neumann and robin problems in a cracked domain with jump conditions on cracks the boundary value problem for the laplace equation is studied on a domain with smooth compact boundary and with smooth internal cracks the neumann or the robin condition is given on the boundary of the domain the jump of the function and the jump of its normal derivative is prescribed on the cracks the solution is looked for in the form of the sum of a single layer potential and a double layer potential the solvability of the corresponding integral equation is determined and the explicit solution of this equation is given in the form of the neumann series estimates for the absolute value of the solution of the boundary value problem and for the absolute value of the gradient of the solution are presented

rough games modeled via l fuzzy ambiguous representations of semilattices abstract monotonic predicates and l fuzzy ambiguous representations of continuous semilattices with bottom elements are applied to describe rough normal form games and rough extensive form two player zero sum games with imperfect information payoff predicates are introduced to find best guaranteed gains of the players these predicates are calculated recursively via backward payoff predicate transformers which are also studied it is shown how payoff predicates determine almost optimal strategies an approximate minimax theorem is also stated

global existence for the einstein vacuum equations in wave coordinates we prove global stability of minkowski space for the einstein vacuum equations in harmonic wave coordinate gauge for the set of restricted data coinciding with the schwarzschild solution in the neighborhood of space like infinity the result contradicts previous beliefs that wave coordinates are unstable in the large and provides an alternative approach to the stability problem originally solved for unrestricted data in a different gauge and with a precise description of the asymptotic behavior at null infinity by d christodoulou and s klainerman

theoretical and semantic distinctions of fuzzy possibilistic and mixed fuzzy possibilistic optimization theoretical semantic and algorithmic distinctions among fuzzy possibilistic and mixed fuzzy possibilistic optimization are presented and illustrated the theory underlying fuzzy possibilistic and mixed fuzzy possibilistic optimization is developed and demonstrated and points to the appropriate use of distinct solution methods associated with each type of optimization dependant on the semantics of the problem semantics is key to both the input where one is obtaining the data and constructing the optimization model in the presence of uncertainty and the output where the meaning of the results is necessary for understanding solutions the case in which the optimization model arises from the data that is a combination of fuzzy and possibilistic distributions is also derived lastly examples illustrate the theory this paper is a modification and an amplification of a presentation made at ifsa 05 w a lodwich k d jamison theory and semantics for fuzzy and possibilistic optimization in fuzzy logic soft computing and computational intelligence eleventh internat fuzzy systems association world congress july 28 31 2005 beijing china vol iii pp 1805 1810 26

extension of a class of decomposable measures using fuzzy pseudometrics in this paper we consider a topological approach to extension of t conorm based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets we prove that every non strict continuous archimedean t conorm based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma algebra generated by this algebra the existence of such an extension follows very simply from the well known caratheodory result however our topological proof offers an intuitive interpretation of the extension of decomposable measures

multiobjective problems with fuzzy parameters and games against nature in the present paper a multiobjective problem with fuzzy parameters is investigated a two person zero sum multiobjective game with the first player as the decision maker and the second as nature and a cuts are used to introduce a concept of solution for this problem the a pareto maxmin solution an interactive procedure for the computation of the introduced solution is provided as well

approaches to multistage one shot decision making abstract in this research multistage one shot decision making under uncertainty is studied in such a decision problem a decision maker has one and only one chance to make a decision at each stage with possibilistic information based on the one shot decision theory approaches to multistage one shot decision making are proposed in the proposed approach a decision maker chooses one state amongst all the states according to his her attitude about satisfaction and possibility at each stage the payoff at each stage is associated with the focus points at the succeeding stages based on the selected states focus points the sequence of optimal decisions is determined by dynamic programming the proposed method is a fundamental alternative for multistage decision making under uncertainty because it is scenario based instead of lottery based as in the other existing methods the one shot optimal stopping problem is analyzed where a decision maker has only one chance to determine stopping or continuing at each stage the theoretical results have been obtained

