11 research outputs found

    The f -index of inclusion as optimal adjoint pair for fuzzy modus ponens

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    We continue studying the properties of the f -index of inclusion and show that, given a fixed pair of fuzzy sets, their f -index of inclusion can be linked to a fuzzy conjunction which is part of an adjoint pair. We also show that, when this pair is used as the underlying structure to provide a fuzzy interpretation of the modus ponens inference rule, it provides the maximum possible truth-value in the conclusion among all those values obtained by fuzzy modus ponens using any other possible adjoint pair.Partially supported by the Spanish Ministry of Science, Innovation and Universities (MCIU), State Agency of Research (AEI), Junta de Andalucía (JA), Universidad de Málaga (UMA) and European Regional Development Fund (FEDER) through the projects PGC2018-095869-B-I00 (MCIU/AEI/FEDER) and UMA2018-FEDERJA-001 (JA/UMA/FEDER). Funding for open access charge: Universidad de Málaga / CBU

    Aggregated fuzzy answer set programming

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    Fuzzy Answer Set programming (FASP) is an extension of answer set programming (ASP), based on fuzzy logic. It allows to encode continuous optimization problems in the same concise manner as ASP allows to model combinatorial problems. As a result of its inherent continuity, rules in FASP may be satisfied or violated to certain degrees. Rather than insisting that all rules are fully satisfied, we may only require that they are satisfied partially, to the best extent possible. However, most approaches that feature partial rule satisfaction limit themselves to attaching predefined weights to rules, which is not sufficiently flexible for most real-life applications. In this paper, we develop an alternative, based on aggregator functions that specify which (combination of) rules are most important to satisfy. We extend upon previous work by allowing aggregator expressions to define partially ordered preferences, and by the use of a fixpoint semantics

    Reducing fuzzy answer set programming to model finding in fuzzy logics

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    In recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalisms allow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining the stable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where many efficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-known technique for classical ASP consists of translating an ASP program P to a propositional theory whose models exactly correspond to the answer sets of P. In this paper, we show how this idea can be extended to fuzzy ASP, paving the way to implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners

    Stable Models of Fuzzy Propositional Formulas

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    Abstract. We introduce the stable model semantics for fuzzy propositional for-mulas, which generalizes both fuzzy propositional logic and the stable model se-mantics of Boolean propositional formulas. Combining the advantages of both for-malisms, the introduced language allows highly configurable default reasoning in-volving fuzzy truth values. We show that several properties of Boolean stable mod-els are naturally extended to this formalism, and discuss how it is related to other approaches to combining fuzzy logic and the stable model semantics.

    A core language for fuzzy answer set programming

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    A number of different Fuzzy Answer Set Programming (FASP) formalisms have been proposed in the last years, which all differ in the language extensions they support. In this paperwe investigate the expressivity of these frameworks. Specificallywe showhowa variety of constructs in these languages can be implemented using a considerably simpler core language. These simulations are important as a compact and simple language is easier to implement and to reason about, while an expressive language offers more options when modeling problems

    Automatic Proving of Fuzzy Formulae with Fuzzy Logic Programming and SMT

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    In this paper we deal with propositional fuzzy formulae containing severalpropositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool. We firstly recall an SMT (Satisfiability Modulo Theories) based method for automatically proving theorems in relevant infinitely valued (including Łukasiewicz and G¨odel) logics. Next, instead of focusing on satisfiability (i.e., proving the existence of at least one model) or unsatisfiability, our interest moves to the problem of finding the whole set of models (with a finite domain) for a given fuzzy formula. We propose an alternative method based on fuzzy logic programming where the formula is conceived as a goal whose derivation tree contains on its leaves all the models of the original formula, by exhaustively interpreting each propositional symbol in all the possible forms according the whole setof values collected on the underlying lattice of truth-degrees

    Digitale predictieve beeldcodering met hoge bitstroom

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