expected utility versus anticipated utility where do we stand abstract as is now widely admitted the expected utility hypothesis as a pattern of rational decision under risk or uncertainty is severely put into question many alternative models have been suggested which however may seem difficult to submit to comparative evaluations after giving a summary account of the issues involved the present paper aims at selecting among these models with the help of recent experimental evidence recent mathematical results and some epistemological arguments as a result the dichotomic models of decision under risk also called anticipated utility or rank dependent utility models independently designed by m allais j quiggin and m yaari appear as gathering strongest support

goal based portfolio choice model with discounted preference abstract this paper proposes goal based portfolio selection model with discounted preference firstly we discuss the goal based portfolio selection problem and then modify the portfolio selection model based on cumulative prospect theory cpt as well as considering investors discounted preference in psychology furthermore our proposed model is solved by martingale methods and an analytical solution with satisfying behavior is derived finally we select six different discounting functions to capture investors strategic changes numerical results show that investor with future bias performs adequate confidence and patience whereas investor with present bias tends to the immediate interests

equal relation between the extra connectivity and pessimistic diagnosability for some regular graphs abstract extra connectivity and the pessimistic diagnosis are two crucial subjects for a multiprocessor system s ability to tolerate and diagnose faulty processor the pessimistic diagnosis strategy is a classic strategy based on the pmc model in which isolates all faulty vertices within a set containing at most one fault free vertex in this paper the result that the pessimistic diagnosability t p g equals the extra connectivity 1 g of a regular graph g under some conditions are shown furthermore the following new results are gotten the pessimistic diagnosability t p s n 2 4 n 9 for split star networks s n 2 t p n 2 n 4 for cayley graphs generated by transposition trees n t p n 4 n 11 for cayley graph generated by the 2 tree n t p b p n 2 n 2 for the burnt pancake networks b p n as corollaries the known results about the extra connectivity and the pessimistic diagnosability of many famous networks including the alternating group graphs the alternating group networks bc networks the k ary n cube networks etc are obtained directly

dynamic decision making without expected utility an operational approach non expected utility theories such as rank dependent utility rdu theory have been proposed as alternative models to eu theory in decision making under risk these models do not share the separability property of expected utility theory this implies that in a decision tree if the reduction of compound lotteries assumption is made so that preferences at each decision node reduce to rdu preferences among lotteries and that preferences at different decision nodes are identical same utility function and same weighting function then the preferences are not dynamically consistent in particular the sophisticated strategy i e the strategy generated by a standard rolling back of the decision tree is likely to be dominated w r t stochastic dominance dynamic consistency of choices remains feasible and the decision maker can avoid dominated choices by adopting a non consequentialist behavior with his choices in a subtree possibly depending on what happens in the rest of the tree we propose a procedure which i although adopting a non consequentialist behavior involves a form of rolling back of the decision tree ii selects a non dominated strategy that realizes a compromise between the decision maker s discordant goals at the different decision nodes relative to the computations involved in the standard expected utility evaluation of a decision problem the main computational increase is due to the identification of non dominated strategies by linear programming a simulation using the rank dependent utility criterion confirms the computational tractability of the model

optimal investments for robust utility functionals in complete market models this paper introduces a systematic approach to the problem of maximizing the robust utility of the terminal wealth of an admissible strategy in a general complete market model where the robust utility functional is defined by a set q of probability measures our main result shows that this problem can often be reduced to determining a least favorable measure q0 q which is universal in the sense that it does not depend on the particular utility function the robust problem is thus equivalent to a standard utility maximization problem with respect to the subjective probability measure q0 by using the huber strassen theorem from robust statistics it is shown that q0 always exists if q is the i core of a 2 alternating capacity besides other examples we also discuss the problem of robust utility maximization with uncertain drift in a black scholes market and the case of weak information

on 3 extra connectivity and 3 extra edge connectivity of folded hypercubes given a graph mbi g and a non negative integer g the g extra connectivity resp g extra edge connectivity of mbi g is the minimum cardinality of a set of vertices resp edges in mbi g if it exists whose deletion disconnects mbi g and leaves each remaining component with more than g vertices this study shows that the 3 extra connectivity resp 3 extra edge connectivity of an mbi n dimensional folded hypercube is 4 n 5 for n geq 6 resp 4 n 4 for n geq 5 this study also provides an upper bound for the g extra connectivity on folded hypercubes for g geq 6