computing rank dependent utility in graphical models for sequential decision problems this paper is devoted to automated sequential decision in ai more precisely we focus here on the rank dependent utility rdu model this model is able to encompass rational decision behaviors that the expected utility model cannot accommodate however the non linearity of rdu makes it difficult to compute an rdu optimal strategy in sequential decision problems this has considerably slowed the use of rdu in operational contexts in this paper we are interested in providing new algorithmic solutions to compute an rdu optimal strategy in graphical models specifically we present algorithms for solving decision tree models and influence diagram models of sequential decision problems for decision tree models we propose a mixed integer programming formulation that is valid for a subclass of rdu models corresponding to risk seeking behaviors this formulation reduces to a linear program when mixed strategies are considered in the general case i e when there is no particular assumption on the parameters of rdu we propose a branch and bound procedure to compute an rdu optimal strategy among the pure ones after highlighting the difficulties induced by the use of rdu in influence diagram models we show how this latter procedure can be extended to optimize rdu in an influence diagram finally we provide empirical evaluations of all the presented algorithms

blow up for quasi linear wave equations in three space dimensions we consider equations of the form u phi x t u u u 1a for a function u u x 1 x n t u x t here denotes the d alembertian square frac partial 2 partial t 2 vartriangle 1b and u represents the vector of first derivatives u that of second derivatives of u with respect to the x k and t on linearizing 1a shall go over into the classical wave equation u 0 this means that and its first derivatives with respect to u u u shall vanish for u u u 0

decision theoretic foundations of qualitative possibility theory abstract this paper presents a justification of two qualitative counterparts of the expected utility criterion for decision under uncertainty which only require bounded linearly ordered valuation sets for expressing uncertainty and preferences this is carried out in the style of savage starting with a set of acts equipped with a complete preordering relation conditions on acts are given that imply a possibilistic representation of the decision maker uncertainty in this framework pessimistic i e uncertainty averse as well as optimistic attitudes can be explicitly captured the approach thus proposes an operationally testable description of possibility theory

the symmetric sugeno integral we propose an extension of the sugeno integral for negative numbers in the spirit of the symmetric extension of choquet integral also called sipos integral our framework is purely ordinal since the sugeno integral has its interest when the underlying structure is ordinal we begin by defining negative numbers on a linearly ordered set and we endow this new structure with a suitable algebra very close to the ring of real numbers in a second step we introduce the mobius transform on this new structure lastly we define the symmetric sugeno integral and show its similarity with the symmetric choquet integral

nodal sets for groundstates of schrodinger operators with zero magnetic field in non simply connected domains we investigate nodal sets of magnetic schrodinger operators with zero magnetic field acting on a non simply connected domain in 2 for the case of circulation 1 2 of the magnetic vector potential around each hole in the region we obtain a characterisation of the nodal set and use this to obtain bounds on the multiplicity of the groundstate for the case of one hole and a fixed electric potential we show that the first eigenvalue takes its highest value for circulation 1 2

fuzzy integral representation abstract in this paper we give representation results for nonlinear functionals in arbitrary spaces as fuzzy integrals the main assumption is that of comonotonic maxitivity i e i f g if ig for comonotonic f g under the more restrictive condition of stochastic dominance we prove a more specific representation as a fuzzy integral with respect to a distorted probability measure we discuss the particular cases of possibility measures and upper fuzzy expectations some partial randon nikodym results are proved for both the choquet and the fuzzy integrals finally an example is shown where the fuzzy integral representation is useful

on the specificity of a possibility distribution abstract the specificity of a possibility distribution measures the degree to which the distribution allows one and only one element as its manifestation as such it is a measure of amount of uncertainty or information we investigate a number of issues related to specificity measures we discuss the connection between the specificity of a possibility distribution and the entropy of a probability distribution we describe unifying view for constructing specificity measures we look at the relationship of the specificity of a distribution and its negation we consider the case where the base set is continuous

eigenvalues variations for aharonov bohm operators we study how the eigenvalues of a magnetic schrodinger operator of aharonov bohm type depend on the singularities of its magnetic potential we consider a magnetic potential defined everywhere in 2 except at a finite number of singularities so that the associated magnetic field is zero on a fixed planar domain we define the corresponding magnetic hamiltonian with dirichlet boundary conditions and study its eigenvalues as functions of the singularities we prove that these functions are continuous and in some cases even analytic we sketch the connection of this eigenvalue problem to the problem of finding spectral minimal partitions of the domain

