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Transitive decomposition of fuzzy preference relations: the case of nilpotent minimum

Susana Díaz, Susana Montes, Bernard De Baets (2004)

Kybernetika

Transitivity is a fundamental notion in preference modelling. In this work we study this property in the framework of additive fuzzy preference structures. In particular, we depart from a large preference relation that is transitive w.r.t. the nilpotent minimum t-norm and decompose it into an indifference and strict preference relation by means of generators based on t-norms, i. e. using a Frank t-norm as indifference generator. We identify the strongest type of transitivity these indifference and...

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2004)

ESAIM: Control, Optimisation and Calculus of Variations

Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness of the...

Turnpike theorems by a value function approach

Alain Rapaport, Pierre Cartigny (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Turnpike theorems deal with the optimality of trajectories reaching a singular solution, in calculus of variations or optimal control problems. For scalar calculus of variations problems in infinite horizon, linear with respect to the derivative, we use the theory of viscosity solutions of Hamilton-Jacobi equations to obtain a unique characterization of the value function. With this approach, we extend for the scalar case the classical result based on Green theorem, when there is uniqueness of...

Two approaches to fuzzification of payments in NTU coalitional game.

Milan Mares (2002)

Mathware and Soft Computing

There exist several possibilities of fuzzification of a coalitional game. It is quite usual to fuzzify, e. g., the concept of coalition, as it was done in [1]. Another possibility is to fuzzify the expected pay-offs, see [3, 4]. The latter possibility is dealt even here. We suppose that the coalitional and individual pay-offs are expected only vaguely and this uncertainty on the input'' of the game rules is reflected also by an uncertainty of the derived output'' concept like superadditivity, core,...

Two variants of the size Ramsey number

Andrzej Kurek, Andrzej Ruciński (2005)

Discussiones Mathematicae Graph Theory

Given a graph H and an integer r ≥ 2, let G → (H,r) denote the Ramsey property of a graph G, that is, every r-coloring of the edges of G results in a monochromatic copy of H. Further, let m ( G ) = m a x F ⊆ G | E ( F ) | / | V ( F ) | and define the Ramsey density m i n f ( H , r ) as the infimum of m(G) over all graphs G such that G → (H,r). In the first part of this paper we show that when H is a complete graph Kₖ on k vertices, then m i n f ( H , r ) = ( R - 1 ) / 2 , where R = R(k;r) is the classical Ramsey number. As a corollary we derive a new proof of the result credited to Chvatál...

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