an explicit approach to the λ operator and the h theorem in the prigogine theory of irreversibility abstract a reformulation of the prigogine theory of irreversible dynamical systems is given in contrast to the previous works a stochastic integral with respect operator valued martingales is employed here this approach provides a mathematically rigorous and simple construction of the operator for dynamical flows it has an explicit random character we derive also the boltzmann h theorem explicitly from the properties of the semigroup only finally the form of the boltzmann kinetic equation for the irreversible dynamics is found

theory and methodologyminimax regret solution to linear programming problems with an interval objective function this paper deals with a linear programming problem with interval objective function coefficients a new treatment of an interval objective function is presented by introducing the minimax regret criterion as used in decision theory the properties of minimax regret solution and the relations with possibly and necessarily optimal solutions are investigated next the minimax regret criterion is applied to the final determination of the solution when a reference solution set is given a method of solution by a relaxation procedure is proposed the solution is obtained by repetitional use of the simplex method the minimax regret solution is obtained by the proposed solution method when the reference solution set is the set of possibly optimal solutions in order to illustrate the proposed solution method a numerical example is given

multiperiod mean absolute deviation fuzzy portfolio selection model with risk control and cardinality constraints abstract this paper considers a multiperiod fuzzy portfolio selection problem maximizing the terminal wealth imposed by risk control in which the returns of assets are characterized by possibilistic mean values a possibilistic absolute deviation is defined as the risk control of portfolio a new multiperiod mean absolute deviation fuzzy portfolio selection model with transaction cost borrowing constraints threshold constraints and cardinality constraints is proposed based on the theory of possibility measure the proposed model is transformed into a crisp nonlinear programming problem because of the transaction cost the multiperiod portfolio selection is a dynamic optimization problem with path dependence the discrete approximate iteration method is designed to obtain the optimal portfolio strategy and is proved convergent finally an example is given to illustrate the behavior of the proposed model and the designed algorithm using real data from the shanghai stock exchange

minimax regret solution to linear programming problems with an interval objective function in this paper a linear programming problem with an interval objective function is treated first the previous approaches to this problem are reviewed and the drawbacks are pointed out to improve the drawbacks a new approach to this problem is proposed by introducing the minimax regret criterion as used in decision theory the properties of minimax regret solution are investigated in order to obtain the minimax regret solution a method of solution by a relaxation procedure is proposed it is shown that the solution is obtained by repetitional use of the simplex method a numerical example is given to illustrate the proposed solution method

on the approach to statistical equilibrium in an infinite particle lattice dynamic model a deterministic reversible model dynamic system of infinite interacting particles on a lattice is studied the model is a modification by de haan of the kac ring model the time evolution of the statistical states can be described by a hierarchy for the reduced distribution functions it is shown that the system is isomorphic to a bernoulli shift the isomorphism is given in terms of the infinite process of observation of the states of one particle in a fixed site the approach to equilibrium is studied and time asymmetric initial states that approach equilibrium are constructed it is shown that these states contain nonvanishing correlations between infinitely distant particles the bernoulli property allows the construction of a markovian irreversible description of the model realized by a nonunitary transformation the action of this transformation on the statistical states the correlations and the rate of the approach to equilibrium is studied

time operator of markov chains and mixing times applications to financial data abstract we extend the notion of time operator from kolmogorov dynamical systems and bernoulli processes to markov processes the general methodology is presented and illustrated in the simple case of binary processes we present a method to compute the eigenfunctions of the time operator internal ages are related to other characteristic times of markov chains namely the kemeny time the convergence rate and goodman s intrinsic time we clarified the concept of mixing time by providing analytic formulas for two state markov chains explicit formulas for mixing times are presented for any two state regular markov chain the mixing time of a markov chain is determined also by the time operator of the markov chain within its age computation we illustrate these results in terms of two realistic examples a markov chain from us gnp data and a markov chain from dow jones closing prices we propose moreover a representation for the kemeny constant in terms of internal ages

