Fuzzy Functional Dependencies Research Articles

Financial literacy and psychological disaster preparedness: applicability of approach based on fuzzy functional dependencies

Recent catastrophes and crises emphasize the necessity of an individual's and household's preparedness for coping with these events. Previous research focuses mainly on short-term preparation and immediate response to catastrophes. The ex ante approach to managing long-term effects can rarely be found in literature, especially with an emphasis on financial preparedness. In this work, we use a soft computing method for analysing the social/psychological effects and implications. Specifically, we focus on data mining and linguistic interpretation of the effects of financial literacy on psychological preparedness for disasters, using fuzzy functional dependencies (FFDs). FFDs determine influences between features in datasets and examine neighbouring categorical answers with a certain degree of similarity, which overcomes indecisiveness when marking a categorical answer. Based on the surveyed data, we show that FFDs offer an approach for discovering additional patterns and explaining those patterns linguistically. Our results are as follows: financial literacy significantly influences anxiety, lack of control, nervousness, and fear of death (in order of intensity). Using this approach, we conclude that being better financially prepared can help in long-term disaster risk management. Financial preparedness is also helpful in mitigating psychological risks related to disasters. This paper provides results that can support the designing knowledge management solutions in order to improve psychological disaster preparedness.

Willmott Fuzzy Implication in Fuzzy Databases

The object of the research are fuzzy functional dependencies on given relation scheme, and the question of their obtaining using the classical and innovated techniques. The attributes of the universal set are associated to the elements of the unit interval, and are turned into fuzzy formulas in this way. We prove that the dependency (which is treated as a fuzzy formula with respect to appropriately chosen valuation) is valid whenever it agrees with the attached two-elements fuzzy relation instance. The opposite direction of the claim is proven to be incorrect in this setting. Generalizing things to sets of attributes, we prove that particular fuzzy functional dependency follows form a set of fuzzy dependencies (in both, the world of two-element and the world of arbitrary fuzzy relation instances) if and only if the dependency is valid with respect to valuation anytime the set of fuzzy formulas agrees with the valuation. The results derived in paper show that the classical techniques in the procedure for generating new fuzzy dependencies may be replaced by the resolution ones, and hence automated. The research is conducted with respect to Willmott fuzzy implication operator

Fuzzy Functional and Multivalued Dependencies for Frank’s Class of Additive Generators

In this paper we consider all possible dependencies that can be built upon similarity-based fuzzy relations, that is, fuzzy functional and fuzzy multivalued dependencies. Motivated by the fact that the classical obtaining of new dependencies via inference rules may be tedious and uncertain, we replace it by the automated one, where the key role is played by the resolution principle techniques and the fuzzy formulas in place of fuzzy dependencies. We prove that some fuzzy multivalued dependency is actively correct with respect to given fuzzy relation instance if and only if the corresponding fuzzy formula is in line with the attached interpretation. Additionally, we require the tuples of the instance to be conformant (up to some extent) on the leading set of attributes. The equivalence as well as the conclusion are generalized to sets of attributes. The research is conducted by representing the attributes and fuzzy dependencies in the form of fuzzy formulas, and the application of fuzzy implication operators derived from carefully selected Frank’s classes of additive generators

On Some Applications of h-generated Fuzzy Implications

In this paper we apply the h-generated fuzzy implications to prove a number of results which are of fundamental importance to the theory of fuzzy and vague functional and multivalued dependencies defined on given scheme. Our research is motivated by the fact that some analogous results already hold true for the families of f- and g-generated fuzzy implications, and the fact that these three collections of implications share many similar mutual properties. While some of the aforementioned implications are introduced in order to be applied in approximate reasoning, the results derived in this paper represent the main tool in the process of automation and are also used to complement the resolution principle. More precisely, the main result of this research states that the fact that some fuzzy (vague) relation instance r, |r| = 2, satisfies some fuzzy (vague) functional or fuzzy (vague) multivalued dependency c /∈ C (under assumption that r satisfies some set C of fuzzy (vague) functional and fuzzy (vague) multivalued dependencies), yields that the fuzzy formula attached to c is valid whenever all of the fuzzy formulas attached to the elements of C are valid. What is more important is that the opposite claim is also proven. Its importance stems from the fact that the verification by hand, which means purely theoretical verification, that C implies c is not required anymore. Now, in order to prove that some C yields some c, it is enough to make the use of the resolution principle, and automatically verify whether or not the set of the attached fuzzy formulas yields the fuzzy formula attached to c. In the case of affirmative answer, the desired dependency follows. The research conducted in this paper represent a natural generalization of our previous research since it includes and considers both, fuzzy and vague theories.

