Averaging linguistic truth values in fuzzy approximate reasoning

The properties of a new rule for fuzzy conditional inference are presented and discussed. The rule is based on the extended mean operator defined on fuzzy numbers. The related propositions have the form “X is A is τ,” where τ is an element of the term set of the linguistic variable truth. The results obtained via the rule match with Fukami's and with the critical analysis carried out by Mizumoto and Zimmermann about the generalized modus ponens. © 1998 John Wiley & Sons, Inc.     

Which truth values in fuzzy logics are definable?

In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0, 1]. There are only denumerable many words and phrases and continuum many real numbers; thus, not every real number corresponds to some common sense degree of uncertainty. In this article, for several fuzzy logics, we describe which numbers are describing such degrees, i.e., in mathematical terms, which real numbers are definable in the corresponding fuzzy logic. © 2003 Wiley Periodicals, Inc.     

语言真值直觉模糊命题逻辑系统的推理规则

提出了一种基于语言真值直觉模糊代数的直觉模糊命题逻辑系统。基于语言真值格蕴涵代数生成语言真值直觉模糊代数,可同时处理具有可比性或不可比性信息。该方法可以同时处理不确定性问题的正面证据和反面证据。研究了语言真值直觉模糊命题逻辑系统LP(S)的性质,得到了其公理及推理规则,也获得了LP(S)中的证明与定理。实例说明,该方法在处理同时具有可比性和不可比性的直觉模糊决策问题中更灵活、更有效。     

Reasoning of fuzzy relational databases with fuzzy ontologies

A significant interest developed regarding the problem of describing databases with expressive knowledge representation techniques in recent years, so that database reasoning may be handled intelligently. Therefore, it is possible and meaningful to investigate how to reason on fuzzy relational databases (FRDBs) with fuzzy ontologies. In this paper, we first propose a formal approach and an automated tool for constructing fuzzy ontologies from FRDBs, and then we study how to reason on FRDBs with constructed fuzzy ontologies. First, we give their respective formal definitions of FRDBs and fuzzy Web Ontology Language (OWL) ontologies. On the basis of this, we propose a formal approach that can directly transform an FRDB (including its schema and data information) into a fuzzy OWL ontology (consisting of the fuzzy ontology structure and instance). Furthermore, following the proposed approach, we implement a prototype construction tool called FRDB2FOnto. Finally, based on the constructed fuzzy OWL ontologies, we investigate how to reason on FRDBs (e.g., consistency, satisfiability, subsumption, and redundancy) through the reasoning mechanism of fuzzy OWL ontologies, so that the reasoning of FRDBs may be done automatically by means of the existing fuzzy ontology reasoner.© 2012 Wiley Periodicals, Inc.     

Extended possibilistic truth values

A problem with the modeling of uncertainty within the context of an information or knowledge‐based system is the handling of missing information. In this article, extended possibilistic truth values are introduced as a formal means to cope with this problem. The notion of an extended possibilistic truth value has been obtained from the assumption that the truth value of a proposition can be undefined. This is the case if the proposition cannot be evaluated due to the non‐applicability of (some of) its elements. By definition, an extended truth value can either be true, false, or undefined. Using these three values, a ternary strong Kleene propositional logic has been built. An uncertainty model for this logic is proposed, in order to model (linguistic) uncertainty concerning the extended truth value of a proposition. This uncertainty model is based on possibility measures, and leads to the concept of an extended possibilistic truth value. Finally, the algebraic properties of extended possibilistic truth values are presented. © 2002 Wiley Periodicals, Inc.     

Reasoning with propositional knowledge based on fuzzy neural logic

In this article, a new kind of reasoning for propositional knowledge, which is based on the fuzzy neural logic initialed by Teh, is introduced. A fundamental theorem is presented showing that any fuzzy neural logic network can be represented by operations: bounded sum, complement, and scalar product. Propositional calculus of fuzzy neural logic is also investigated. Linear programming problems risen from the propositional calculus of fuzzy neural logic show a great advantage in applying fuzzy neural logic to answer imprecise questions in knowledge-based systems. An example is reconsidered here to illustrate the theory. © 1996 John Wiley & Sons, Inc.     

