738 research outputs found
Distorted Copulas: Constructions and Tail Dependence
Given a copula C, we examine under which conditions on an order isomorphism Ï of [0, 1] the distortion C Ï: [0, 1]2 â [0, 1], C Ï(x, y) = Ï{C[Ïâ1(x), Ïâ1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on Ï that ensures that any distortion of C by means of Ï is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails
Neutrality and Many-Valued Logics
In this book, we consider various many-valued logics: standard, linear,
hyperbolic, parabolic, non-Archimedean, p-adic, interval, neutrosophic, etc. We
survey also results which show the tree different proof-theoretic frameworks
for many-valued logics, e.g. frameworks of the following deductive calculi:
Hilbert's style, sequent, and hypersequent. We present a general way that
allows to construct systematically analytic calculi for a large family of
non-Archimedean many-valued logics: hyperrational-valued, hyperreal-valued, and
p-adic valued logics characterized by a special format of semantics with an
appropriate rejection of Archimedes' axiom. These logics are built as different
extensions of standard many-valued logics (namely, Lukasiewicz's, Goedel's,
Product, and Post's logics). The informal sense of Archimedes' axiom is that
anything can be measured by a ruler. Also logical multiple-validity without
Archimedes' axiom consists in that the set of truth values is infinite and it
is not well-founded and well-ordered. On the base of non-Archimedean valued
logics, we construct non-Archimedean valued interval neutrosophic logic INL by
which we can describe neutrality phenomena.Comment: 119 page
Weighted Constraints in Fuzzy Optimization
Many practical optimization problems are characterized by someflexibility in the problem constraints, where this flexibility canbe exploited for additional trade-off between improving theobjective function and satisfying the constraints. Especially indecision making, this type of flexibility could lead to workablesolutions, where the goals and the constraints specified bydifferent parties involved in the decision making are traded offagainst one another and satisfied to various degrees. Fuzzy setshave proven to be a suitable representation for modeling this typeof soft constraints. Conventionally, the fuzzy optimizationproblem in such a setting is defined as the simultaneoussatisfaction of the constraints and the goals. No additionaldistinction is assumed to exist amongst the constraints and thegoals. This report proposes an extension of this model forsatisfying the problem constraints and the goals, where preferencefor different constraints and goals can be specified by thedecision-maker. The difference in the preference for theconstraints is represented by a set of associated weight factors,which influence the nature of trade-off between improving theoptimization objectives and satisfying various constraints.Simultaneous weighted satisfaction of various criteria is modeledby using the recently proposed weighted extensions of(Archimedean) fuzzy t-norms. The weighted satisfaction of theproblem constraints and goals are demonstrated by using a simplefuzzy linear programming problem. The framework, however, is moregeneral, and it can also be applied to fuzzy mathematicalprogramming problems and multi-objective fuzzy optimization.wiskundige programmering;fuzzy sets;optimalisatie
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