Fuzzy Implication and Functional Dependency on Formal Context

Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.

Fuzzy functional dependencies and linguistic interpretations employed in knowledge discovery tasks from relational databases

Knowledge discovery from databases copes with several problems including the heterogeneity of data and interpreting the solution in an understandable and convenient form for domain experts. Fuzzy logic approaches based on the computing with words paradigm are very appealing since they offer the possibility to express useful knowledge from a large volume of data by linguistic terms, which are easily understandable for diverse users. In this paper, the novel descriptive data mining algorithm based on fuzzy functional dependencies has been proposed. In the first step, data are fuzzified, which ensures the same manipulation of crisp and fuzzy data. The data mining step is based on revealing fuzzy functional dependencies among considered attributes. In the final step, the mined knowledge is interpreted linguistically by the fuzzy modifiers and quantifiers. The proposed algorithm has been explained on illustrative data and tested on real-world dataset. Finally, its benefits, weak points and possible future research topics are discussed.

Fuzzy Functional Dependencies as a Method of Choice for Fusion of AIS and OTHR Data.

Maritime situational awareness at over-the-horizon (OTH) distances in exclusive economic zones can be achieved by deploying networks of high-frequency OTH radars (HF-OTHR) in coastal countries along with exploiting automatic identification system (AIS) data. In some regions the reception of AIS messages can be unreliable and with high latency. This leads to difficulties in properly associating AIS data to OTHR tracks. Long history records about the previous whereabouts of vessels based on both OTHR tracks and AIS data can be maintained in order to increase the chances of fusion. If the quantity of data increases significantly, data cleaning can be done in order to minimize system requirements. This process is performed prior to fusing AIS data and observed OTHR tracks. In this paper, we use fuzzy functional dependencies (FFDs) in the context of data fusion from AIS and OTHR sources. The fuzzy logic approach has been shown to be a promising tool for handling data uncertainty from different sensors. The proposed method is experimentally evaluated for fusing AIS data and the target tracks provided by the OTHR installed in the Gulf of Guinea.

Fuzzy Implication and Functional Dependency on Formal Context

Fuzzy formal concept analysis(FFCA) is a development of formal concept analysis(FCA) with the degree of relation between objects and attributes. Using FCA approach, we will investigate the condition logical implication for fuzzy functional dependency. We also use Armstrong's rule to define soundness and completeness of our implication and fuzzy functional dependency model. We show difference and equivalence condition between fuzzy implication and fuzzy functional dependency. This condition can be used to develop the algorithm for finding attribute dependency.

A FUZZY PROBABILISTIC RELATIONAL DATABASE MODEL AND ALGEBRA

This paper introduces a complete extended relational data base model based on probability theory and fuzzy theory, called FPRDB, for representing and handling vague and uncertain information of objects in the real world applications. FPRDB is built by first extending probabilistic triples with fuzzy sets, associating the probability of such fuzzy sets for expressing and computing uncertain degree of imprecise information. Then, schemas, fuzzy probabilistic relations, fuzzy probabilistic functional dependencies and algebraic operations are defined coherently and consistently for FPRDB. A set of the properties of the probabilistic relational algebraic operations in FPRDB is also formulated and proven.

Fuzzy functional dependencies: A comparative survey

Similarity search and related issues are current topic in databases. Over the last ten years more then 6500 papers dealing with similarity in databases were published according to Web of Science. The rising in the number of articles in the recent years shows that the research in this direction is still in its early stage. From the wide range of topics related with similarities in databases, one received a considerable attention already, namely functional dependencies which take similarities into account. Our main concern in this paper is to review and critically examine the existing work on this topic.