fuzzy measure of fuzzy events defined by fuzzy integrals abstract we define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by murofushi called fuzzy t conorm integral encompassing previous definitions zadeh defined the probability measure of a fuzzy event and later the possibility measure of fuzzy event using a duality property of fuzzy t conorm integral we propose a general definition of fuzzy measure of fuzzy events which is compatible with previous definitions of zadeh and possesses all properties of a fuzzy measure in particular the duality property using our definition we examine the case of decomposable measures and belief functions a comparison with previous works is provided

reformulating decision theory using fuzzy set theory and shafer s theory of evidence abstract utilities and probabilities in decision theory are usually assessed by asking individuals to indicate their preferences between various uncertain choices in this paper we argue that 1 the utility of a consequence can be assessed as the membership function of the consequence in the fuzzy set satisfactory 2 the probability of an event instead of being directly assessed should be inferred from the evidence associated with that event the degree of evidence is quantified using shaferian basic probability assignments in addition we use the heisenberg uncertainty principle to argue for a change in one of the technical assumptions underlying decision theory as a result of this change some kinds of evidence will be observable in certain experiments but unobservable in others since probabilities are defined over the potential outcomes of an experiment they will only be defined over some but not all the evidence as a result the probabilities associated with different experiments could be inconsistent this formulation emphasizes the importance of new distinctions and not just new information in updating probabilities we argue that this formulation addresses many of the observed empirical deviations between decision theory and experiment it also addresses the anomalies of quantum physics we close with a brief discussion of directions for further research

an axiomatic treatment of three qualitative decision criteria the need for computationally efficient decision making techniques together with the desire to simplify the processes of knowledge acquisition and agent specification have led various researchers in artificial intelligence to examine qualitative decision tools however the adequacy of such tools is not clear this paper investigates the foundations of maximin minmax regret and competitive ratio three central qualitative decision criteria by characterizing those behaviors that could result from their use this characterizaton provides two important insights 1 under what conditions can we employ an agent model based on these basic qualitative decision criteria and 2 how rational are these decision procedures for the competitive ratio criterion in particular this latter issue is of central importance to our understanding of current work on on line algorithms our main result is a constructive representation theorem that uses two choice axioms to characterize maximin minmax regret and competitive ratio

on multiple eigenvalues for aharonov bohm operators in planar domains abstract we study multiple eigenvalues of a magnetic aharonov bohm operator with dirichlet boundary conditions in a planar domain in particular we study the structure of the set of the couples position of the pole circulation which keep fixed the multiplicity of a double eigenvalue of the operator with the pole at the origin and half integer circulation we provide sufficient conditions for which this set is made of an isolated point the result confirms and validates a lot of numerical simulations available in preexisting literature

qualitative decision theory from savage s axioms to nonmonotonic reasoning this paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible in the scope of artificial intelligence contrary to classical approaches to decision theory we try to rank acts without resorting to any numerical representation of utility or uncertainty and without using any scale on which both uncertainty and preference could be mapped our approach is a variant of savage s where the setting is finite and the strict preference on acts is a partial order it is shown that although many axioms of savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts the approach is inconsistent with a probabilistic representation of uncertainty the latter leads to the kind of paradoxes encountered in the theory of voting it is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty originally due to lewis and usual in nonmonotonic reasoning our axiomatic investigation thus provides decision theoretic foundations to the preferential inference of lehmann and colleagues however the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions although their basic principles look sound this paper points out some limitations of purely ordinal approaches to savage like decision making under uncertainty in perfect analogy with similar difficulties in voting theory

meta clustering of possibilistically segmented retail datasets this paper proposes a possibilistic meta clustering algorithm the possibility theory is used for possibilistic segmentation of the input data as well as for determining the possibilistic membership of objects to multiple clusters the meta clustering uses connections between information granules to send clustering knowledge from one granule to another the approach is demonstrated with the help of the k modes clustering algorithm for a real world retail store where a customer is connected to the products bought and products are connected to customers who buy them the meta clustering approach uses the results from clustering of customers as an input to cluster the products and recursively uses clustering of products as input to the clustering customers the customer granule is represented using static information from the database and dynamic information from the clustering of the products bought similarly a product granule is represented by static information from the database and dynamic part from the clustering of the customers who buy the product the static information from the database is represented using possibilistic segments

