1998, Vol. V, Núm. 1http://hdl.handle.net/2099/20662024-03-28T10:20:28Z2024-03-28T10:20:28ZVagueness and its representations: a unifying lookWygralak, Maciejhttp://hdl.handle.net/2099/35092017-02-07T16:04:32Z2007-09-19T08:54:52ZVagueness and its representations: a unifying look
Wygralak, Maciej
Using the notion of a vaguely defined object, we systematize and unify different existing approaches to vagueness and its mathematical representations, including fuzzy sets and derived concepts. Moreover, a new, approximative approach to vaguely defined objects will be introduced and investigated.
2007-09-19T08:54:52ZWygralak, MaciejUsing the notion of a vaguely defined object, we systematize and unify different existing approaches to vagueness and its mathematical representations, including fuzzy sets and derived concepts. Moreover, a new, approximative approach to vaguely defined objects will be introduced and investigated.On Boolean modus ponensRudeanu, Sergiuhttp://hdl.handle.net/2099/35082017-02-07T16:04:32Z2007-09-19T08:47:04ZOn Boolean modus ponens
Rudeanu, Sergiu
An abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].
2007-09-19T08:47:04ZRudeanu, SergiuAn abstract form of modus ponens in a Boolean algebra was suggested in [1]. In this paper we use the general theory of Boolean equations (see e.g. [2]) to obtain a further generalization. For a similar research on Boolean deduction theorems see [3].The distribution of mathematical expectations of a randomized fuzzy variableKuz'min, V. B.Travkin, S.I.http://hdl.handle.net/2099/35072017-02-07T16:04:32Z2007-09-18T14:01:03ZThe distribution of mathematical expectations of a randomized fuzzy variable
Kuz'min, V. B.; Travkin, S.I.
The Shaffer's definition of the upper and lower expectations of fuzzy variables is considered with respect to randomized fuzzy sets. The notion of randomized fuzzy sets is introduced in order to evaluate fuzzy statistical indices for an arbitrary chosen fuzzy variable. Provided the distribution of the mathematical expectation of a randomized fuzzy variable is known, it is possible to adopt the traditional methods of testing statistical hypotheses for fuzzy variables.
We show that this distribution has a specific analytical structure and may be represented by means of Wan-der-Mond determinant derivatives. The relation between the notions of expectations of fuzzy variables and the Pareto optimality is demonstrated.
The mathematical expectation of the upper and lower expected values of a randomized fuzzy variable and their asymptotics are calculated.
2007-09-18T14:01:03ZKuz'min, V. B.Travkin, S.I.The Shaffer's definition of the upper and lower expectations of fuzzy variables is considered with respect to randomized fuzzy sets. The notion of randomized fuzzy sets is introduced in order to evaluate fuzzy statistical indices for an arbitrary chosen fuzzy variable. Provided the distribution of the mathematical expectation of a randomized fuzzy variable is known, it is possible to adopt the traditional methods of testing statistical hypotheses for fuzzy variables.
We show that this distribution has a specific analytical structure and may be represented by means of Wan-der-Mond determinant derivatives. The relation between the notions of expectations of fuzzy variables and the Pareto optimality is demonstrated.
The mathematical expectation of the upper and lower expected values of a randomized fuzzy variable and their asymptotics are calculated.Triangular norm-based addition preserving linearity of t-sums of linear fuzzy intervalsKolesárová, Annahttp://hdl.handle.net/2099/35062017-02-07T16:04:32Z2007-09-18T13:50:46ZTriangular norm-based addition preserving linearity of t-sums of linear fuzzy intervals
Kolesárová, Anna
The addition of fuzzy intervals based on a triangular norm $T$ is studied. It is shown that the addition based on a t-norm $T$ weaker than the Lukasiewicz t-norm $T_L$ acts on linear fuzzy intervals just as the $T_L$-based addition. Some examples are given.
2007-09-18T13:50:46ZKolesárová, AnnaThe addition of fuzzy intervals based on a triangular norm $T$ is studied. It is shown that the addition based on a t-norm $T$ weaker than the Lukasiewicz t-norm $T_L$ acts on linear fuzzy intervals just as the $T_L$-based addition. Some examples are given.On (anti) conditional independence in Dempster-Shafer theoryKlopotek, Mieczyslaw A.http://hdl.handle.net/2099/35052017-02-07T16:04:32Z2007-09-18T13:42:38ZOn (anti) conditional independence in Dempster-Shafer theory
Klopotek, Mieczyslaw A.
This paper verifies a result of [9] concerning graphoidal
structure of Shenoy's notion of independence for Dempster-Shafer theory of
belief functions.
Shenoy proved that his notion of independence has graphoidal properties
for positive normal valuations.
The requirement of strict positive normal valuations as
prerequisite for application of graphoidal properties excludes a wide class of
DS belief functions. It excludes especially so-called probabilistic belief
functions. It is demonstrated that the requirement of positiveness of
valuation may be weakened in that it may be required that commonality
function is non-zero for singleton sets instead, and the graphoidal
properties for independence of belief function variables are then preserved.
This means especially that probabilistic belief
functions with all singleton sets as focal points possess graphoidal
properties for independence
2007-09-18T13:42:38ZKlopotek, Mieczyslaw A.This paper verifies a result of [9] concerning graphoidal
structure of Shenoy's notion of independence for Dempster-Shafer theory of
belief functions.
Shenoy proved that his notion of independence has graphoidal properties
for positive normal valuations.
