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Granular Computing: An Emerging Paradigm
, 2001
"... We provide an overview of Granular Computing a rapidly growing area of information processing aimed at the construction of intelligent systems. We highlight the main features of Granular Computing, elaborate on the underlying formalisms of information granulation and discuss ways of their developme ..."
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We provide an overview of Granular Computing a rapidly growing area of information processing aimed at the construction of intelligent systems. We highlight the main features of Granular Computing, elaborate on the underlying formalisms of information granulation and discuss ways of their development. We also discuss the concept of granular modeling and present the issues of communication between formal frameworks of Granular Computing. © 2007 World Academic Press, UK. All rights reserved.
The pseudolinear semantics of intervalvalued fuzzy logics, Information Sciences 179
, 2009
"... Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called intervalvalued residuated lattices (IVRLs). Triangle algebras have been used to construct Triangle Logic (TL), a formal fuzzy logic that is sound and co ..."
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Triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals, which are called intervalvalued residuated lattices (IVRLs). Triangle algebras have been used to construct Triangle Logic (TL), a formal fuzzy logic that is sound and complete w.r.t. the class of IVRLs. In this paper, we prove that the socalled pseudoprelinear triangle algebras are subdirect products of pseudolinear triangle algebras. This can be compared with MTLalgebras (prelinear residuated lattices) being subdirect products of linear residuated lattices. As a consequence, we are able to prove the pseudochain completeness of Pseudolinear Triangle Logic (PTL), an axiomatic extension of TL introduced in this paper. This kind of completeness is the analogue of the chain completeness of MTL (Monoidal Tnorm based Logic). This result also provides a better insight in the structure of triangle algebras; it enables us, amongst others, to prove properties of pseudoprelinear triangle algebras more easily. It is known that there is a onetoone correspondence between triangle algebras and couples (L, α), in which L is a residuated lattice and α an element in that residuated lattice. We give a schematic overview of these properties (and a number of others that can be imposed on a triangle algebra), and the corresponding necessary and sufficient conditions on L and α. Key words: intervalvalued fuzzy set theory, residuated lattices, formal logic
Toward problems for mathematical fuzzy logic, in
 Proc. of IEEE International Conference on Fuzzy Systems
, 2006
"... The paper discusses some open problems in the field of mathematical fuzzy logic which may have a decisive influence for the future development of fuzzy logic within the next decade. 1 ..."
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The paper discusses some open problems in the field of mathematical fuzzy logic which may have a decisive influence for the future development of fuzzy logic within the next decade. 1
E.: The standard completeness of intervalvalued monoidal tnorm based logic. Information Sciences Under review
"... based logic ..."
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"... We live in the world of digital technology that surrounds us and without which we can barely function. There are myriads of examples (which we take for granted) in which computers bring a wealth of services. Computers constitute an omnipresent fabric of the society (Vasilakos and Pedrycz, 2006). As ..."
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We live in the world of digital technology that surrounds us and without which we can barely function. There are myriads of examples (which we take for granted) in which computers bring a wealth of services. Computers constitute an omnipresent fabric of the society (Vasilakos and Pedrycz, 2006). As once
Formalization of Generalized Constraint Language: A Crucial Prelude to Computing With Words
"... introduced by Zadeh, serves as a basis for computing with words (CW). It provides an agenda to express the imprecise and fuzzy information embedded in natural language and allows reasoning with perceptions. Despite its fundamental role, the definition of GCL has remained informal since its introduct ..."
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introduced by Zadeh, serves as a basis for computing with words (CW). It provides an agenda to express the imprecise and fuzzy information embedded in natural language and allows reasoning with perceptions. Despite its fundamental role, the definition of GCL has remained informal since its introduction by Zadeh, and to our knowledge, no attempt has been made to formulate a rigorous theoretical framework for GCL. Such formalization is necessary for further theoretical and practical advancement of CW for two important reasons: first, it provides the underlying infrastructure for the development of new inference rules based on sound theories. Second, it determines the scope of the language as well as its set of wellformed formula and hence facilitates the translation of natural language expressions into GCL. This paper is an attempt to step in this direction by providing a formal recursive syntax together with a compositional semantics for GCL. A soundness theorem is established for GCL which proves the validity of Zadeh’s deduction rules and provides a benchmark for extending Cw inference system. Index Terms — computing with words, Fuzzy Logic, generalized constraint language, test score semantics
IntervalValued Algebras and Fuzzy Logics
"... Abstract In this chapter, we present a propositional calculus for several intervalvalued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise inf ..."
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Abstract In this chapter, we present a propositional calculus for several intervalvalued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of ‘p implies q ’ and ‘p and q’, given the truth values of p and q, we use operations from residuated lattices. This truthfunctional approach is similar to the methods developed for the wellstudied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of intervalvalued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter. 1
Automatic Revision of the Control Knowledge used by Trial and Error Methods: Application to Cartographic
, 2012
"... Humans frequently have to face complex problems. A classical approach to solve them is to search the solution by means of a trial and error method. This approach is often used with success by artificial systems. However, when facing highly complex problems, it becomes necessary to introduce control ..."
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Humans frequently have to face complex problems. A classical approach to solve them is to search the solution by means of a trial and error method. This approach is often used with success by artificial systems. However, when facing highly complex problems, it becomes necessary to introduce control knowledge (heuristics) in order to limit the number of trials needed to find the optimal solution. Unfortunately, acquiring and maintaining such knowledge can be fastidious. In this paper, we propose an automatic knowledge revision approach for systems based on a trial and error method. Our approach allows to revise the knowledge offline by means of experiments. It is based on the analysis of solved instances of the considered problem and on the exploration of the knowledge space. Indeed, we formulate the revision problem as a search problem: we search the knowledge set that maximises the performances of the system on a sample of problem instances. Our knowledge revision approach has been implemented for a realworld industrial application: automated cartographic generalisation, a complex task of the cartography domain. In this implementation, we demonstrate that our approach improves the quality of the knowledge and thus the performance of the system.