an interactive possibilistic programming approach for multiple objective supply chain master planning providing an efficient production plan that integrates the procurement and distribution plans into a unified framework is critical to achieving competitive advantage in this paper we consider a supply chain master planning model consisting of multiple suppliers one manufacturer and multiple distribution centers we first propose a new multi objective possibilistic mixed integer linear programming model mopmilp for integrating procurement production and distribution planning considering various conflicting objectives simultaneously as well as the imprecise nature of some critical parameters such as market demands cost time coefficients and capacity levels then after applying appropriate strategies for converting this possibilistic model into an auxiliary crisp multi objective linear model molp we propose a novel interactive fuzzy approach to solve this molp and finding a preferred compromise solution the proposed model and solution method are validated through numerical tests computational results indicate that the proposed fuzzy method outperforms other fuzzy approaches and is very promising not only for solving our problem but also for any molp model especially multi objective mixed integer models

a nonequilibrium entropy for dynamical systems it is proposed to define entropy for nonequilibrium ensembles using a method of coarse graining which partitions phase space into sets which typically have zero measure these are chosen by considering the totality of future possibilities for observation on the system it is shown that this entropy is necessarily a nondecreasing function of the timet there is no contradiction with the reversibility of the laws of motion because this method of coarse graining is asymmetric under time reversal under suitable conditions which are stated explicitly this entropy approaches the equilibrium entropy ast and the fine grained entropy ast in particular the conditions can always be satisfied if the system is ak system as in the sinai billiard models some theorems are given which give information about whether it is possible to generate the partition used here for coarse graining from time translates of a finite partition and at the same time elucidate the connection between our concept of entropy and the entropy invariant of kolmogorov and sinai

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

intrinsic irreversibility of kolmogorov dynamical systems we give the mathematical details and various extensions of the results stated in previous work of courbage and prigogine intrinsic random systems are deterministic and conservative dynamical systems for which we can associate two dissipative markov processes through a one to one change of representation the first leading to equilibrium for t and the second for t the microscopic formulation of the second principle of thermodynamics permits to lift the degeneracy by the exclusion of all states that do not approach equilibrium for t the set of admitted initial conditions d is then characterized by a non equilibrium entropy functional which is infinite for rejected initial states and takes finite values for admitted initial conditions thus rejected initial states correspond to an infinite amount of information to realize this selection rule we consider general probability measures on phase space that are not necessarily absolutely continuous and we extend the theory of transition to markov processes to such measures owing to the non invariance of d under the time inversion the evolution of these states in the new representation can only be given by one of the two possible markov processes

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

possibilistic linear programming a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem in this paper we review some fuzzy linear programming methods and techniques from a practical point of view in the rst part the general history and the approach of fuzzy mathematical programming are introduced using a numerical example some models of fuzzy linear programming are described in the second part of the paper fuzzy mathematical programming approaches are compared to stochastic programming ones the advantages and disadvantages of fuzzy mathematical programming approaches are exemplied in the setting of an optimal portfolio selection problem finally some newly developed ideas and techniques in fuzzy mathematical programming are briey reviewed c 2000 elsevier science b v all rights reserved

evolution semigroups and time operators on banach spaces we present new general methods to obtain shift representation of evolution semigroups defined on banach spaces we introduce the notion of time operator associated with a generalized shift on a banach space and give some conditions under which time operators can be defined on an arbitrary banach space we also tackle the problem of scaling of time operators and obtain a general result about the existence of time operators on banach spaces satisfying some geometric conditions the last part of the paper contains some examples of explicit constructions of time operators on function spaces

on the shortest distance between orbits and the longest common substring problem abstract in this paper we study the behaviour of the shortest distance between orbits and show that under some rapidly mixing conditions the decay of the shortest distance depends on the correlation dimension for irrational rotations we prove a different behaviour depending on the irrational exponent of the angle of the rotation for random processes this problem corresponds to the longest common substring problem we extend the result of 6 on sequence matching to mixing processes with exponential decay

critical phenomena for sequence matching with scoring consider two independent sequences x 1 x n and y 1 y n suppose that x 1 x n are i i d x and y 1 y n are i i d y where x and y are distributions on finite alphabets x and y respectively a score f x x y r is assigned to each pair x i y j and the maximal nonaligned segment score is m n max 0 i j n 0 l 1 f x i l y j l our result is that m n log n x y a s with determined by a tractable variational formula moreover the pair empirical measure of x i l y j l during the segment where m n is achieved converges to a probability measure which is accessible by the same formula these results generalize to x i y j taking values in any polish space to intrasequence scores under shifts to long quality segments and to more than two sequences

