Linguistic modelling based on semantic similarity relation among linguistic labels

Hierarchical quotient space structure (HQSS), as a typical description of granular computing (GrC), focuses on hierarchically granulating fuzzy data and mining hidden knowledge. The key step of constructing HQSS is to transform the fuzzy similarity relation into fuzzy equivalence relation. However, on one hand, the transformation process has high time complexity. On the other hand, it is difficult to mine knowledge directly from fuzzy similarity relation due to its information redundancy, i.e., sparsity of effective information. Therefore, this article mainly focuses on proposing an efficient granulation approach for constructing HQSS by quickly extracting the effective value of fuzzy similarity relation. First, the effective value and effective position of fuzzy similarity relation are defined according to whether they could be retained in fuzzy equivalence relation. Second, the number and composition of effective values are presented to confirm that which elements are effective values. Based on these above theories, redundant information and sparse effective information in fuzzy similarity relation could be completely distinguished. Next, both isomorphism and similarity between two fuzzy similarity relations are researched based on the effective value. The isomorphism between two fuzzy equivalence relations is discussed based on the effective value. Then, the algorithm with low time complexity for extracting effective values of fuzzy similarity relation is introduced. On the basis, the algorithm for constructing HQSS is presented to realize efficient granulation of fuzzy data. The proposed algorithms could accurately extract effective information from the fuzzy similarity relation and construct the same HQSS with the fuzzy equivalence relation while greatly reducing the time complexity. Finally, relevant experiments on 15 UCI datasets, 3 UKB datasets, and 5 image datasets are shown and analyzed to verify the effectiveness and efficiency of the proposed algorithm.

Recently, many methods based on fuzzy rough sets are proposed to reduce fuzzy attributes. The common characteristic of these methods is that all of them are based on fuzzy equivalence relation. In other words, the underlying concept of rough sets, indispensability relation, is generalized to fuzzy equivalence relation. Here fuzzy equivalence relation is the binary relation, which is reflexive, symmetric and transitive. This paper tries to generalize the fuzzy equivalence relation to fuzzy similarity relation, which is more helpful to keeping the fuzzy information of initial data than fuzzy equivalence relation. Based on the fuzzy similarity relation, fuzzy matrix computation for information system is proposed which can be used to reduce fuzzy attributes. Firstly, fuzzy similarity relation who is isomorphic with the fuzzy similarity matrix is given as fuzzy indispensability relation. Then all the information of initial data, such as the similarity among objects and fuzzy inconsistence degree between two objects, can be represented by fuzzy similarity matrix. Secondly, by considering that the small perturbation of the fuzzy similarity matrix can be ignorable, we propose some basic concepts of knowledge reduction such as fuzzy attributes reduct, core and fuzzy significance of attributes etc in this paper. Thirdly, a heuristic algorithm based on the fuzzy significance of attributes is proposed to find close-to-minimal fuzzy attributes reduct. Finally, experimental comparisons with other methods of attributes reduction are given. The experimental results show that our method is feasible and effective

Extending the fuzzy database with fuzzy numbers

Fuzzy similarity relations form the basis for many developments and applications of fuzzy systems. Measures of fuzzy similarity have been proposed in the literature for comparing objects. In this paper, aggregated fuzzy relations are generated between academic journals to compare their performance with respect to different journal impact indicators. In particular, various indicators may be employed to construct several distinctive fuzzy similarity relations, which may be subsequently combined via the use of the Ordered Weighted Average (OWA) operator. This proposed aggregated measure preserves reflexivity and symmetry, with T-transitivity conditionally preserved if appropriate weighting vectors are selected. Different similarity measures and weighting vectors are compared for the task of journal clustering, in an effort to estimate the ranking of academic journals. The results of experimental evaluation demonstrate that by using OWA-aggregated relations, simple techniques such as C-means can perform well in terms of standard accuracy and within-1 accuracy. The proposed method also exhibits the advantages of being more intuitive and interpretable.

Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets

Fuzzy relations and fuzzy relational databases

In this paper we present a proposal of a flexible query answering system based on fuzzy logic. We introduce a fuzzy logic programming with a threshold cut and with connectives being arbitrary conjunctors, disjunctors (i.e. they do not need to be associative) and implicators. We use three types of unification: first of syntactical strings based on a similarity relation; second based on linguistic variables; third based on fuzzy conceptual lattices. Our systems assumes a fuzzy logic programming interpreter runs at the remote site. We propose a query dialogue where user can specify thresholds, number of truth values, finite (linear) approximations of fuzzy sets and connectives which are subject of tuning and learning, fuzzy conceptual lattice, fuzzy similarity relations and the form of answer required. This is intended to lower communication (retrieval) complexity. We present a computational (procedural) semantics which is sound and complete wrt. to declarative semantic.

This paper deals with the problem of handling semantic heterogeneity during schema integration. Semantics refer to the meaning of data in contrast to syntax, which solely defines the structure of schema elements. We focus on the part of semantics related to the meanings of terms used to name schema elements. Our approach does not rely on the names of the schema elements or the structure of the schema. Instead, we present an approach based on formal ontologies presented in a logical language for integrating schemas to generate a global schema. Semantic similarity relations between definitions in formal ontologies are defined and used for merging ontologies. We show how similarity relations are discovered by a reasoning system using a higher-level ontology. The result of the merging process is used for schema integration. Schema integration is used to obtain the global schema of a tightly-coupled federated database system. Afterwards, we illustrate how the produced global schema can help for the mapping of data elements.KeywordsSchema IntegrationGlobal SchemaLocal SchemaReasoning SystemSchema ElementThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this paper we argue that fuzzy sets and rough sets aim to different purposes and that it is more natural to try to combine the two models of uncertainty (vagueness for fuzzy sets and coarseness for rough sets) in order to get a more accurate account of imperfect information. First, the upper and lower approximations of a fuzzy set are defined, when the universe of discourse of a fuzzy sets is coarsened by means of an equivalence relation. We then come close to Caianiello’s C-calculus. Shafer’s concept of coarsened belief functions also belongs to the same line of thought and is reviewed here. Another idea is to turn the equivalence relation relation into a fuzzy similarity relation, for a more expressive modeling of coarseness. New results on the representation of similarity relations by means of a fuzzy partition of fuzzy clusters of more or less indiscernible points are surveyed. The properties of upper and lower approximations of fuzzy sets by similarity relations are thoroughly studied. Lastly the potential usefulness of the fuzzy rough set notions for logical inference in the presence of both fuzzy predicates and graded indiscernibility is indicated. Especially fuzzy rough sets may provide a nice semantic background for modal logic involving fuzzy modalities and/or fuzzy sentences.

Attribute reduction based on neighborhood constrained fuzzy rough sets

In this chapter, first we construct some topologies on the AFS structures, discuss the topological molecular lattice structures on EI, * EI, EII, * EII algebras, and elaborate on the main relations between these topological structures. Second, we apply the topology derived by a family of fuzzy concepts in EM, where M is a set of simple concepts, to analyze the relations among the fuzzy concepts. Thirdly, we propose the differential degrees and fuzzy similarity relations based on the topological molecular lattices generated by the fuzzy concepts on some features. Furthermore, the fuzzy clustering problems are explored using the proposed differential degrees and fuzzy similarity relations. Compared with other fuzzy clustering algorithms such as the Fuzzy C-Means and k-nearest-neighbor fuzzy clustering algorithms, the proposed fuzzy clustering algorithm can be applied to data sets with mixed feature variables such as numeric, Boolean, linguistic rating scale, sub-preference relations, and even descriptors associated with human intuition. Finally, some illustrative examples show that the proposed differential degrees are very effective in pattern recognition problems whose data sets do not form a subset of a metric space such as the Eculidean one. This approach offers a promising avenue that could be helpful in understanding mechanisms of human recognition.