fuzzy scheduling modelling flexible constraints vs coping with incomplete knowledge abstract an overview of some fuzzy set based approaches to scheduling is proposed emphasizing two distinct uses of fuzzy sets representing preference profiles and modelling uncertainty distributions the first setting leads to a valued non compensatory generalization of constraint directed scheduling the other setting yields a possibility theoretic counterpart of pert where probability distributions of activity durations are changed into possibility distributions for the purpose of modelling incomplete information it is pointed out that a special case of the latter interval valued pert is a difficult ill known problem regarding the determination of critical activities latest starting times and floats lastly when flexible constraints and uncertain processing times are to be jointly considered the use of possibilistic decision theory leads to the computation of robust schedules

two axiomatic approaches to decision making using possibility theory this paper proposes a utility theory for decision making under uncertainty that is described by possibility theory we show that our approach is a natural generalization of the two axiomatic systems that correspond to pessimistic and optimistic decision criteria proposed by dubois et al the generalization is achieved by removing axioms that are supposed to reflect attitudes toward uncertainty namely pessimism and optimism in their place we adopt an axiom that imposes an order on a class of canonical lotteries that realize either in the best or in the worst prize we prove an expected utility theorem for the generalized axiomatic system based on the newly introduced concept of binary utility

composite multilinearity epistemic uncertainty and risk achievement worth abstract risk achievement worth is one of the most widely utilized importance measures raw is defined as the ratio of the risk metric value attained when a component has failed over the base case value of the risk metric traditionally both the numerator and denominator are point estimates relevant literature has shown that inclusion of epistemic uncertainty i induces notable variability in the point estimate ranking and ii causes the expected value of the risk metric to differ from its nominal value we investigate the conditions under which the equality of the nominal and expected values of a reliability risk metric holds we then study how the presence of epistemic uncertainty affects raw and the associated ranking we propose an extension of raw called eraw which allows one to obtain a ranking robust to epistemic uncertainty we discuss the properties of eraw and the conditions under which it coincides with raw we apply our findings to a probabilistic risk assessment model developed for the safety analysis of nasa lunar space missions

almgren type monotonicity methods for the classification of behaviour at corners of solutions to semilinear elliptic equations a monotonicity approach to the study of the asymptotic behavior near corners of solutions to semilinear elliptic equations in domains with a conical boundary point is discussed the presence of logarithms in the first term of the asymptotic expansion is excluded for boundary profiles sufficiently close to straight conical surfaces

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

qualitative possibilistic influence diagrams based on qualitative possibilistic utilities this paper proposes a new approach for decision making under uncertainty based on influence diagrams and possibility theory the so called qualitative possibilistic influence diagrams extend standard influence diagrams in order to avoid difficulties attached to the specification of both probability distributions relative to chance nodes and utilities relative to value nodes in fact generally it is easier for experts to quantify dependencies between chance nodes qualitatively via possibility distributions and to provide a preferential relation between different consequences in such a case the possibility theory offers a suitable modeling framework different combinations of the quantification between chance and utility nodes offer several kinds of possibilistic influence diagrams this paper focuses on qualitative ones and proposes an indirect evaluation method based on their transformation into possibilistic networks the proposed approach is implemented via a possibilistic influence diagram toolbox pidt

