Possibilistic functional dependencies and their relationship to possibility theory

This paper introduces possibilistic functional dependencies. These dependencies are associated with a particular possibility distribution over possible worlds of a classical database. The possibility distribution reflects a layered view of the database. The highest layer of the (classical) database consists of those tuples that certainly belong to it, while the other layers add tuples that only possibly belong to the database, with different levels of possibility. The relation between the confidence levels associated with the tuples and the possibility distribution over possible database worlds is discussed in detail in the setting of possibility theory. A possibilistic functional dependency is a classical functional dependency associated with a certainty level that reflects the highest confidence level where the functional dependency no longer holds in the layered database. Moreover, the relationship between possibilistic functional dependencies and possibilistic logic formulas is established. Related work is reviewed, and the intended use of possibilistic functional dependencies is discussed in the conclusion

Discovering Fuzzy Functional Dependencies as Semantic Knowledge in Large Databases

Fuzzy functional dependency (FFD) is a kind of semantic knowledge and can be discovered from a large volume of business data. Sectional FFD and Attribute FFD are discussed so as to reflect semantics of the business world and express useful information that is natural for people to comprehend. The experimental results on an insurance data set show that the proposed method can extract knowledge efficiently and effectively

Relaxed Functional Dependencies - A Survey of Approaches

Recently, there has been a renovated interest in functional dependencies due to the possibility of employing them in several advanced database operations, such as data cleaning, query relaxation, record matching, and so forth. In particular, the constraints defined for canonical functional dependencies have been relaxed to capture inconsistencies in real data, patterns of semantically related data, or semantic relationships in complex data types. In this paper, we have surveyed 35 of such functional dependencies, providing a classification criteria, motivating examples, and a systematic analysis of them

Study on Rough Sets and Fuzzy Sets in Constructing Intelligent Information System

Since human being is not an omniscient and omnipotent being, we are actually living in an uncertain world. Uncertainty was involved and connected to every aspect of human life as a quotation from Albert Einstein said: �As far as the laws of mathematics refer to reality, they are not certain. And as far as they are certain, they do not refer to reality.� The most fundamental aspect of this connection is obviously shown in human communication. Naturally, human communication is built on the perception1-based information instead of measurement-based information in which perceptions play a central role in human cognition [Zadeh, 2000]. For example, it is naturally said in our communication that �My house is far from here.� rather than let say �My house is 12,355 m from here�. Perception-based information is a generalization of measurement-based information, where perception-based information such as �John is excellent.� is hard to represent by measurement-based version. Perceptions express human subjective view. Consequently, they tend to lead up to misunderstanding. Measurements then are needed such as defining units of length, time, etc., to provide objectivity as a means to overcome misunderstanding. Many measurers were invented along with their methods and theories of measurement. Hence, human cannot communicate with measurers including computer as a product of measurement era unless he uses measurement-based information. Perceptions are intrinsic aspect in uncertainty-based information. In this case, information may be incomplete, imprecise, fragmentary, not fully reliable, vague, contradictory, or deficient in some other way. 1In psychology, perception is understood as a process of translating sensory stimulation into an organized experience Generally, these various information deficiencies may express different types of uncertainty. It is necessary to construct a computer-based information system called intelligent information system that can process uncertainty-based information. In the future, computers are expected to be able to make communication with human in the level of perception. Many theories were proposed to express and process the types of uncertainty such as probability, possibility, fuzzy sets, rough sets, chaos theory and so on. This book extends and generalizes existing theory of rough set, fuzzy sets and granular computing for the purpose of constructing intelligent information system. The structure of this book is the following: In Chapter 2, types of uncertainty in the relation to fuzziness, probability and evidence theory (belief and plausibility measures) are briefly discussed. Rough set regarded as another generalization of crisp set is considered to represent rough event in the connection to the probability theory. Special attention will be given to formulation of fuzzy conditional probability relation generated by property of conditional probability of fuzzy event. Fuzzy conditional probability relation then is used to represent similarity degree of two fuzzy labels. Generalization of rough set induced by fuzzy conditional probability relation in terms of covering of the universe is given in Chapter 3. In the relation to fuzzy conditional probability relation, it is necessary to consider an interesting mathematical relation called weak fuzzy similarity relation as a generalization of fuzzy similarity relation proposed by Zadeh [1995]. Fuzzy rough set and generalized fuzzy rough set are proposed along with the generalization of rough membership function. Their properties are examined. Some applications of these methods in information system such as α-redundancy of object and dependency of domain attributes are discussed. In addition, multi rough sets based on multi-context of attributes in the presence of multi-contexts information system is defined and proposed in Chapter 4. In the real application, depending on the context, a given object may have different values of attributes. In other words, set of attributes might be represented based on different context, where they may provide different values for a given object. Context can be viewed as background or situation in which somehow it is necessary to group some attributes as a subset of attributes and consider the subset as a context. Finally, Chapter 5 summarizes all discussed in this book and puts forward some future topics of research

A weighted rough set based fuzzy axiomatic design approach for the selection of AM processes

Additive manufacturing (AM) or 3D printing, as an enabling technology for mass customization or personalization, has been developed rapidly in recent years. Various design tools, materials, machines and service bureaus can be found in the market. Clearly, the choices are abundant, but users can be easily confused as to which AM process they should use. This paper first reviews the existing multi-attribute decision-making methods for AM process selection and assesses their suitability with regard to two aspects, preference rating flexibility and performance evaluation objectivity. We propose that an approach that is capable of handling incomplete attribute information and objective assessment within inherent data has advantages over other approaches. Based on this proposition, this paper proposes a weighted preference graph method for personalized preference evaluation and a rough set based fuzzy axiomatic design approach for performance evaluation and the selection of appropriate AM processes. An example based on the previous research work of AM machine selection is given to validate its robustness for the priori articulation of AM process selection decision support

Reasoning with linguistic preferences using NPN logic

Negative-positive-neutral logic provides an alternative framework for fuzzy cognitive maps development and decision analysis. This paper reviews basic notion of NPN logic and NPN relations and proposes adaptive approach to causality weights assessment. It employs linguistic models of causality weights activated by measurement-based fuzzy cognitive maps' concepts values. These models allow for quasi-dynamical adaptation to the change of concepts values, providing deeper understanding of possible side effects. Since in the real-world environments almost every decision has its consequences, presenting very valuable portion of information upon which we also make our decisions, the knowledge about the side effects enables more reliable decision analysis and directs actions of decision maker

Conceptual Based Hidden Data Analytics and Reduction Method for System Interface Enhancement Through Handheld devices

With the increasing demand placed on online systems by users, many organizations and companies are seeking to enhance their online interfaces to facilitate the search process on their hidden databases. Usually, users issue queries to a hidden database by using the search template provided by the system. In this thesis, a new approach based mainly on hidden database reduction preserving functional dependencies is developed for enhancing the online system interface through a small screen device. The developed approach is applied to online market systems like eBay. Offline hidden data analysis is used to discover attributes and their domains and different functional dependencies. In this thesis, a comparative study between several methods for mining functional dependencies shows the advantage of conceptual methods for data reduction. In addition, by using online consecutive reductions on search results, we adopted a method of displaying results in order of decreasing relevance. The validation of the proposed designed and developed methods prove their generality and suitability for system interfacing through continuous data reductions.NPRP-07-794-1-145 grant from the Qatar National Research Fund (a member of Qatar foundation