2007, Vol. XIV, núm. 3
http://hdl.handle.net/2099/9866
Sun, 19 Jan 2020 19:28:01 GMT2020-01-19T19:28:01ZMixed integer programming, general concept inclusions and fuzzy description logics
http://hdl.handle.net/2099/11013
Mixed integer programming, general concept inclusions and fuzzy description logics
Straccia, U.; Bobillo, F.
Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to
describe structured knowledge with vague concepts. In [19], a solution based
on Mixed Integer Linear Programming has been proposed to deal with fuzzy
DLs under Lukasiewicz semantics in which typical membership functions,
such as triangular and trapezoidal functions, can be explicitly represented in
the language.
A major theoretical and computational limitation so far is the inability to
deal with General Concept Inclusions (GCIs), which is an important feature
of classical DLs. In this paper, we address this issue and develop a calculus
for fuzzy DLs with GCIs under various semantics: classical logic, \Zadeh
semantics", and Lukasiewicz logic.
Thu, 20 Oct 2011 15:50:34 GMThttp://hdl.handle.net/2099/110132011-10-20T15:50:34ZStraccia, U.Bobillo, F.Fuzzy Description Logics (fuzzy DLs) have been proposed as a language to
describe structured knowledge with vague concepts. In [19], a solution based
on Mixed Integer Linear Programming has been proposed to deal with fuzzy
DLs under Lukasiewicz semantics in which typical membership functions,
such as triangular and trapezoidal functions, can be explicitly represented in
the language.
A major theoretical and computational limitation so far is the inability to
deal with General Concept Inclusions (GCIs), which is an important feature
of classical DLs. In this paper, we address this issue and develop a calculus
for fuzzy DLs with GCIs under various semantics: classical logic, \Zadeh
semantics", and Lukasiewicz logic.Advanced inference in fuzzy systems by rule base compression
http://hdl.handle.net/2099/11012
Advanced inference in fuzzy systems by rule base compression
Gegov, N.; Gobalakrishnan, N.
This paper describes a method for rule base compression of fuzzy systems. The method compresses a fuzzy system with an arbitrarily large number of rules into a smaller fuzzy system by removing the redundancy in the fuzzy rule base. As a result of this compression, the number of on-line operations during the fuzzy inference process is significantly reduced without compromising the solution. This rule base compression method outperforms significantly other known methods for fuzzy rule base reduction.
Thu, 20 Oct 2011 15:19:41 GMThttp://hdl.handle.net/2099/110122011-10-20T15:19:41ZGegov, N.Gobalakrishnan, N.This paper describes a method for rule base compression of fuzzy systems. The method compresses a fuzzy system with an arbitrarily large number of rules into a smaller fuzzy system by removing the redundancy in the fuzzy rule base. As a result of this compression, the number of on-line operations during the fuzzy inference process is significantly reduced without compromising the solution. This rule base compression method outperforms significantly other known methods for fuzzy rule base reduction.Approximation of proximities by aggregating T-indistinguishability operators
http://hdl.handle.net/2099/10936
Approximation of proximities by aggregating T-indistinguishability operators
Garmendia, L.; Recasens, J.
For a continuous Archimedean t-norm T a method to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T-transitive one is provided.
It consists of aggregating the transitive closure R of R with a (maximal) T-transitive relation B contained in R using a suitable weighted quasi-arithmetic mean to maximize the similarity or minimize the distance to R.
Tue, 18 Oct 2011 16:10:48 GMThttp://hdl.handle.net/2099/109362011-10-18T16:10:48ZGarmendia, L.Recasens, J.For a continuous Archimedean t-norm T a method to approximate a proximity relation R (i.e. a reflexive and symmetric fuzzy relation) by a T-transitive one is provided.
It consists of aggregating the transitive closure R of R with a (maximal) T-transitive relation B contained in R using a suitable weighted quasi-arithmetic mean to maximize the similarity or minimize the distance to R.On completeness results for predicate lukasiewicz, product, gödel and nilpotent minimum logics expanded with truth-constants
http://hdl.handle.net/2099/10931
On completeness results for predicate lukasiewicz, product, gödel and nilpotent minimum logics expanded with truth-constants
Esteva Massaguer, Francesc; Godo, L.; Noguera, C.
