy reasoning method is achieved.Lastly,the validity of the function granular model and function modeling algorithm is validated.Through our method,the reasonable function granular model can be quickly achieved from function requirements,and the fuzzy character of conceptual design can be well handled,which greatly improves conceptual design.     

Modeling data uncertainty on electric load forecasting based on Type-2 fuzzy logic set theory

Real applications based on type-2 (T2) fuzzy sets are rare. The main reason is that the T2 fuzzy set theory requires massive computation and complex determination of secondary membership function. Thus most real-world applications are based on one simplified method, i.e. interval type-2 (IT2) fuzzy sets in which the secondary membership function is defined as interval sets. Consequently all computations in three-dimensional space are degenerated into calculations in two-dimensional plane, computing complexity is reduced greatly. However, ability on modeling information uncertainty is also reduced. In this paper, a novel methodology based on T2 fuzzy sets is proposed i.e. T2SDSA-FNN (Type-2 Self-Developing and Self-Adaptive Fuzzy Neural Networks). Our novelty is that (1) proposed system is based on T2 fuzzy sets, not IT2 ones; (2) it tackles one difficult problem in T2 fuzzy logic systems (FLS), i.e. massive computing time of inference so as not to be applicable to solve real world problem; and (3) membership grades on third dimensional space can be automatically determined from mining input data. The proposed method is validated in a real data set collected from Macao electric utility. Simulation and test results reveal that it has superior accuracy performance on electric forecasting problem than other techniques shown in existing literatures.     

The structural analysis of fuzzy measures

From quotient space based granular computing theory we explore the fuzzy measures of fuzzy sets. Based on the structural analysis of fuzzy sets,we present anisotropismassumption.Under this assumption we achieved the following insights:(1)the uniqueness of a fuzzy measure being isotropic on a finite complete semi-ordered set;(2)the necessary and suffcient condition of the isomorphism for fuzzy measure functions in fuzzy mathematics;(3)the necessary and suffcient condition that fuzzy measures have fuzzy and g...     

模糊度的结构分析

从商空间的粒度计算理论出发,本文讨论模糊集的模糊度量问题,即模糊度的定义.根据模糊集的结构分析,我们提出各向同性的假设,在这个假设下得出以下结果:(1)在有限完备半序集上具有各向同性的模糊度是唯一的.(2)得出模糊数学中的模糊度函数同构的充分必要条件.(3)得出模糊度具有模糊单调性和粒度单调性的充分必要条件.(4)在一定的假设下,给出模糊度的解析表达式.这些结果阐明了模糊度与粒计算的关系,揭示了模糊度的本质,同时提供一种构造模糊度的简易方法.     

Shadowed sets of type‐II: Representing and computing shadowiness in shadowed sets

Shadowed sets were developed to interpret and determine the required pair of thresholds, which resolves the issue with Zadeh's proposal about a three‐way approximation of fuzzy sets. However, a serious shortcoming of shadowed sets is that they are not capable of coming to grips with the degree of shadowiness (or doubt) associated with the elements of a shadowed set, especially the elements in the doubtful zone (i.e., shadow region) and as a result, all the elements in the shadow region are shown no commitment during the process of decision making. This paper proposes an alternative construct that keeps record of the degree of doubt associated with the elements in a shadowed set. It aims at introducing, discussing the concepts of shadowed sets of type‐II, and studying their related operations. Shadowed sets of type‐II provide a capable framework that despite localizing the uncertainty associated with fuzzy sets; adheres to the gradual transition of membership grades of the elements in the doubtful zone.     

粗糙集理论与应用研究综述

在阐释粗糙集理论基本体系结构的基础上,从多个角度探讨粗糙集模型的研究思路,分析粗糙集理论与模糊集、证据理论、粒计算、形式概念分析、知识空间等其它理论之间的联系,介绍国内外关于粗糙集理论研究的主要方向和发展状况,讨论当前粗糙集理论研究的热点研究领域以及将来需要重点研究的主要问题.     