preference foundations for nonexpected utility a generalized and simplified technique this paper examines a tradeoff consistency technique for testing and axiomatically founding decision models the technique modifies earlier tradeoff consistency techniques by only considering indifferences not strict preferences the resulting foundations are both more general and more accessible than earlier results and they are so regarding both the technical and the intuitive axioms axiomatizations based on other bisymmetry like conditions also follow as corollaries from the results of this paper the tradeoff technique is applied to three popular theories of individual decision under uncertainty and risk i e expected utility choquet expected utility and prospect theory the conditions used are better suited for empirical measurements of utility than earlier tradeoff conditions and accordingly are easier to test

the t k diagnosability of the bc graphs processor fault diagnosis takes an important role in fault tolerant computing on multiprocessor systems there are two classical diagnosis strategies the precise strategy and the pessimistic strategy both of which are based on the well known pmc diagnostic model nevertheless the degree of diagnosability of the system is limited under these two strategies a better method called the t k diagnosis strategy is proposed by somani and peleg in which the identified fault set is allowed to contain at most k fault free processors using this diagnosis strategy the degree of diagnosability of the hypercube increases greatly as the number of the fault free processors in the fault set increases we study the t k diagnosability of so called bc graphs that include hypercubes crossed cubes mobius cubes and twisted cubes etc we show that any n dimensional bc graph is t n k k diagnosable when n spl ges 4 and 0 spl les k spl les n where t n k k 1 n 1 2 k 1 k 2 1 therefore the crossed cube the mobius cube and the twisted cube all have the same t k diagnosability as the hypercube as a result the algorithms developed for diagnosis on the hypercube may also be used to diagnose multiprocessor systems whose network topologies are based on bc graphs

risk ambiguity and the separation of utility and beliefs we introduce a general model of static choice under uncertainty arguably the weakest model achieving a separation of cardinal utility and a unique representation of beliefs most of the nonexpected utility models existing in the literature are special cases of it such separation is motivated by the view that tastes are constant whereas beliefs change with new information the model has a simple and natural axiomatization elsewhere forthcoming we show that it can be very helpful in the characterization of a notion of ambiguity aversion as separating utility and beliefs allows us to identify and remove aspects of risk attitude from the decision maker s behavior here we show that the model allows us to generalize several results on the characterization of risk aversion in betting behavior these generalizations are of independent interest as they show that some traditional results for subjective expected utility preferences can be formulated only in terms of binary acts

a parameter free elicitation of the probability weighting function in medical decision analysis an important reason why people violate expected utility theory is probability weighting previous studies on the probability weighting function typically assume a specific parametric form exclude heterogeneity in individual preferences and exclusively consider monetary decision making this study presents a method to elicit the probability weighting function in rank dependent expected utility theory that makes no prior assumptions about the functional form of the probability weighting function we use both aggregate and individual subject data thereby allowing for heterogeneity of individual preferences and we examine probability weighting in a new domain medical decision making there is significant evidence of probability weighting both at the aggregate and at the individual subject level the modal probability weighting function is inverse s shaped displaying both lower subadditivity and upper subadditivity probability weighting is in particular relevant at the boundaries of the unit interval compared to studies involving monetary outcomes we generally find more elevation of the probability weighting function the robustness of the empirical findings on probability weighting indicates its importance ignoring probability weighting in modeling decision under risk and in utility measurement is likely to lead to descriptively invalid theories and distorted elicitations

consistent modeling of risk averse behavior with spectral risk measures this paper introduces a new method for modeling risk averse behavior with spectral risk measures it is shown that recent approaches using phenomenological correspondences or results from robust statistics generally do not generate consistent results our method is based on the dual theory of choice we show that it is possible to encode preference relations in distorted probability measures which themselves induce admissible spectral risk measures this way risk averse behavior can be mapped onto the risk spectrum defining a spectral risk measure and can be quantified using a local pratt arrow like coecient