Multivalued Dependencies in Fuzzy Multivalued Relational Databases Using Fuzzy Functions

In this paper we discuss an important integrity constraint called multivalued dependency (mvd), which occurs as a result of the first normal form, in the framework of a newly proposed model called fuzzy multivalued relational data model. The fuzzy multivalued relational data model proposed in this paper accommodates a wider class of ambiguities by representing the domain of attributes as a “set of fuzzy subsets”. We show that our model is able to represent multiple types of impreciseness occurring in the real world. To compute the equality of two fuzzy sets/values (which occur as tuple-values), we use the concept of fuzzy functions. So the main objective of this paper is to extend the mvds in context of fuzzy multivalued relational model so that a wider class of impreciseness can be captured. Since the mvds may not exist in isolation, a complete axiomatization for a set of fuzzy functional dependencies (ffds) and mvds in fuzzy multivalued relational schema is provided and the role of fmvds in obtaining the lossless join decomposition is discussed. We also provide a set of sound Inference Rules for the fmvds and derive the conditions for these Inference Rules to be complete. We also derive the conditions for obtaining the lossless join decomposition of a fuzzy multivalued relational schema in the presence of the fmvds. Finally we extend the ABU's Algorithm to find the lossless join decomposition in context of fuzzy multivalued relational databases. We apply all of the concepts of fmvds developed by us to a real world application of “Technical Institute” and demonstrate that how the concepts fit well to capture the multiple types of impreciseness.

On some normal forms in the fuzzy databases with linguistic data

The viewpoint that each attribute domain of the fuzzy databases with linguistic data corresponds to an appropriate hegde algebras, the fuzzy functional dependencies and the fuzzy multivalued dependencies are studied. In this paper, we continue to study a number of fuzzy normal forms. Such concepts as k-keys, super k-keys and the normal forms F1NF, kF2NF, kF3NF, kFBCNF are defined in fuzzy databases with linguistic data. The paper focuses on researching the fuzzy dependency preserving decomposition into kF3NF and the lossless join decomposition into kFBCNF.

Lossless Join Decomposition for Extended Possibility-Based Fuzzy Relational Databases

Functional dependency is the basis of database normalization. Various types of fuzzy functional dependencies have been proposed for fuzzy relational database and applied to the process of database normalization. However, the problem of achieving lossless join decomposition occurs when employing the fuzzy functional dependencies to database normalization in an extended possibility-based fuzzy data models. To resolve the problem, this study defined fuzzy functional dependency based on a notion of approximate equality for extended possibility-based fuzzy relational databases. Examples show that the notion is more applicable than other similarity concept to the research related to the extended possibility-based data model. We provide a decomposition method of using the proposed fuzzy functional dependency for database normalization and prove the lossless join property of the decomposition method.

Analysis of fuzzy -ary relations with the use of interval-valued fuzzy functional dependencies

The paper contains an analysis of integrity constraints for -ary relations in fuzzy databases. Apart from dependencies between all attributes there may be also dependencies describing relationships of fewer attributes. However, there is no complete arbitrariness. Relationships comprising (1) attributes must not infringe integrity constraints of the -ary relation. The analysis is carried out using the theory of functional dependencies. In this paper, we assume that attribute values are represented by means of interval-valued possibility distributions. The notion of fuzzy functional dependency has been appropriately extended according to the representation of fuzzy data. The paper formulates the rules to which fuzzy functional dependencies between (1) attributes of the -ary relation must be subordinated.

A new method for computing fuzzy functional dependencies in relational database systems

In this paper, we present a new method for computing fuzzy functional dependencies between attributes in fuzzy relational database systems. The method is based on the use of fuzzy implications. A literature analysis has shown that there is no algorithm that would enable the identification of attribute relationships in fuzzy relational schemas. This fact was the motive for development a new methodology in the analysis of fuzzy functional dependencies over a given set of attributes. Solving this, not so new problem, is not only research challenge having theoretical importance, but it also has practical significance. Possible applications of the proposed methodology include GIS, data mining, information retrieval, reducing data redundancy in fuzzy relations through implementation of logical database model, estimation of missing values etc.

Fuzzy functional dependencies with liguistic quantifiers.

Fuzzy functional dependencies with liguistic quantifiers.