On intuitionistic fuzzy rough sets and their topological structures

In this paper, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of intuitionistic fuzzy approximation operators are examined. Relationships between intuitionistic fuzzy rough set approximations and intuitionistic fuzzy topologies are then discussed. It is proved that the set of all lower approximation sets based on an intuitionistic fuzzy reflexive and transitive approximation space forms an intuitionistic fuzzy topology; and conversely, for an intuitionistic fuzzy rough topological space, there exists an intuitionistic fuzzy reflexive and transitive approximation space such that the topology in the intuitionistic fuzzy rough topological space is just the set of all lower approximation sets in the intuitionistic fuzzy reflexive and transitive approximation space. That is to say, there exists an one-to-one correspondence between the set of all intuitionistic fuzzy reflexive and transitive approximation spaces and the set of all intuitionistic fuzzy rough topological spaces. Finally, intuitionistic fuzzy pseudo-closure operators in the framework of intuitionistic fuzzy rough approximations are investigated.     

Soft sets combined with fuzzy sets and rough sets: a tentative approach

Theories of fuzzy sets and rough sets are powerful mathematical tools for modelling various types of uncertainty. Dubois and Prade investigated the problem of combining fuzzy sets with rough sets. Soft set theory was proposed by Molodtsov as a general framework for reasoning about vague concepts. The present paper is devoted to a possible fusion of these distinct but closely related soft computing approaches. Based on a Pawlak approximation space, the approximation of a soft set is proposed to obtain a hybrid model called rough soft sets. Alternatively, a soft set instead of an equivalence relation can be used to granulate the universe. This leads to a deviation of Pawlak approximation space called a soft approximation space, in which soft rough approximations and soft rough sets can be introduced accordingly. Furthermore, we also consider approximation of a fuzzy set in a soft approximation space, and initiate a concept called soft–rough fuzzy sets, which extends Dubois and Prade’s rough fuzzy sets. Further research will be needed to establish whether the notions put forth in this paper may lead to a fruitful theory.     

直觉模糊集的商空间

把商空间理论推广到直觉模糊集理论中,建立直觉模糊商空间。定义直觉模糊等价关系和直觉模糊距离。建立基于直觉模糊等价关系的商空间基本定理。证明由有序的直觉模糊等价关系簇诱导的直觉模糊商空间构成一个完备半序格。     

Version spaces and the consistency problem

A version space is a collection of concepts consistent with a given set of positive and negative examples. Mitchell [Artificial Intelligence 18 (1982) 203-226] proposed representing a version space by its boundary sets: the maximally general (G) and maximally specific consistent concepts (S). For many simple concept classes, the size of G and S is known to grow exponentially in the number of positive and negative examples. This paper argues that previous work on alternative representations of version spaces has disguised the real question underlying version space reasoning. We instead show that tractable reasoning with version spaces turns out to depend on the consistency problem, i.e., determining if there is any concept consistent with a set of positive and negative examples. Indeed, we show that tractable version space reasoning is possible if and only if there is an efficient algorithm for the consistency problem. Our observations give rise to new concept classes for which tractable version space reasoning is now possible, e.g., 1-decision lists, monotone depth two formulas, and halfspaces.     

积模糊粗集模型及其模糊知识粒的表示和分解

为处理人工智能中不精确和不确定的数据和知识,Pawlak提出了粗集理论。之后粗集理论被推广,其方法主要有二:一是减弱对等价关系的依赖;二是把研究问题的论域从一个拓展到多个。结合这两种思想,研究基于两个模糊近似空间的积模糊粗集模型及其模糊粗糙集的表示和分解。根据这种思想,可以从论域分解的角度探索降低高维模糊粗糙集计算的复杂度问题。先对模糊近似空间的分层递阶结构———λ-截近似空间进行研究,得到不同层次知识粒的相互关系;然后定义模糊等价关系的积,并研究其性质及算法;最后构建基于积模糊等价关系的积模糊粗集模型,并讨论了该模型中模糊粗糙集的表示及分解问题,分别从λ-截近似空间和一维模糊近似空间的角度去处理,给出了可分解集的上(下)近似的一个刻画,及模糊可分解集的上(下)近似的λ-截集分解算法。     

A general type‐2 fuzzy model for computing with words

As a methodology, computing with words (CW) allows the use of words, instead of numbers or symbols, in the process of computing and reasoning and thus conforms more to humans’ inference when it is used to describe real‐world problems. In the line of developing a computational theory for CW, in this paper we develop a formal general type‐2 fuzzy model of CW by exploiting general type‐2 fuzzy sets (GT2 FSs) since GT2 FSs bear greater potential to model the linguistic uncertainty. On the one hand, we generalize the interval type‐2 fuzzy sets (IT2 FSs)‐based formal model of CW into general type‐2 fuzzy environments. Concretely, we present two kinds of general type‐2 fuzzy automata (i.e., general type‐2 fuzzy finite automata and general type‐2 fuzzy pushdown automata) as computational models of CW. On the other hand, we also give a somewhat universally general type‐2 fuzzy model of computing with (some special) words and establish a retraction principle from computing with words to computing with values for handling crisp inputs in general type‐2 fuzzy setting and a generalized extension principle from computing with words to computing with all words for handling general type‐2 fuzzy inputs.     

