Measuring Concept Similarity between Fuzzy Ontologies

Fuzzy ontology is based on the concept that each index object is related to every other object in the ontology, with a degree of membership assigned to that relationship based on fuzzy set theory. This paper proposes use cases based on the related process of the terrorism event extraction using fuzzy ontology, especially the terrorism fuzzy ontology construction methodology. The related use cases are represented using the Web Ontology Language (OWL) which is designed to support the representation ontology relation. Additionally, to make the proposed use cases more relevant to implementing the system, the paper presents linguistic variables which serve as a mean of approximate characterization of fuzzy phenomena concepts and also the appropriate characterization of the terrorism fuzzy relations in their properties.

This paper proposes a novel extension of blockchain systems with fuzzy ontologies. The main advantage is to let the users have flexible restrictions, represented using fuzzy sets, and to develop smart contracts where there is a partial agreement among the involved parts. We propose a general architecture based on four fuzzy ontologies and a process to develop and run the smart contracts, based on a reduction to a well-known fuzzy ontology reasoning task (Best Satisfiability Degree). We also investigate different operators to compute Pareto-optimal solutions and implement our approach in the Ethereum blockchain.

Ontologies represent a method of formally expressing a shared understanding of information, and have paved the way for sharing concepts across applications in an unambiguous way. However, these ontologies are assumed to be hand-crafted, pre-defined structures with crisp concept descriptions and inter-concept relations. Crisp definitions however are not sufficient for real-world applications like ontology-based information extraction from unstructured text. In this paper we propose an enhancement of the ontology structure to a fuzzy ontology, which provides a mechanism to store imprecise concept definitions. The proposed fuzzy ontology framework can also help in ascertaining similarities and dissimilarities of concept definitions across distributed ontologies representing the same domain. Our design of fuzzy ontology is motivated by fuzzy set theoretic representation and reasoning, and is entirely different from other fuzzy ontology designs, which use only co-occurrence of concepts to determine their closeness. We have cited examples from various domains to show the necessity and capability of the structure in representing real-world knowledge.

Fuzzy concepts are represented by fuzzy sets, so a fuzzy knowledge is defined to be a collection of fuzzy sets (concepts) which includes two constants, 1 (true) and 0 (false). Abstractly, a logical derivation is a finite series of logical operations acting on a given knowledge. In fuzzy world, logical operations are defined by mathematical operations. So fuzzy logical derivations are mathematical derivations, and vice versa In this paper, the closure of fuzzy reasoning is characterized by fuzzy rough sets, and by topologies (neighborhood systems). A new fuzzy concept F N is derivable from the old knowledge K iff the membership function of F N is continuous in K-topology, or equivalently, iff F N is a rough fuzzy set (concept) of I N D(K),or plainly, iff the membership function of F N is a “step” function in the sense that it takes a constant value in each equivalence class of I N D(K).A fuzzy set L partitions the universe into equivalence classes; each equivalence class consists of those elements which have the same degree of membership. The indiscernibility relation I N D(K)over K is the “intersection” of all the equivalence relations induced by the fuzzy sets in K. The membership function of a fuzzy set is a real valued function, so U can be given the minimal topology such that the membership function of each fuzzy set in K is a continuous function. Such topology is called K-topology.

Ontology is adopted as a standard for knowledge representation on the Semantic Web, and Resource Description Framework (RDF) is used to add structure and meaning to Web applications. In order to incorporate fuzzy systems into the Semantic Web, this paper utilizes fuzzy ontology to represent formally the fuzzy linguistic variables, considering the semantic relationships between fuzzy concepts. Then fuzzy rule is described as a RDF resource with properties: “IF” and “THEN”, and rule's antecedent and consequent is represented in RDF statement. Taking the fuzzy control system of industrial washing machine for example, the fuzzy system with ontology and RDF is built, which shows that this research enables distributed fuzzy applications on the Semantic Web.

Ontology is the basis of sharing and reusing knowledge on the Semantic Web, and ontology-based semantic retrieval is a hotspot of current research. Fuzzy ontology is an extension of domain ontology for solving the uncertainty problems. To represent fuzzy knowledge more effectively, this paper presents a new series of fuzzy ontology models that consists of fuzzy domain ontology and fuzzy linguistic variable ontologies, considering semantic relationships of concepts, including set relation, order relation, equivalence relation and semantic association relation etc. The process to construct linguistic variables ontology is discussed. Using ontology and RDFS, the knowledge model for product information is created. To achieve semantic retrieval, the semantic query expansion in SeRQL is constructed by semantic relations between fuzzy concepts. The application shows that these models can overcome the localization of other fuzzy ontology models, and this research facilitates the fuzzy knowledge sharing and semantic retrieval on the Semantic Web.

Fuzzy Description Logics generalize crisp ones by providing membership degree semantics for concepts and roles by fuzzy sets. Recently, answering of conjunctive queries has been investigated and implemented in optimized reasoner systems based on the rewriting approach for crisp DLs. In this paper we investigate how to employ such existing implementations for crisp query answering in \(DL\text {-}Lite_{R}\) over fuzzy ontologies. To this end we give an extended rewriting algorithm for the case of fuzzy \(DL\text {-}Lite_{R}\)-ABoxes that employs the one for crisp \(DL\text {-}Lite_{R}\) and investigate the limitations of this approach. We also tested the performance of our proto-type implementation FLite of this method.

Building and managing fuzzy ontologies with heterogeneous linguistic information

Data integration becomes even more necessary given the increasing availability of data from distributed and heterogeneous sources. To address such heterogeneity, crisp ontologies have been employed in order to represent the semantics of integrated data. However, it is interesting to use fuzzy logic concepts in these ontologies, for a more expressive representation of vague information relevant to some domains. In this context, this paper presents DISFOQuE system for data integration based on fuzzy ontology, which provides a homogeneous view of data sources and also performs query expansions in order to retrieve more comprehensive answers to the user. We have executed a real experiment in the domain of watershed analysis, which provided a homogeneous view of the watershed data sources and more effective answers to researchers.