computation of convex bounds for present value functions with random payments in this contribution we study the distribution of the present value function of a series of random payments in a stochastic financial environment such distributions occur naturally in a wide range of applications within fields of insurance and finance we obtain accurate approximations by developing upper and lower bounds in the convex order sense for present value functions technically speaking our methodology is an extension of the results of dhaene et al insur math econom 31 1 2002 3 33 insur math econom 31 2 2002 133 161 to the case of scalar products of mutually independent random vectors

conditional diagnosability of alternating group graphs let an be the alternating group of degree n with n 3 set s 1 2 i 1 i 2 3 i n the alternating group graph denoted by agn is defined as the cayley graph on an with respect to s jwo et al networks 23 1993 315 326 introduced alternating group graph agn as an interconnection network topology for computing systems conditional diagnosability a new measure of diagnosability introduced by lai et al ieee transactions on computers 54 2 2005 165 175 can better measure the diagnosability of regular interconnection networks this paper determines that under pmc model the conditional diagnosability of agn is 4 for n 4 and 6n 18 for each n 5

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

great expectations part ii generalized expected utility as a universal decision rule many different rules for decision making have been introduced in the literature we show that a notion of generalized expected utility proposed in f chu j y halpern great expectation part i on the customizability of generalized expected utility in proc ijcai 03 acapulco mexico 2003 is a universal decision rule in the sense that it can essentially all other decision rules this approach gives us a general technique for designing new decision rules as well as providing a framework for comparing decision rules to each other

the extra connectivity of bubble sort star graphs connectivity plays an important role in measuring the fault tolerance of a multiprocessor system in the case of vertices failures extra connectivity is an important indicator of a network s ability for diagnosis and fault tolerance in this paper we analyze the fault tolerance ability of the bubble sort star network denoted by b s n a well known interconnection network proposed for multiprocessor systems and establish the g extra connectivity for 1 g 3

risk preferences on the space of quantile functions we propose a novel approach to quantification of risk preferences on the space of nondecreasing functions when applied to law invariant risk preferences among random variables it compares their quantile functions the axioms on quantile functions impose relations among comonotonic random variables we infer the existence of a numerical representation of the preference relation in the form of a quantile based measure of risk using conjugate duality theory by pairing the banach space of bounded functions with the space of finitely additive measures on a suitable algebra varsigma we develop a variational representation of the quantile based measures of risk furthermore we introduce a notion of risk aversion based on quantile functions which enables us to derive an analogue of kusuoka representation of coherent law invariant measures of risk

inverse stochastic dominance constraints and rank dependent expected utility theory we consider optimization problems with second order stochastic dominance constraints formulated as a relation of lorenz curves we characterize the relation in terms of rank dependent utility functions which generalize yaari s utility functions we develop optimality conditions and duality theory for problems with lorenz dominance constraints we prove that lagrange multipliers associated with these constraints can be identified with rank dependent utility functions the problem is numerically tractable in the case of discrete distributions with equally probable realizations

incremental elicitation of choquet capacities for multicriteria choice ranking and sorting problems this paper proposes incremental preference elicitation methods for multicriteria decision making with a choquet integral the choquet integral is an evaluation function that performs a weighted aggregation of criterion values using a capacity function assigning a weight to any coalition of criteria thus enabling positive and or negative interactions among them and covering an important range of possible decision behaviors however the specification of the capacity involves many parameters which raises challenging questions both in terms of elicitation burden and guarantee on the quality of the final recommendation in this paper we investigate the incremental elicitation of the capacity through a sequence of preference queries questions selected one by one using a minimax regret strategy so as to progressively reduce the set of possible capacities until the regret the worst case loss due to reasoning with only partially specified capacities is low enough we propose a new approach designed to efficiently compute minimax regret for the choquet model and we show how this approach can be used in different settings 1 the problem of recommending a single alternative 2 the problem of ranking alternatives from best to worst and 3 sorting several alternatives into ordered categories numerical experiments are provided to demonstrate the practical efficiency of our approach for each of these situations