二型模糊粗糙属性约简模型

属性约简是粗糙集理论的重要应用之一,其目的是在保持分类能力不变的前提下去掉冗余的属性,从而简化信息系统。由于经典粗糙集等价关系的要求过于严格,为了更好地解决实际问题,将粗糙集与二型模糊集结合,得到二型模糊粗糙集。利用论域和特征空间的积空间上的两个一型模糊集来构造论域的一个二型模糊划分,将模糊粗糙集属性约简的模型推广到二型模糊粗糙集框架中,得到了一个二型模糊粗糙属性约简的模型,并举例说明了用此模型进行属性约简的方法。     

时态外推推理诊断模型

本文通过引入时态一致覆盖集的概念,提出一个基于时态推理与覆盖技术的时态外推推理诊断模型TGSC.TGSC利用模糊集描述有关征兆、故障及相互间关系的时态知识,文中建立了TGSC的基本框架,给出了基于假设图搜索的诊断问题的求解方法,并给出计算示例。     

时态覆盖集诊断模型TGSC

本文通过引入时态一致覆盖集的概念，提出了一个基于时态推理与覆盖技术的时态覆盖集诊断模型ＴＧＳＣ。ＴＧＳＣ利用模糊描述有关征兆、故障及相互间关系的时态知识。文中建立了ＴＧＳＣ的基本框架。给出了基于假设图搜索的诊断问题求解方法，并伴以计算示例。     

基于等腰归一化距离的模糊粒度空间研究

本文将等腰归一化距离引入到模糊商空间中,提出了基于等腰归一化距离的模糊粒度空间理论.研究了它的结构和性质,并得到了四个重要结论.首先,下面3个叙述是等价的(定理3.2): (1) 给定X上的一个模糊等价关系;(2)给定X上的一个等腰归一化距离;(3)给定X上的一个分层递阶结构(或有序的粒度空间).其次,讨论了等腰归一化距离与Fuzzy等价关系间相互确定的对应关系,且都是一对多的关系(定理2.2,定理2.3).最后,给出了通过X上的模糊等价关系R诱导的等腰归一化距离d确定其引导的粒度上的度量dλ,且dλ正好是d在粒度X(λ)上压缩的等腰归一化距离(定理4.1), 同时给出了确定粒度空间上等腰归一化距离的方法.这些研究结论为模糊粒度计算的理论研究和应用提供了强有力的数字模型和工具, 同时表明模糊商空间的粒度计算可以在等腰归一化距离的范畴内进行,为模糊粒度计算提供了更为直观的几何解释.     

基于双空间模糊辨识关系的多标记特征选择

已有的基于模糊粗糙集的多标记特征选择算法多从单一的样本空间刻画属性区分能力,忽视属性对标记的区分能力.基于这一认识,文中同时从样本和标记两个空间出发,提出基于双空间模糊辨识关系的多标记特征选择算法.首先,基于模糊辨识关系分别从样本和标记角度定义两种多标记属性重要性度量,然后通过权重融合的方式融合两种度量,基于融合后的度量,运用前向贪心算法构建多标记特征选择算法.在5个数据集上的对比实验验证本文算法的有效性     

粒度计算中的商结构

基于商空间的粒度计算理论是目前三个主要的粒度计算理论之一.主要讨论商空间理论中的结构问题,并与粗糙集方法进行比较,指出结构在粒度计算理论中的重要性.讨论如何从结构着手来建立商空间模型.文中给出了从结构上取不同粒度来构造商空间的新方法,最后通过相关例子说明所提出的方法的合理性、可行性.     

粒度计算中的商结构

基于商空间的粒度计算理论是目前三个主要的粒度计算理论之一。主要讨论商空间理论中的结构问题,并与粗糙集方法进行比较,指出结构在粒度计算理论中的重要性。讨论如何从结构着手来建立商空间模型。文中给出了从结构上取不同粒度来构造商空间的新方法,最后通过相关例子说明所提出的方法的合理性、可行性。