The fuzzy set concept is often used in solution of problems in which the initial data is difficult or impossible to represent in the form of specific numbers or sets. Geo-information objects are distinguished by their uncertainty, their characteristics are often vague and have some error. Therefore, in the study of such objects is introduced the concept of "fuzziness" — fuzzy sets, fuzzy logic, linguistic variables, etc. The fuzzy set concept is given in the form of membership function. An ordinary set is a special case of a fuzzy one. If we consider a fuzzy object on the map, for example, a lake that changes its shape depending on the time of year, we can build up for it a characteristic function from two variables (the object’s points coordinates) and put a certain number in accordance with each point of the object. That is, we can describe a fuzzy set using its two-dimensional graphical image. Thus, we obtain an approximate view of a surface z = μ(x, y) in three-dimensional space. Let us now draw planes parallel to the plane. We’ll obtain intersections of our surface with these planes at 0 ≤ z ≤ 1. Let's call them as isolines. By projecting these isolines on the OXY plane, we’ll obtain an image of our fuzzy set with an indication of intermediate values μ(x, y) linked to the set’s points coordinates. So we’ll construct generalized Euler — Venn diagrams which are a generalization of well-known Euler — Venn diagrams for ordinary sets. Let's consider representations of operations on fuzzy sets A a n d B. Th e y u s u a l l y t a k e : μA B = min (μA,μB ), μA B = max (μA,μB ), μA = 1 − μA. Algebraic operations on fuzzy sets are defined as follows: μ A B x μ A x μ B x ( ) = ( ) + ( ) − −μ A (x)μ B (x), μ A B x μ A x μ B x ( ) = ( ) ( ), μ A (x) = 1 − μ A (x). Let's construct for a particular problem a generalized Euler — Venn diagram corresponding to it, and solve subtasks graphically, using operations on fuzzy sets, operations of intersection and integrating of the diagram’s bars.

Approximation of fuzzy concepts in decision making

This paper presents a common framework for the conceptual information of MPEG-7, interoperable with the semantic Web, and providing high performance search capabilities, using fuzzy set theory and ontology relations. Starting from the meta-data model of the MPEG-7, to which we add few layers while keeping the existent, so as to guarantee compatibility with the standard, we then link MPEG-7 descriptions to ontologies. These ontologies are used to define precisely each element used in the description scheme of MPEG-7. In order to allow similarities estimations and performing searches, the model is projected into a 5-dimensional space that permits to describe easily the content of multimedia documents.

Granular structure plays a very important role in the model construction, theoretical analysis and algorithm design of a granular computing method. The granular structures of classical rough sets and fuzzy rough sets have been proven to be clear. In classical rough set theory, equivalence classes are basic granules, and the lower and upper approximations of a set can be computed by those basic granules. In the theory of fuzzy rough set, granular fuzzy sets can be used to describe the lower and upper approximations of a fuzzy set. This paper discusses the granular structure of type-2 fuzzy rough sets over two universes. Definitions of type-2 fuzzy rough sets over two universes are given based on a wavy-slice representation of type-2 fuzzy sets. Two granular type-2 fuzzy sets are deduced and then proven to be basic granules of type-2 fuzzy rough sets over two universes. Then, the properties of lower and upper approximation operators and these two granular type-2 fuzzy sets are investigated. At last, several examples are given to show the applications of type-2 fuzzy rough sets over two universes.

With the increase of data, data mining has been introducing to solve the overloading problem and to discover valid, novel, potentially useful patterns in existing data. However, to discover quantitative data, we face a sharp boundary problem that the traditional data mining techniques can not overcome. To pinpoint this problem, a lot of researches have been applied fuzzy sets to discover patterns, especially in sequential patterns . As we know, U. Fayyad et al proposed a unifying process-centric framework for Knowledge Discovery in Database (KDD) which can explain the process from top to toe for the traditional data mining problems. Unfortunately, it fails to be workable in part to describe the process for discovering sequential patterns based on fuzzy concept. Therefore, to have more general viewpoint for discovering of that sort patterns, we devote to proposing a general framework modified from the KDD process. An application is proposed to demonstrate that the framework can be a generalization of the realm problem.

Nowadays, video surveillance systems are part of our daily life, because of their role in ensuring the security of goods and people this generates a huge amount of video data. Thus, several research works based on the ontology paradigm have tried to develop an efficient system to index and search precisely a very large volume of videos. Due to their semantic expressiveness, ontologies are undoubtedly very much in demand in recent years in the field of video surveillance to overcome the problem of the semantic gap between the interpretation of the data extracted from the low level and the high-level semantics of the video. Despite its good expressiveness of semantics, a classical ontology may not be sufficient for good handling of uncertainty, which is however commonly present in the video surveillance domain, hence the need to consider a new ontological approach that will better represent uncertainty. Fuzzy logic is recognized as a powerful tool for dealing with vague, incomplete, imperfect, or uncertain data or information. In this work, we develop a new ontological approach based on fuzzy logic. All the relevant fuzzy concepts such as Video_Objects, Video_Events, Video_Sequences, that could appear in a video surveillance domain are well represented with their fuzzy Ontology DataProperty and the fuzzy relations between them (Ontology ObjectProperty). To achieve this goal, the new fuzzy video surveillance ontology is implemented using the fuzzy ontology web language 2 (fuzzy owl2) which is an extension of the standard semantic web language, ontology web language 2 (owl2).