A class of hierarchical fuzzy systems with constraints on the fuzzy rules

This paper presents a class of hierarchical fuzzy systems where previous layer outputs are used not in IF-parts, but only in THEN-parts of the fuzzy rules of the current layer. The proposed scheme is shown to be a universal approximator to any real continuous function on a compact set if complete fuzzy sets are used in the IF-parts of the fuzzy rules with singleton fuzzifier and center average defuzzifier. From the example of ball-and-beam control system simulation, it is demonstrated that the proposed scheme approximates with high accuracy a model nonlinear controller with fewer fuzzy rules than a centralized fuzzy system, and its control performance is comparable to that of a nonlinear controller.     

Generating weighted fuzzy rules from relational database systems for estimating values using genetic algorithms

In recent years, some methods have been proposed to estimate values in relational database systems. However, the estimated accuracy of the existing methods are not good enough. In this paper, we present a new method to generate weighted fuzzy rules from relational database systems for estimating values using genetic algorithms (GAs), where the attributes appearing in the antecedent part of generated fuzzy rules have different weights. After a predefined number of evolutions of the GA, the best chromosome contains the optimal weights of the attributes, and they can be translated into a set of rules to be used for estimating values. The proposed method can get a higher average estimated accuracy rate than the methods we presented in two previous papers.     

Content reference: Reasoning about rules

In a companion paper [1] we described the concept of saturation, the situation in a program in which so many knowledge sources (KSs) are potentially useful at each invocation cycle that it is unrealistic to consider unguided, exhaustive invocation. We argued that saturation appears almost inevitable in large AI programs.We suggested that the process of invocation can be viewed as occurring in three steps: retrieval (selecting some subset of KSs from the knowledge base), refinement (pruning or reordering that subset), and execution (executing one or more of the KSs). We then argued that one useful approach to dealing with saturation is by embedding intelligence in the refinement phase, and described meta-rules, a means of encoding knowledge used to effect refinement.In this paper we consider a more detailed, ‘engineering’ issue, but one with a number of interesting implications: While there are many ways to implement refinement, we suggest that one particular technique—which we call content reference—offers a number of advantages, including giving the system some ability to reason about the content of its knowledge.     

直觉模糊粗糙推理的规则互作用性研究

针对直觉模糊粗糙逻辑(IFRL)推理的规则库检验问题,提出了IFRL规则库的互作用性检验方法.互作用性检验是逻辑规则库检验的一项重要内容,它可以有效地分析出规则间的关系.利用直觉模糊粗糙集(IFRS)及其包含关系的概念,提出了正规IFRS和IFRL规则库的互作用性定义.在此基础上,将直觉模糊逻辑(IFL)的3个定理推广到IFRL领域,并给予了证明.提出的互作用性定义和推广后的3个定理可以作为检验规则间互作用性的方法.     

A new approach to generate weighted fuzzy rules using genetic algorithms for estimating null values

In this paper, we present a new method to generate weighted fuzzy rules using genetic algorithms for estimating null values in relational database systems, where there are negative functional dependency relationships between attributes. The proposed method can get higher average estimated accuracy rates than the method presented in [Chen, S. M., & Huang, C. M. (2003). Generating weighted fuzzy rules from relational database systems for estimating null values using genetic algorithms. IEEE Transactions on Fuzzy Systems, 11(4), 495–506].     

Automatic refinement of knowledge bases with fuzzy rules

The knowledge-acquisition bottleneck obstructs the development of expert systems. Refinement of existing knowledge bases is a subproblem of the knowledge-acquisition problem. The paper presents a HEuristic REfinement System (HERES), which refines rules with mixed fuzzy and nonfuzzy concepts represented in a variant of the rule representation language Z-II automatically. HERES employs heuristics and analytical methods to guide its generation of plausible refinements. The functionality and effectiveness of HERES are verified through various case studies. It has been verified that HERES can successfully refine knowledge bases. The refinement methods can handle imprecise and uncertain examples and generate approximate rules. In this aspect, they are better than other famous learning algorithms such as ID3^15–18, AQ11, and INDUCE^{14, 19, 20} because HERES' methods are currently unique in processing inexact examples and creating approximate rules.     