on the aharonov bohm operators with varying poles the boundary behavior of eigenvalues we consider a magnetic schrodinger operator with magnetic field concentrated at one point the pole of a domain and half integer circulation and we focus on the behavior of dirichlet eigenvalues as functions of the pole although the magnetic field vanishes almost everywhere it is well known that it affects the operator at the spectral level the aharonov bohm effect phys rev 2 115 485 491 1959 moreover the numerical computations performed in bonnaillie noel et al anal pde 7 6 1365 1395 2014 noris and terracini indiana univ math j 59 4 1361 1403 2010 show a rather complex behavior of the eigenvalues as the pole varies in a planar domain in this paper in continuation of the analysis started in bonnaillie noel et al anal pde 7 6 1365 1395 2014 noris and terracini indiana univ math j 59 4 1361 1403 2010 we analyze the relation between the variation of the eigenvalue and the nodal structure of the associated eigenfunctions we deal with planar domains with dirichlet boundary conditions and we focus on the case when the singular pole approaches the boundary of the domain then the operator loses its singular character and the k th magnetic eigenvalue converges to that of the standard laplacian we can predict both the rate of convergence and whether the convergence happens from above or from below in relation with the number of nodal lines of the k th eigenfunction of the laplacian the proof relies on the variational characterization of eigenvalues together with a detailed asymptotic analysis of the eigenfunctions based on an almgren type frequency formula for magnetic eigenfunctions and on the blow up technique

new axiomatisations of discrete quantitative and qualitative possibilistic integrals necessity resp possibility measures are very simple min decomposable resp max decomposable representations of epistemic uncertainty due to incomplete knowledge they can be used in both quantitative and qualitative settings in the present work we revisit choquet and sugeno integrals as criteria for decision under uncertainty and propose new axioms when uncertainty is representable in possibility theory first a characterization of choquet integral with respect to a possibility or a necessity measure is proposed we respectively add an optimism or a pessimism axiom to the axioms of the choquet integral with respect to a general capacity this new axiom enforces the maxitivity or the minitivity of the capacity without requiring the same property for the functional it essentially assumes that the decision maker preferences only reflect the plausibility ordering between states of nature the obtained pessimistic resp optimistic criterion is an average maximin resp maximax criterion of wald across cuts of a possibility distribution on the state space the additional axiom can be also used in the axiomatic approach to sugeno integral and generalized forms thereof to justify possibility and necessity measures the axiomatization of these criteria for decision under uncertainty in the setting of preference relations among acts is also discussed we show that the new axiom justifying possibilistic choquet integrals can be expressed in this setting in the case of sugeno integral we correct a characterization proof for an existing set of axioms on acts and study an alternative set of axioms based on the idea of non compensation

a unified approach to define fuzzy integrals recently the two most general and well known fuzzy integrals sugeno s integral and choquet s integral were characterized it was also shown how both integrals fitted the same formal model and they only differed in the operators used in this paper we try to analyze whether it is possible to improve those characterization theorems and we also study the possibility of defining other fuzzy integrals following the same model but using other operators in a recent paper campos and bolafios 6 characterized two general and well known fuzzy integrals sugeno s integral 11 and choquet s integral 7 the last one also called monotone expectation 2 4 5 6 the two characterization theorems are based on the same formal model of four properties which only differ in the operators used sum and product for choquet s integral maximum and minimum for sugeno s integral two important questions remained open one involved the characterization theorems of these integrals in an attempt to further refine them the second question was to investigate the possibility of defining other fuzzy integrals using different operators but following the same model in this paper we give answers to those problems section 2 is devoted to describing fuzzy integrals defined on sugeno s fuzzy measures particularly sugeno s and choquet s integrals and their characterizations in section 3 we show how the characterization of choquet s integral can be refined whereas the same cannot be made for sugeno s integral finally other fuzzy integrals fitting our formal model are obtained in section 4

on nonlinear functional spaces based on triangular conorms abstract in this paper we discuss the nonlinear functional spaces based on triangular conorms particularly we discuss the properties of the upper closures of the regular subspaces of the nonlinear functional space based on a continuous triangular conorm furthermore we prove that with respect to a strict triangular conorm a subset of the nonlinear functional space is an upper complete normal subspace if and only if the family of all sets whose characteristic functionals are contained in the given subset of the nonlinear functional space is a sigma algebra

scalar curvature deformation and a gluing construction for the einstein constraint equations on a compact manifold the scalar curvature map at generic metrics is a local surjection f m we show that this result may be localized to compact subdomains in an arbitrary riemannian manifold the method is extended to establish the existence of asymptotically flat scalar flat metrics on n n 3 which are spherically symmetric hence schwarzschild at infinity i e outside a compact set such metrics provide cauchy data for the einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically schwarzschild near spatial infinity

