The application of ontology information system based on rough formal concept analysis

Complex and noisy financial eco-system requires reliable models and proven techniques to predict the market movements and investor decisions. This study uses competent soft computing techniques: rough set theory (RST) and formal concept analysis (FCA) to study the investors' preferences, behavioural drivers and their actual behaviour in Gold-ETF (G-ETF) market. G-ETF, though a safe-haven and an alternate for reducing portfolio risks, inherits all complexities of financial markets. The employed RST helps in generating decision rules; and FCA to identify key factors affecting investment decision. This study is first of its kind, as integration of the foresaid techniques was not employed to study financial behaviour, earlier. The study has analysed 250 responses of G-ETF investors, in 12 listed G-ETFs, to conclude with a rich insight on the investment decisions discretised by different decision rules, strongly recommending the combined use of RST and FCA for data driven decisions.

The theory introduced, presented and developed in this paper, is concerned with Rough Concept Analysis. This theory is a synthesis of the theory of Rough Sets pioneered by Zdzislaw Pawlak [10] with the theory of Formal Concept Analysis pioneered by Rudolf Wille [11]. The central notion in this paper of a rough formal concept combines in a natural fashion the two notions of rough set and formal concept — to use a slogan: “rough set + formal concept = rough formal concept”. This paper is an extension of the paper [5] presented at the international workshop on Rough Sets and Knowledge Discovery (RSKD'93). A related paper [8] using distributed constraints provides a synthesis of the two important data modeling techniques: conceptual scaling of Formal Concept Analysis, and Entity-Relationship database modeling. A follow-up paper [9] will extend rough concept analysis from formal contexts to distributed constraints.

Convergence of information and communication on technology changed the life of a common man over the last few years. At the same time it increases threats to a common man. In order to overcome these situations lots of research is carried out in the direction network and internet security. In addition identification of various attacks is of great challenge before taking any security measures. Identification of phishing attacks such as fake e-mails or websites is one such critical attack in internetworking. It is an illegal trick game that collects personal information from a legitimate user. The fake e-mails or website looking like a true one and even in the web pages where users are asked to send their personal information may look like a legitimate. Identification of such websites, e-mails is one of great challenge today. To this end, in this paper, we propose a model for identification of phishing attacks and chief attributes that make an object phishing object using rough set and formal concept analysis. The concept is explained with an illustration and followed by a case study. The results obtained show the viability of the proposed research.

Local rough set: A solution to rough data analysis in big data

Rough set theory for the interval-valued fuzzy information systems

Formal concept analysis (FCA) is an important theory on the study of hierarchical structures caused by a binary relation between objects and attributes. And it is well known that a soft set always induces a binary relationship between objects and attributes for a formal context. Based on these facts, we study a new system called a soft context, which is induced using a soft set instead of a binary relation in the formal context, and investigate its theoretical foundations. First, we introduce the notions of soft context and soft concept for objects and study some basic properties. In particular, for the purpose of studying soft concepts, we introduce and study the notions of independent and dependent soft concepts. And we obtain the important things: (1) the set of all soft concepts can be decomposed into the set of independent soft concepts and the set of dependent soft concepts; (2) every dependent soft concept is generated by some independent soft concepts. Second, we obtain important properties about the relationship between formal context and soft contexts as the following: (1) each formal context always induces an associated soft context; (2) for a given formal context, there exists a bijection between the set of all formal concepts and the set of all soft concepts of the associated soft context induced by the given formal context. And we apply the above-mentioned properties to get the set of all formal concepts of a given formal context and explain that this method is more effective than the traditional way of computing all formal concepts in formal contexts using the example. Finally, we introduce the notion of soft concept lattice. Also, for a given formal context, we show that the formal concept lattice is order-isomorphic to the soft concept lattice of the associated soft context.

The definition of basic rough sets [3] depends upon either a single equivalence relation defined on a universe or several equivalence relations defined over the universe, taken one each taken at a time. In the view of granular computing, classical rough set theory is based upon single granulation. Extending this notion, a rough set model based on multi-granulations (MGRS) was introduced in [5]. In this approach, approximations of sets were defined through multiple equivalence relations on the universe and their properties were investigated. Using hybridization of fuzzy set [13] with rough set the concept of rough fuzzy set was introduced by Dubois and Prade [1]. Recently, a Rough Fuzzy Set Model was introduced and studied by Wu and Kou [12], which is based on Multiple Granulation. Topological properties of rough sets introduced by Pawlak in terms of their types were recently studied by Tripathy and Mitra [10]. These were extended to the context of incomplete multi granulation by Tripathy and Raghavan [11]. In this paper we introduce incomplete multigranulation on rough fuzzy sets, study their basic properties and extend the topological properties in [11] to this context. Our findings are true for both complete and incomplete fuzzy rough set models based upon multi granulation.KeywordsRough SetsFuzzy rough setsequivalence relationstolerance relationstype of rough setsmulti granular fuzzy rough sets

Formal contexts is a common framework for rough set theory and formal concept analysis, and some rough set models in formal contexts have been proposed. In this paper, based on the theory of abstract approximation spaces presented by Cattaneo [1], a Brouwer orthocomplementation on the set of objects of a formal context is presented, as a result, a pair of new lower and upper rough approximation operators is introduced. Comparison between the new approximation operators and the existing approximation operators is made, and two necessary and sufficient conditions about equivalence of the operators are obtained. Relationships and algebraic structures among the definable subsets of these approximation operators are investigated.

