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

Belief functions on lattices

We extend the notion of belief function to the case where the underlying structure is no more the Boolean lattice of subsets of some universal set, but any lattice, which we will endow with a minimal set of properties according to our needs. We show that all classical constructions and definitions (e.g., mass allocation, commonality function, plausibility functions, necessity measures with nested focal elements, possibility distributions, Dempster rule of combination, decomposition w.r.t. simple support functions, etc.) remain valid in this general setting. Moreover, our proof of decomposition of belief functions into simple support functions is much simpler and general than the original one by Shafer

A Model for an Intelligent Support Decision System in Aquaculture

The paper purpose an intelligent software system agents–based to support decision in aquculture and the approach of fish diagnosis with informatics methods, techniques and solutions. A major purpose is to develop new methods and techniques for quick fish diagnosis, treatment and prophyilaxis at infectious and parasite-based known disorders, that may occur at fishes raised in high density in intensive raising systems. But, the goal of this paper is to presents a model of an intelligent agents-based diagnosis method will be developed for a support decision system.support decision system, diagnosis, multi-agent system, fish diseases

Hybridization of Bayesian networks and belief functions to assess risk. Application to aircraft deconstruction

This paper aims to present a study on knowledge management for the disassembly of end-of-life aircraft. We propose a model using Bayesian networks to assess risk and present three approaches to integrate the belief functions standing for the representation of fuzzy and uncertain knowledge

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

Monte Carlo and fuzzy interval propagation of hybrid uncertainties on a risk model for the design of a flood protection dike

International audienceA risk model may contain uncertainties that may be best represented by probability distributions and others by possibility distributions. In this paper, a computational framework that jointly propagates probabilistic and possibilistic uncertainties is compared with a pure probabilistic uncertainty propagation. The comparison is carried out with reference to a risk model concerning the design of a flood protection dike

Incorporating knowledge uncertainty into species distribution modelling

Monitoring progress towards global goals and biodiversity targets require reliable descriptions of species distributions over time and space. Current gaps in accessible information on species distributions urges the need for integrating all available data and knowledge sources, and intensifying cooperations to more effectively support global environmental governance. For many areas and species groups, experts can constitute a valuable source of information to fill the gaps by offering their knowledge on species-environment interactions. However, expert knowledge is always subject to uncertainty, and incorporating that into species distribution mapping poses a challenge. We propose the use of the dempster–shafer theory of evidence (DST) as a novel approach in this field to extract expert knowledge, to incorporate the associated uncertainty into the procedure, and to produce reliable species distribution maps. We applied DST to model the distribution of two species of eagle in Spain. We invited experts to fill in an online questionnaire and express their beliefs on the habitat of the species by assigning probability values for given environmental variables, along with their confidence in expressing the beliefs. We then calculated evidential functions, and combined them using Dempster’s rules of combination to map the species distribution based on the experts’ knowledge. We evaluated the performances of our proposed approach using the atlas of Spanish breeding birds as an independent test dataset, and further compared the results with the outcome of an ensemble of conventional SDMs. Purely based on expert knowledge, the DST approach yielded similar results as the data driven SDMs ensemble. Our proposed approach offers a strong and practical alternative for species distribution modelling when species occurrence data are not accessible, or reliable, or both. The particular strengths of the proposed approach are that it explicitly accounts for and aggregates knowledge uncertainty, and it capitalizes on the range of data sources usually considered by an expert

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

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