NORMALIZATION IN TYPE-2 FUZZY RELATIONAL DATA MODEL BASED ON FUZZY FUNCTIONAL DEPENDENCY USING FUZZY FUNCTIONS

In fuzzy relational databases, the data dependencies, especially the fuzzy functional dependency(ffd) plays an important role in maintaining the consistency of the database and in avoiding the redundant storage of the data. In the past, it has been shown that the type-2 fuzzy relational databases captures impreciseness and incompleteness in data in a better way. The aim of this paper is to provide the concepts for database normalization in a type-2 fuzzy relational database, so that the normalized schemas can be obtained. Here, we deal with the fuzzy functional dependency(ffd) based normalization of type-2 fuzzy relational databases. We use the concepts of fuzzy functions to derive the fuzzy equality and using this fuzzy equality, we define a new definition of fuzzy functional dependency. First we discuss various approaches proposed by the researchers in this context and show why our fuzzy functional dependency is better, as compared to the earlier ffds proposed by the researchers. We call our ffd as non-0 LHS ffd. We identify an anomaly called "spurious ffd" and show that some of the significant contributions proposed by the earlier researchers are suffering from this anomaly, but the non-0 LHS ffd does not suffer from it. Then, we prove that the set of inference rules for the non-0 LHS ffd are sound and complete. We use the definition of non-0 LHS ffd in obtaining the first three normal forms upto BCNF for type-1 and type-2 fuzzy relational schemas. The result of the decomposition and the procedure to obtain the membership value of the decomposed relations is proposed. The associated concepts like the fuzzy key, fuzzy superkey, fuzzy foreign key are defined in terms of non-0 LHS ffd. On the basis of these concepts, we define full ffd, partial ffd etc. In the last, we show that in our case, the relationship of total-ordering between the three normal forms in classical relational databases is also observed.

An Extension of Semantic Proximity for Fuzzy Multivalued Dependencies in Fuzzy Relational Database

Following the development of fuzzy logic theory by Lotfi Zadeh, its applications were investigated by researchers in different fields. Presenting and working with uncertain data is a complex problem. To solve for such a complex problem, the structure of relationships and operators dependent on such relationships must be repaired. The fuzzy database has integrity limitations including data dependencies. In this paper, first fuzzy multivalued dependency based semantic proximity and its problems are studied. To solve these problems, the semantic proximity's formula is modified, and fuzzy multivalued dependency based on the concept of extension of semantic proximity with \alpha degree is defined in fuzzy relational database which includes Crisp, NULL and fuzzy values, and also inference rules for this dependency are defined, and their completeness is proved. Finally, we will show that fuzzy functional dependency based on this concept is a special case of fuzzy multivalued dependency in fuzzy relational database.

Fuzzy Subset Dependencies

The fuzzy relational databases which use the special types of constraints, called dependencies, as a semantic tool for expressing properties of the data like a classical relational databases. Fuzzy functional dependencies(ffd) and fuzzy multivalued dependencies(fmvd) are the most common types of dependencies. Similar to classical relational database, a full utilization of fuzzy multivalued dependencies in the design of fuzzy relational databases requires that fuzzy embedded multivalued dependencies(fEmvd) and fuzzy subset dependencies(fsd). These multivalued dependencies hold in a projection of a relation but not necessarily in the relation itself. The main object of this paper is to extend the concept of Embedded Multivalued Dependency (EMVD) and Subset Dependency (SD) to fuzzy relational database.

Probabilistic Inference Channel Detection and Restriction Applied to Patients’ Privacy Assurance

Traditional access control models protect sensitive data from unauthorised direct accesses; however, they fail to prevent indirect inferences. Information disclosure via inference channels occurs when secret information is derived from unclassified (non-secure) information and other sources like metadata and public observations. Previously, techniques using precise and fuzzy functional dependencies were proposed to detect inference channels. However, such methods are inappropriate when probabilistic relationships exist among data items that may be used to infer information with a predictable likelihood of accuracy. In this paper, the authors present definitions and algorithms for detecting inference channels in a probabilistic knowledge base and maximising an attacker’s uncertainty by restricting selected inference channels to comply with data confidentiality and privacy requirements. As an illustration, a healthcare scenario is used to show how inference control can be performed on probabilistic relations to address patients’ privacy concerns over Electronic Medical Records. To limit an attacker’s ability to know secret data selected inference channels are restricted by using a Bayesian network that incorporates the information stored within a medical knowledge base to decide which facts must be hidden to limit undesired inferences.