Updating generalized association rules with evolving fuzzy taxonomies

Mining generalized association rules with fuzzy taxonomic structures has been recognized as an important extension of generalized associations mining problem. To date most work on this problem, however, required the taxonomies to be static, ignoring the fact that the taxonomies of items cannot necessarily be kept unchanged. For instance, some items may be reclassified from one hierarchy tree to another for more suitable classification, abandoned from the taxonomies if they will no longer be produced, or added into the taxonomies as new items. Additionally, the membership degrees expressing the fuzzy classification may also need to be adjusted. Under these circumstances, effectively updating the discovered generalized association rules is a crucial task. In this paper, we examine this problem and propose two novel algorithms, called FDiff_ET and FDiff_ET*, to update the discovered generalized frequent itemsets. Empirical evaluations show that our algorithms can maintain their performance even in high degree of taxonomy evolution, and are significantly faster than applying the contemporary fuzzy generalized association mining algorithm FGAR to the database with evolving taxonomy.     

Learning fuzzy rules from fuzzy samples based on rough set technique

Although the traditional rough set theory has been a powerful mathematical tool for modeling incompleteness and vagueness, its performance in dealing with initial fuzzy data is usually poor. This paper makes an attempt to improve its performance by extending the traditional rough set approach to the fuzzy environment. The extension is twofold. One is knowledge representation and the other is knowledge reduction. First, we provide new definitions of fuzzy lower and upper approximations by considering the similarity between the two objects. Second, we extend a number of underlying concepts of knowledge reduction (such as the reduct and core) to the fuzzy environment and use these extensions to propose a heuristic algorithm to learn fuzzy rules from initial fuzzy data. Finally, we provide some numerical experiments to demonstrate the feasibility of the proposed algorithm. One of the main contributions of this paper is that the fundamental relationship between the reducts and core of rough sets is still pertinent after the proposed extension.     

Functional dependencies with null values, fuzzy values, and crispvalues

Based on the concepts of the semantic proximity, we present a definition of the fuzzy functional dependency, We show that the inference rules for fuzzy functional dependencies, which are the same as Armstrong's axioms for the crisp case, are correct and complete. We also show that dependent constraints with dull values constitute a lattice. Functional dependencies in classical relational databases and null functional dependencies can be viewed as a special case of fuzzy functional dependencies. By applying the unified functional dependencies to the relational database design, we can represent the data with fuzzy values, null values and crisp values under relational database management systems, By using fuzzy functional dependencies, we can compress the range of a fuzzy value and make this fuzzy value “clearer”     

Regular grammars with truth values in lattice-ordered monoid and their languages

In this study, we introduce the concept of lattice-valued regular grammars. Such grammars have become a necessary tool for the analysis of fuzzy finite automata. The relationship between lattice-valued finite automata (LA) and lattice-valued regular grammars (LRG) are discussed and we get the following results, for a given LRG, there exists an LA such that they accept the same languages, and vice versa. We also show the equivalence between deterministic lattice-valued regular grammars and deterministic lattice-valued finite automata.     

基于模糊聚类的模糊关联规则在流程企业中的应用

采用数据挖掘中的模糊聚类分析了流程企业中历史数据的区间值,然后用模糊关联规则挖掘出有用的规则。首先阐述了模糊聚类的RFCM算法和关联规则的Apriori算法的内容,分析了实现模糊关联规则的Fuzzy_ClustApriori算法流程,并用RFCM算法对实际数据进行分析,得到不同类别的模糊数。根据Fuzzy_ClustApriori算法的步骤对模糊化的参数点进行处理,得到了有价值的模糊规则,为流程企业的生产优化提供了理论依据。