Formal concept analysis and rough set theory provide two different methods for data analysis and knowledge processing. Knowledge reduct in this paper combines the two models. For an initial data sets described by formal context, look for absolute necessary attribute sets by applying rough set theory. The sets can image the concepts and hiberarchy structure completely. Then calculate the value cores of attributes values for all objects and delete redundant attributes. At last, delete repeated instances and get the minimum formal context. Construct the concept lattice of the minimum formal context can diminish the size of concept lattice of the initial table at a certain extent.

Effective identification of interdependence information between decision variables is crucial for variable grouping in large-scale global optimization (LSGO). This paper introduces a novel approach called FCA-G (Formal Concept Analysis-Driven Grouping) to solve LSGO problems. FCA, an effective tool for data analysis, is employed in this approach. The primary contribution involves transforming decision variables into the formal context within FCA and utilizing the FCA methodology to solve LSGO problems based on a cooperative coevolution framework. Based on the formal context, a formal concept lattice is constructed, from which equivalent concepts are extracted. All variables within these concepts exhibit explicit interactions. This approach ensures a high degree of correlation among variables within subgroups and a low degree of correlation between subgroups, thereby enhancing cooperative coevolution. Experimental results indicate the significant potential of FCA-G in LSGO, as it outperforms state-of-the-art LSGO algorithms across the majority of LSGO test problems, including those with up to 1000 decision variables and a large-scale cloud task scheduling problem.

Rough computational methods for information systems

With the growing adoption of role-based access control (RBAC) in commercial security and identity management products, how to facilitate the process of migrating a non-RBAC system to an RBAC system has become a problem with significant business impact. Researchers have proposed to use data mining techniques to discover roles to complement the costly top-down approaches for RBAC system construction. A key problem that has not been adequately addressed by existing role mining approaches is how to discover roles with semantic meanings. In this paper, we study the problem in two settings with different information availability. When the only information is user-permission relation, we propose to discover roles whose semantic meaning is based on formal concept lattices. We argue that the theory of formal concept analysis provides a solid theoretical foundation for mining roles from userpermission relation. When user-attribute information is also available, we propose to create roles that can be explained by expressions of user-attributes. Since an expression of attributes describes a real-world concept, the corresponding role represents a real-world concept as well. Furthermore, the algorithms we proposed balance the semantic guarantee of roles with system complexity. Our experimental results demonstrate the effectiveness of our approaches.

With the growing adoption of Role-Based Access Control (RBAC) in commercial security and identity management products, how to facilitate the process of migrating a non-RBAC system to an RBAC system has become a problem with significant business impact. Researchers have proposed to use data mining techniques to discover roles to complement the costly top-down approaches for RBAC system construction. An important problem is how to construct RBAC systems with low complexity. In this article, we define the notion of weighted structural complexity measure and propose a role mining algorithm that mines RBAC systems with low structural complexity. Another key problem that has not been adequately addressed by existing role mining approaches is how to discover roles with semantic meanings. In this article, we study the problem in two primary settings with different information availability. When the only information is user-permission relation, we propose to discover roles whose semantic meaning is based on formal concept lattices. We argue that the theory of formal concept analysis provides a solid theoretical foundation for mining roles from a user-permission relation. When user-attribute information is also available, we propose to create roles that can be explained by expressions of user-attributes. Since an expression of attributes describes a real-world concept, the corresponding role represents a real-world concept as well. Furthermore, the algorithms we propose balance the semantic guarantee of roles with system complexity. Finally, we indicate how to create a hybrid approach combining top-down candidate roles. Our experimental results demonstrate the effectiveness of our approaches.

Rough set theory is an important tool to deal with imprecise, uncertainty and fuzzy information, and has gained great success in machine learning, data mining and intelligent data analysis. When it was proposed, many researchers worked on it in different views such as constructive methods, algebraic methods, formal concept analysis, and etc. We analyze it in view of entropy theory, and present a new concept - knowledge entropy. We discuss properties of it and apply it to discuss basic concepts in rough set theory. From the analysis, we construct a mapping between knowledge entropy theory and rough set theory, and we also hope to find effective algorithms by the application of it.

The paper examines Formal Concept Analysis (FCA) and Rough Set Theory (RST) against the background of the theory of finite approximations of continuous topological spaces. We define the operators of FCA and RST by means of the specialisation order on elements of a topological space X which induces a finite approximation of X. On this basis we prove that FCA and RST together provide a semantics for tense logic S4.t. Moreover, the paper demonstrates that a topological space X cannot be distinguished from its finite approximation by means of the basic temporal language. It means that from the perspective of topology S4.t is a better account of approximate reasoning then unimodal logics, which have been typically employed.