In fuzzy clustering, we always use fuzzy equivalence matrix to find the clustering results. Although fuzzy equivalence matrix is one of the most important tools in fuzzy clustering, it’s hard to judge whether a fuzzy matrix is a fuzzy equivalence matrix directly. In this paper, some simple and useful properties of the fuzzy equivalence matrices have been proposed based on the basic properties proposed in the classi cal articles. Using these properties, the judgment whether a fuzzy matrix is a fuzzy equivalence matrix may become an easy work. Keywords: Fuzzy clustering, fuzzy equivalence matrix 1. INTRODUCTION Given a finite set of objects X, and a measure of similarity for an arbitrary pair of objects, the problem of clustering is to find a partition of X such that the degree of similarity is high for objects within each block (cluster) and low for objects in different blocks. The purpose of clustering is to find a natural classification of given objects on the basis of a conceived concept of similarity. The classification may help to uncover a structure in given data, improve our understanding of a complex system, or suggest a meaningful simplification of a given system [1]. The requirement that given objects be classified into pairwise disjoint subsets (crisp clusters) is overly strong in many practical applications. Fuzzy set theory allows us to weaken it and, hence, make clustering more realistic. So, fuzzy clustering becomes one of the hottest research branches of data mining. One of the approaches to fuzzy clustering is based on fuzzy equivalence relations defined on X. Every fuzzy equivalence relation induces a crisp partition in each of its .-cuts. Using this approach, the fuzzy clustering problem becomes the problem of identifying a fuzzy equivalence relation on X in terms of a conceived concept of similarity. Although this may not be possible to do directly, it is usually easy to determine a fuzzy compatibility relation in terms of an appropriate distance function defined on X. A distance function is always reflexive and symmetric, but it is not transitive. However, once we have a compatibility relation, we can readily obtain a meaningful fuzzy equivalence relation by calculating its transitive closure. The resulting fuzzy equivalence relation offers the user a sequence of crisp partitions on X, which are linearly ordered by refinement ordering and graded by values of . [0, 1]. The user is given a flexibility to choose one of these partitions on the basis of additional criteria [2-4]. But, to calculate the transitive closure of a N×N fuzzy matrix , we need to calculate the 2kth power of the matrix, where k = 1, 2, , N. In the processing, after we calculate the 2k+1th power of the matrix and find that the 2k+1th power of the matrix is equal to the 2kth power of the matrix, the 2kth power of the matrix is the transitive closure of the matrix. In fact, if we can find the 2kth power of the matrix is a fuzzy equivalence matrix directly, we do not need to calculate the 2k+1th power of the matrix. If we can judge a fuzzy matrix is a fuzzy equivalence matrix by means of some simple properties of the equivalence matrix, it may be helpful. In this paper, some properties of the fuzzy equivalence matrix have been proposed and the judgment whether a fuzzy *white70121@163.com

Geometrical interpretation and applications of membership functions with fuzzy rough sets

Linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems, and fuzzy logic represents one of the most effective algorithms to build such linguistic models. In this paper, a linguistic (qualitative) modeling approach is proposed. The approach combines the merits of the fuzzy logic theory, neural networks, and genetic algorithms (GA's). The proposed model is presented in a fuzzy-neural network (FNN) form which can handle both quantitative (numerical) and qualitative (linguistic) knowledge. The learning algorithm of an FNN is composed of three phases. The first phase is used to find the initial membership functions of the fuzzy model. In the second phase, a new algorithm is developed and used to extract the linguistic-fuzzy rules. In the third phase, a multiresolutional dynamic genetic algorithm (MRD-GA) is proposed and used for optimized tuning of membership functions of the proposed model. Two well-known benchmarks are used to evaluate the performance of the proposed modeling approach, and compare it with other modeling approaches.

This paper proposes a cooperative query answering approach that relaxes query conditions to provide approximate answers by utilizing similarity relationships between data values. The proposed fuzzy abstraction hierarchy (FAH) represents a similarity relationship based on the integrated notion of data abstraction and fuzzy relations. Based on FAH, the authors develop query relaxation operators like query generalization, approximation, and specialization of a value. Compared with existing approaches, FAH supports more effective information retrieval by processing various kinds of cooperative queries through elaborate relaxation control and providing ranked query results according to fitness scores. Moreover, FAH reduces maintenance cost by decreasing the number of similarity relationships to be managed.