Wyniki wyszukiwania - BazTech

1

Structures of Opposition in Fuzzy Rough Sets

Ciucci D., Dubois D., Prade H.

Fundamenta Informaticae

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2015

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Vol. 142, nr 1-4

1--19

EN

The square of opposition is as old as logic. There has been a recent renewal of interest on this topic, due to the emergence of new structures (hexagonal and cubic) extending the square. They apply to a large variety of representation frameworks, all based on the notions of sets and relations. After a reminder about the structures of opposition, and an introduction to their gradual extensions (exemplified on fuzzy sets), the paper more particularly studies fuzzy rough sets and rough fuzzy sets in the setting of gradual structures of opposition.

2

Interval-Valued Fuzzy Galois Connections: Algebraic Requirements and Concept Lattice Construction

Djouadi Y., Prade H.

Fundamenta Informaticae

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2010

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Vol. 99, nr 2

169-186

EN

Fuzzy formal concept analysis is concernedwith formal contexts expressing scalar-valued fuzzy relationships between objects and their properties. Existing fuzzy approaches assume that the relationship between a given object and a given property is a matter of degree in a scale L (generally [0,1]). However, the extent to which "object o has property a" may be sometimes hard to assess precisely. Then it is convenient to use a sub-interval from the scale L rather than a precise value. Such formal contexts naturally lead to interval-valued fuzzy formal concepts. The aim of the paper is twofold. We provide a sound minimal set of algebraic requirements for interval-valued implications in order to fulfill the fuzzy closure properties of the resulting Galois connection. Secondly, a new approach based on a generalization of Gödel implication is proposed for building the complete lattice of all interval-valued fuzzy formal concepts.

3

A Framework for Iterated Belief Revision Using Possibilistic Counterparts to Jeffrey's Rule

Benferhat S., Dubois D., Prade H., Williams M-A.

Fundamenta Informaticae

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2010

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Vol. 99, nr 2

147-168

EN

Intelligent agents require methods to revise their epistemic state as they acquire new information. Jeffrey’s rule, which extends conditioning to probabilistic inputs, is appropriate for revising probabilistic epistemic states when new information comes in the form of a partition of events with new probabilities and has priority over prior beliefs. This paper analyses the expressive power of two possibilistic counterparts to Jeffrey's rule for modeling belief revision in intelligent agents. We show that this rule can be used to recover several existing approaches proposed in knowledge base revision, such as adjustment, natural belief revision, drastic belief revision, and the revision of an epistemic state by another epistemic state. In addition, we also show that some recent forms of revision, called improvement operators, can also be recovered in our framework.

4

Quasi-Possibilistic Logic and its Measures of Information and Conflict

Dubois D., Konieczny S., Prade H.

Fundamenta Informaticae

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2003

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Vol. 57, nr 2-4

101--125

EN

Possibilistic logic and quasi-classical logic are two logics that were developed in artificial intelligence for coping with inconsistency in different ways, yet preserving the main features of classical logic. This paper presents a new logic, called quasi-possibilistic logic, that encompasses possibilistic logic and quasi-classical logic, and preserves the merits of both logics. Indeed, it can handle plain conflicts taking place at the same level of certainty (as in quasi-classical logic), and take advantage of the stratification of the knowledge base into certainty layers for introducing gradedness in conflict analysis (as in possibilistic logic). When querying knowledge bases, it may be of interest to evaluate the extent to which the relevant available information is precise and consistent. The paper review measures of (im)precision and inconsistency/conflict existing in possibilistic logic and quasi-classical logic, and proposes generalized measures in the unified framework.

5

A definition of subjective possibility

Dubois D., Prade H., Smets P.

Badania Operacyjne i Decyzje

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2003

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nr 4

7-22

EN

The problem of finding a suitable belief function consistent with a given possibility distribution is considered. It is proved that this function is unique and consonant thus representable by means of a possibility distribution. The possibility distribution is subjective and unique. The results obtained in the paper allow us to define subjective possibility degrees, hence the membership function of fuzzy number.

PL

W pracy proponuje się subiektywne spojrzenie na teorię możliwości, polegające na założeniu, że kiedy konstruuje się pewien rozkład prawdopodobieństwa jest on faktycznie indukowany przez pewną funkcję ufności (belief function) reprezentującą rzeczywisty stan wiedzy. Zakłada się również, że przejście pewnej funkcji ufności do rozkładu prawdopodobieństwa jest realizowane za pomocą transformacji ( pignistic transformation), znanej jako wartość Shapleya. Rozważa się problem znalezienia odpowiedniej funkcji ufności zgodnej z danym rozkładem prawdopodobieństwa. Dowodzi się, ze funkcja ta jest jednoznacznie określona i zgodna. Można ją zatem reprezentować za pomocą rozkładu możliwości. Rozkład ten jest subiektywny i jednoznaczny. Otrzymane w pracy wyniki pozwalają na definiowanie subiektywnych stopni możliwości, a co za tym idzie - funkcji przynależności liczby mnogiej.

6

Using possibilistic logic for modeling qualitative decision: ATMS-based algorithms

Dubois D., Le Berre D., Prade H., Sabbadin R.

Fundamenta Informaticae

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1999

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Vol. 37, Nr 1,2

1-30

EN

This paper describes a logical machinery for computing decision, where the available knowledge on the state of the world is described by a possibilistic prepositional logic base (i.e., a collection of logical statements associated with qualitative certainty levels), and where the preferences of the user are also described by another possibilistic logic base whose formula weights are interpreted in terms of priorities. Two attitudes are allowed for the decision maker: a pessimistic risk-averse one and an optimistic one. The computed decisions are in agreement with a qualitative counterpart to the classical theory of expected utility, recently developed by three of the authors. A link is established between this logical view of qualitative decision making and an ATMS-based computation procedure. Efficient algorithms for computing pessimistic and optimistic optimal decisions are finally given in this logical setting (using some previous work of the fourth author).