lower bounds for the first eigenvalue of the magnetic laplacian abstract we consider a riemannian cylinder endowed with a closed potential 1 form a and study the magnetic laplacian a with magnetic neumann boundary conditions associated with those data we establish a sharp lower bound for the first eigenvalue and show that the equality characterizes the situation where the metric is a product we then look at the case of a planar domain bounded by two closed curves and obtain an explicit lower bound in terms of the geometry of the domain we finally discuss sharpness of this last estimate

qualitative decision theory with preference relations and comparative uncertainty an axiomatic approach this paper investigates a purely qualitative approach to decision making under uncertainty since the pioneering work of savage most models of decision under uncertainty rely on a numerical representation where utility and uncertainty are commensurate giving up this tradition we relax this assumption and introduce an axiom of ordinal invariance requiring that the decision maker s preference between two acts only depends on the relative position of their consequences for each state within this qualitative framework we determine the only possible form of the corresponding decision rule then assuming the transitivity of the strict preference the underlying partial confidence relations are those at work in non monotonic inference and thus satisfy one of the main properties of possibility theory the satisfaction of additional postulates of unanimity and anonymity enforces the use of a necessity measure unique up to a monotonic transformation for encoding the relative likelihood of events

lexicographic refinements in possibilistic decision trees and finite horizon markov decision processes possibilistic decision theory has been proposed twenty years ago and has had several extensions since then even though ap pealing for its ability to handle qualitative decision problems possibilisticdecision theory suffers from an important drawback qualitative possibilistic utility criteria compare acts through min and max operators which leads to a drowning effect to over come this lack of decision power of the theory several refinements have been proposed lexicographic refinements are particularly appealing since they allow to benefit from the expected utility background while remaining qualitative this article aims at extend ing lexicographic refinements to sequential decision problems i e to possibilistic decision trees and possibilistic markov decision processes when the horizon is finite we present two criteria that refine qualitative possibilistic utilities and provide dynamic programming algorithms for calculating lexicographically optimal policies

characterization and comparison of sugeno and choquet integrals abstract starting from the concept of equiordered functions we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure sugeno and choquet integrals the characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals pointing out their formal similarities and their conceptual differences

on the use of aggregation operations in information fusion processes this position paper discusses the role of the existing body of fuzzy set aggregation operations in various kinds of problems where the process of fusion of items coming from several sources is central several kinds of membership functions can be useful according to the nature of the information to be merged numerical vs ordinal inputs preferences vs uncertain data observations vs constraints in each case some aggregation operations look more plausible or feasible than others the aim of this discussion is to suggest directions for putting at work the results of recent mathematical investigations in the structure of aggregation operations

complexity results and algorithms for possibilistic influence diagrams in this article we present the framework of possibilistic influence diagrams pid which allows to model in a compact form problems of sequential decision making under uncertainty when only ordinal data on transitions likelihood or preferences are available the graphical part of a pid is exactly the same as that of usual influence diagrams however the semantics differ transition likelihoods are expressed as possibility distributions and rewards are here considered as satisfaction degrees expected utility is then replaced by anyone of the two possibilistic qualitative utility criteria optimistic and pessimistic for evaluating strategies in a pid we then describe decision tree based methods for evaluating pid and computing optimal strategies and we study the computational complexity of pid optimisation problems for both cases finally we propose a dedicated variable elimination algorithm that can be applied to both optimistic and pessimistic cases for solving pid

possibility and necessity measure specification using modifiers for decision making under fuzziness in this paper we propose an approach to possibility and necessity measure specification this approach is more adequate to human reasoning than direct specification of conjunction and implication functions using the proposed approach a possibility measure is specified by two modifier functions and a strong negation while a necessity measure is specified by two modifier functions only it is demonstrated that many possibility and necessity measures defined by famous conjunction and implication functions are obtained by the proposed approach conditions for specified measures to have good properties are also given finally a simple example of application of possibility and necessity measures to a decision problem is given

interval linear systems as a necessary step in fuzzy linear systems this article clarifies what it means to solve a system of fuzzy linear equations relying on the fact that they are a direct extension of interval linear systems of equations already studied in a specific interval mathematics literature we highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals each of which based on a generalization of scalar equality to intervals each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals we also consider the smallest multidimensional intervals containing the solution sets we propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals this unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies

a simple axiomatization of nonadditive expected utility textabstractthis paper provides an extension of savage s subjective expected utility theory for decisions under uncertainty it includes in the set of events both unambiguous events for which probabilities are additive and ambiguous events for which probabilities are permitted to be nonadditive the main axiom is cumulative dominance which adapts stochastic dominance to decision making under uncertainty we derive a choquet expected utility representation and show that a modification of cumulative dominance leads to the classical expected utility representation the relationship of our approach with that of schmeidler who uses a two stage formulation to derive choquet expected utility is also explored our work may be viewed as a unification of schmeidler 1989 and gilboa 1987

handling uncertainty in route choice models from probabilistic to possibilistic approaches abstract in order to design effective advanced traffic information systems atis suitable mathematical models have to be defined to simulate the effects of information on users route choice behaviour and then to incorporate it into traffic assignment models to estimate how traffic demand loads the roads network to face this problem it is necessary to deal with uncertainty that plays a crucial role in the users decision making processes to this purpose this paper first analyses how uncertainty affects users route choice process and how traffic assignment models may take it into account in literature route choice behaviour modelling is widely solved within the random utility theory framework but we show in this paper that such an approach only considers one type of uncertainty more precisely the consideration of randomness of traffic by drivers is for example hardly ever represented in classical models in spite of its importance in the management of information by drivers starting from the presented analysis a new route choice model is also proposed to represent explicitly the uncertainty lying in users route choice behaviour it is based on recent developments in possibility theory which is an alternate way to probability theory in order to represent or measure uncertainty

continuous time fuzzy decision processes with discounted rewards a continuous time decision process with fuzzy transitions which is termed fuzzy decision process is discussed from a viewpoint of a dynamic fuzzy system by the authors the discounted total reward is given by a fuzzy number and is discussed by the fuzzy max order this paper gives the optimality equation for the fuzzy decision model by a fuzzy differential equation the optimization problem of the discounted total rewards is also discussed by a fuzzy expectation generated from a fuzzy goal and an optimal policy and the permissible range of the decision maker s optimal expected payoffs are given for this problem also an illustrated example is given to explain the idea of the paper

subjective foundation of possibility theory this paper presents a new characterization of subjective possibility theory anscombe and aumann 1 pioneered a multiple variable approach to characterize the subjective probability on the basis of its relationship with objective probability we generalize the anscombe aumann approach to define subjective possibility theory to characterize the uncertainty of the variable of interest h we consider its relationship with a variable of probability and a variable of ignorance our axiomatization assumes that the preference over the acts contingent on the outcomes of the variables is a weak order and satisfies a monotonicity property the preference over probabilistic lotteries is represented by linear utility and the preference over acts under ignorance by a recently developed anchor utility theory we show that if h and the variable of ignorance are completely reversible in anscombe aumann s sense and h and the variable of probability are partially reversible then the uncertainty of h must obey the laws of possibility theory we outline a framework to manage heterogeneous uncertainty that includes probability possibility and ignorance in decision making

subjective probability and expected utility without additivity comonotic acts are defined and an axiom of comonotomic independence 19 introduced that weakens the von newmann morgenstern axiom of independence if a nondegenerate continuous and monotonic state independent weak order over acts satisfies comonotonic independence then it induces a unique non necessarily additive probability and a von neumann morgenstern utility an extension of theexpected utility theory covers situations as the ellsberg paradox which are inconsistent with additive expected utility the concept of uncertainty aversion and interpretation of comonotonic independence in the context of social welfare functions are included

sharp boundary behavior of eigenvalues for aharonov bohm operators with varying poles abstract in this paper we investigate the behavior of the eigenvalues of a magnetic aharonov bohm operator with half integer circulation and dirichlet boundary conditions in a bounded planar domain we establish a sharp relation between the rate of convergence of the eigenvalues as the singular pole is approaching a boundary point and the number of nodal lines of the eigenfunction of the limiting problem i e of the dirichlet laplacian ending at that point the proof relies on the construction of a limit profile depending on the direction along which the pole is moving and on an almgren type monotonicity argument for magnetic operators