The requirement of strict positive normal valuations as
prerequisite for application of graphoidal properties excludes a wide class of
DS belief functions. It excludes especially so-called probabilistic belief
functions. It is demonstrated that the requirement of positiveness of
valuation may be weakened in that it may be required that commonality
function is non-zero for singleton sets instead, and the graphoidal
properties for independence of belief function variables are then preserved.
This means especially that probabilistic belief
functions with all singleton sets as focal points possess graphoidal
properties for independenceOn some geomtric transformation of t-normsKlement, E. P. (Erich Peter)Mesiar, RadkoPap, Endrehttp://hdl.handle.net/2099/35042017-02-07T16:04:32Z2007-09-18T13:26:10ZOn some geomtric transformation of t-norms
Klement, E. P. (Erich Peter); Mesiar, Radko; Pap, Endre
Given a triangular norm $T$, its $t$-reverse $T^*$, introduced by C. Kimberling ({\it Publ. Math. Debrecen} 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have $ T^{**} = T$ is completely solved. The $t$-reverses of ordinal sums of $t$-norms are investigated and a complete description of continuous, self-reverse $t$-norms is given, leading to a new characterization of the continuous $t$-norms $T$ such that the function $ G(x,y) = x + y - T(x,y)$ is a $t$-conorm, a problem originally studied by M.J. Frank ({\it Aequationes Math.} 19, 194-226, 1979). Finally, some open problems are formulated.
2007-09-18T13:26:10ZKlement, E. P. (Erich Peter)Mesiar, RadkoPap, EndreGiven a triangular norm $T$, its $t$-reverse $T^*$, introduced by C. Kimberling ({\it Publ. Math. Debrecen} 20, 21-39, 1973) under the name invert, is studied. The question under which conditions we have $ T^{**} = T$ is completely solved. The $t$-reverses of ordinal sums of $t$-norms are investigated and a complete description of continuous, self-reverse $t$-norms is given, leading to a new characterization of the continuous $t$-norms $T$ such that the function $ G(x,y) = x + y - T(x,y)$ is a $t$-conorm, a problem originally studied by M.J. Frank ({\it Aequationes Math.} 19, 194-226, 1979). Finally, some open problems are formulated.Convex isomorphisms of Archimedean lattice ordered groupsJakubík, Jánhttp://hdl.handle.net/2099/35032017-02-07T16:04:32Z2007-09-18T13:18:55ZConvex isomorphisms of Archimedean lattice ordered groups
Jakubík, Ján
This paper contains a result of Cantor-Bernstein type concerning archiemedean lattice ordered groups.
2007-09-18T13:18:55ZJakubík, JánThis paper contains a result of Cantor-Bernstein type concerning archiemedean lattice ordered groups.On some inexact relations in probabilized Boolean algebrasCubillo Villanueva, Susanahttp://hdl.handle.net/2099/35022017-02-07T16:04:32Z2007-09-18T13:08:40ZOn some inexact relations in probabilized Boolean algebras
Cubillo Villanueva, Susana
This paper is devoted to characterize monotonicity, conditionality and transitivity of some rational relations defined in a probabilized Boolean Algebra
2007-09-18T13:08:40ZCubillo Villanueva, SusanaThis paper is devoted to characterize monotonicity, conditionality and transitivity of some rational relations defined in a probabilized Boolean AlgebraThe logic of neural networksCastro Peña, Juan LuisTrillas i Gay, Enrichttp://hdl.handle.net/2099/35012020-02-12T16:01:27Z2007-09-18T12:58:30ZThe logic of neural networks
Castro Peña, Juan Luis; Trillas i Gay, Enric
This paper establishes the equivalence between multilayer feedforward
networks and linear combinations of Lukasiewicz propositions. In this sense,
multilayer forward networks have a logic interpretation, which should permit to apply
logical techniques in the neural networks framework.
2007-09-18T12:58:30ZCastro Peña, Juan LuisTrillas i Gay, EnricThis paper establishes the equivalence between multilayer feedforward
networks and linear combinations of Lukasiewicz propositions. In this sense,
multilayer forward networks have a logic interpretation, which should permit to apply
logical techniques in the neural networks framework.The embedding if the formal concept analysis inte the L-fuzzy concept theoryBurusco Juandeaburre, AnaFuentes-González, Ramónhttp://hdl.handle.net/2099/35002017-02-07T16:04:32Z2007-09-18T12:40:03ZThe embedding if the formal concept analysis inte the L-fuzzy concept theory
Burusco Juandeaburre, Ana; Fuentes-González, Ramón
In this work, we study the relation between the concept lattice of
Wille ([5], [6]) and
the $L-Fuzzy$ concept lattice ([2]) developed by us.
To do it, we have defined an application $g$ that associates
to each concept of Wille an $L-Fuzzy$ concept. The main point of this
work is to
prove that if we are working with a crisp relation between an object set and an
attribute set, the concept lattice of Wille is a sublattice of the
$L-Fuzzy$ concept
lattice.
At the end, we show a typical example in the formal concept theory where we have
constructed the $L-Fuzzy$ concept lattice.
2007-09-18T12:40:03ZBurusco Juandeaburre, AnaFuentes-González, RamónIn this work, we study the relation between the concept lattice of
Wille ([5], [6]) and
the $L-Fuzzy$ concept lattice ([2]) developed by us.
To do it, we have defined an application $g$ that associates
to each concept of Wille an $L-Fuzzy$ concept. The main point of this
work is to
prove that if we are working with a crisp relation between an object set and an
attribute set, the concept lattice of Wille is a sublattice of the
$L-Fuzzy$ concept
lattice.
At the end, we show a typical example in the formal concept theory where we have
constructed the $L-Fuzzy$ concept lattice.