In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completeness results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics with truth-constants are conservative, which already implies the failure of standard completeness for the case of Product logic. In contrast, the expansions of predicate Gödel and Nilpotent Minimum logics are proved to be strong standard complete but, when the semantics is restricted to the canonical algebra, they are proved to be complete only for tautologies. Moreover, when the language is restricted to evaluated formulae we prove canonical completeness for deductions from finite sets of premises.
Fri, 14 Oct 2011 16:08:56 GMThttp://hdl.handle.net/2099/109312011-10-14T16:08:56ZEsteva Massaguer, FrancescGodo, L.Noguera, C.In this paper we deal with generic expansions of first-order predicate logics of some left-continuous t-norms with a countable set of truth-constants. Besides already known results for the case of Lukasiewicz logic, we obtain new conservativeness and completeness results for some other expansions. Namely, we prove that the expansions of predicate Product, Gödel and Nilpotent Minimum logics with truth-constants are conservative, which already implies the failure of standard completeness for the case of Product logic. In contrast, the expansions of predicate Gödel and Nilpotent Minimum logics are proved to be strong standard complete but, when the semantics is restricted to the canonical algebra, they are proved to be complete only for tautologies. Moreover, when the language is restricted to evaluated formulae we prove canonical completeness for deductions from finite sets of premises.On the order type L-valued relations on L-powersets
http://hdl.handle.net/2099/10930
On the order type L-valued relations on L-powersets
Uljane, I.
The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc.) on an ordinary set $X$, while $L$-valued sets $X$ (that are sets equipped with some $L$-valued equalities $E: X\times X \to L$, or, more generally, with $L$-valued relations $R: X \times X \to L$) are the starting point for the second one. ($L$ being a lattice usually with an additionally algebraic structure). The aim of this work is to discuss the problem how an $L$-valued relation given on a set $X$ can be extended to the $L$-valued relation $\R$ on the $L$-powerset $L^X$. This problem, is important, among other for the theory of $L$-fuzzy topological spaces in the sense of [15], [16].
Fri, 14 Oct 2011 16:02:23 GMThttp://hdl.handle.net/2099/109302011-10-14T16:02:23ZUljane, I.The research in the field of the so called Fuzzy Mathematics can be conditionally devided into two mainstreams: the first one emphasizes on the study of different fuzzy structures (topological, algebraic, analytical, etc.) on an ordinary set $X$, while $L$-valued sets $X$ (that are sets equipped with some $L$-valued equalities $E: X\times X \to L$, or, more generally, with $L$-valued relations $R: X \times X \to L$) are the starting point for the second one. ($L$ being a lattice usually with an additionally algebraic structure). The aim of this work is to discuss the problem how an $L$-valued relation given on a set $X$ can be extended to the $L$-valued relation $\R$ on the $L$-powerset $L^X$. This problem, is important, among other for the theory of $L$-fuzzy topological spaces in the sense of [15], [16].Towards automatic modeling of economic texts
http://hdl.handle.net/2099/10583
Towards automatic modeling of economic texts
Dvořák, Antonin; Novák, Vilém
In this paper, we present an application of perception-based logical deduction in the modeling of an economic analysis given in natural language. We use fuzzy IF-THEN rules and the theory of evaluative linguistic expressions in the frame of fuzzy type theory. We outline a description of our formal tools and discuss our methodology as well as its relations to other approaches. Finally, we present an example taken from free economic analysis on the Internet.
Fri, 08 Jul 2011 12:18:06 GMThttp://hdl.handle.net/2099/105832011-07-08T12:18:06ZDvořák, AntoninNovák, VilémIn this paper, we present an application of perception-based logical deduction in the modeling of an economic analysis given in natural language. We use fuzzy IF-THEN rules and the theory of evaluative linguistic expressions in the frame of fuzzy type theory. We outline a description of our formal tools and discuss our methodology as well as its relations to other approaches. Finally, we present an example taken from free economic analysis on the Internet.