on possibilistic mean value and variance of fuzzy numbers dubois and prade introduced the mean value of a fuzzy number as a closed interval bounded by the expectations calculated from its upper and lower distribution functions in this paper introducing the notations of lower possibilistic and upper possibilistic mean values we definine the interval valued possibilistic mean and investigate its relationship to the interval valued probabilistic mean we also introduce the notation of crisp possibilistic mean value and crisp possibilistic variance of continuous possibility distributions which are consistent with the extension principle we also show that the variance of linear combination of fuzzy numbers can be computed in a similar manner as in probability theory

maximal length of common words among random letter sequences on considere des suites de lettres aleatoires basees sur un alphabet fini genere par des processus stationnaires uniformement melangeants on etudie les proprietes des distributions asymptotiques de la longueur du plus grand mot commun

nonunitary transformations and hydrodynamic limit in the one dimensional hard point gas abstract the ergodic theoretical formalism of nonunitary transformations is compared with the derivation of kinetic equations by the hydrodynamic scaling limit the one dimensional hard point system is used as an illustration both methods rest on the k mixing property of the physical systems considered we show that the specific form of the operator is important only on the microscopic time scale on the macroscopic scale it acts like a projector with broken time reversal symmetry we also discuss the connection between the kolmogorov sinai k s entropy of the model dynamical system the relative entropy production rate in the nonunitary formalism and the macroscopic entropy production rate

a multi objective robust possibilistic programming approach to sustainable public transportation network design abstract as a critical component of sustainable development a transportation system should be designed such that it has a positive impact on the economic environmental and social sustainability of the served region in response this study introduces the concept of passenger dissatisfaction with additional walking and waiting as an indicator of social sustainability and uses the concept while optimizing the transit network for economic environmental and social perfectives due to a lack of knowledge about the actual value of different passenger dissatisfaction levels and uncertainty in demand a multi objective robust possibilistic programming approach rpp is proposed and solved by using an interactive fuzzy programming approach different from other robust possibilistic approaches rpp optimizes not only the mean of the objective function and chance constraint violations but also the risk value inherited by uncertain parameters through considering the absolute deviation of the objective function both the advantage of rpp versus the deterministic model and its superiority against several robust possibilistic approaches are demonstrated in the numerical studies furthermore the outcomes of the numerical study demonstrate that the transportation network should be designed in a decentralized way as the risk coefficients i e risk taking attitude increase

the mean value of a fuzzy number abstract the notion of expectation is defined for fuzzy numbers of intervals viewing them as consonant random sets this expectation is interval valued and remains additive in the sense of fuzzy interval addition as a by product some light is shed on the debate between probability and possibility theory and the problem of how to carry measure theoretic notions into the field of possibility theory

nonlocality of the misra prigogine courbage semigroup we show that the markov semigroups constructed by misra prigogine and courbage through nonunitary similarity transformations of kolmogorov systems are not implementable by local point transformations i e they are not the frobenius perron semigroups associated with noninvertible point transformations in contrast with the semigroups obtained by coarse graining projections our result is a straightforward generalization of the proof of the nonlocality of the similarity transformation given by goldstein misra and courbage and also of the previous illustration by misra and prigogine for the baker transformation and completes the characterization of the misra prigogine courbage semigroups

a comparison of scores of two protein structures with foldings let x i i 1 y i i 1 u u i i 1 and v v i i 1 be four i i d sequences of random variables suppose u and v are uniformly distributed on 0 1 3 for each realization of u j 1 j n x i p 1 p n is constructed as a certain permutation of x p 1 p n for any 1 i n also y j p 1 p n 1 j n are constructed the same way based on y j and v j for a score function f we show that formula math has an asymptotic extreme distribution with the same parameters as in the one dimensional case this model is constructed for a comparison of scores of protein structures with foldings

on intrinsic randomness of dynamical systems we discuss the problem of nonunitary equivalence via positivity preserving similarity transformations between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes dynamical systems admitting such nonunitary equivalence with stochastic markov processes are said to beintrinsically random in a previous work it was found that the so called bernoulli systems discrete time are intrinsically random in this sense this result is extended here by showing that a more general class of dynamical systems the so calledk systems andk flows are intrinsically random the connection of intrinsic randomness with local instability of motion is briefly discussed we also show that markov processes associated through nonunitary equivalence tononisomorphic k flows are necessarily non isomorphic