on fault identification in diagnosable systems this paper begins by giving a characterization of t1 t1 diagnosable systems then a class of t0 diagnosable systems denoted by d n t0 x is considered it is shown for any member of this class that 1 necessary and sufficient conditions for t1 t1 diagnosability are greatly simplified 2 optimal diagnosis algorithms of time complexity 0 nt0 exist and most importantly 3 given the test results any set f of faults with f t1 can be identified to within a set f with f f and f min t1 f 1

response of the parameters of a neural network to pseudoperiodic time series abstract we propose a representation plane constructed from parameters of a multilayer neural network with the aim of characterizing the dynamical character of a learned time series we find that fluctuation of this plane reveals distinct features of the time series specifically a periodic representation plane corresponds to a periodic time series even when contaminated with strong observational noise or dynamical noise we present a theoretical explanation for how the neural network training algorithm adjusts parameters of this representation plane and thereby encodes the specific characteristics of the underlying system this ability which is intrinsic to the architecture of the neural network can be employed to distinguish the chaotic time series from periodic counterparts it provides a new path toward identifying the dynamics of pseudoperiodic time series furthermore we extract statistics from the representation plane to quantify its character we then validate this idea with various numerical data generated by the known periodic and chaotic dynamics and experimentally recorded human electrocardiogram data

the dual theory of choice under risk in this essay a new theory of choice under risk is being proposed it is a theory which in a sense that will become clear is dual to expected utility theory hence the title dual theory risky prospects are evaluated in this theory by a cardinal numerical scale which resembles an expected utility except that the roles of payments and probabilities are reversed this theme the reversal of the roles of probabilities and payments will recur throughout the paper i should emphasize that playing games with probabilities masquerading as payments and payments masquerading as probabilities is not my object rather i hope to convince the reader that the dual theory has intrinsic economic significance and that in some areas its predictions are superior to those of expected utility theory while in other areas the reverse will be the case two reasons have prompted me to look for an alternative to expected utility theory the first reason is methodological in expected utility theory the agent s attitude towards risk and the agent s attitude towards wealth are forever bonded together at the level of fundamental principles risk aversion and diminishing marginal utility of wealth which are synonymous under expected utility theory are horses of different colors the former expresses an attitute towards risk increased uncertainty hurts while the latter expresses an attitude towards wealth the loss of a sheep hurts more when the agent is poor than when the agent is rich a question arises therefore as to whether these two notions can be kept separate from each other in a full fledged theory of cardinal utility the dual theory will have this property the second reason that leads me to look for an alternative to expected utility theory is empirical behavior patterns which are systematic yet inconsistent with expected utility theory have often been observed two prominent references among many others are allais 1953 and kahneman tversky 1979 so deeply

what common ground exists for descriptive prescriptive and normative utility theories descriptive and normative modeling of decision making under risk and uncertainty have grown apart over the past decade psychological models attempt to accommodate the numerous violations of rationality axioms including independence and transitivity meanwhile normatively oriented decision analysts continue to insist on the applied usefulness of the subjective expected utility seu model as this gap has widened two facts have remained largely unobserved first most people in real situations attempt to behave in accord with the most basic rationality principles even though they are likely to fail in more complex situations second the seu model is likely to provide consistent and rational answers to decision problems within a given problem structure but may not be invariant across structures thus people may be more rational than the psychological literature gives them credit for and applications of the seu model may be susceptible to some violations of invariance principles this paper attempts

stochastic comparisons of residual lifetimes and inactivity times of coherent systems with dependent identically distributed components abstract in this paper we compare the residual lifetime of a used coherent system of age t 0 with the lifetime of the similar coherent system made up of used components of age t here similar means that the system has the same structure and the component lifetimes have the same dependence joint reliability copula some comparison results are obtained for the likelihood ratio order failure rate order reversed failure rate order and the usual stochastic order similar results are reported for comparing inactivity time of a coherent system with lifetime of similar coherent system having component lifetimes same as inactivity times of failed components

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

risk aversion in cumulative prospect theory this paper characterizes the conditions for strong risk aversion and second order stochastic dominance for cumulative prospect theory strong risk aversion implies a convex weighting function for gains and a concave one for losses it does not necessarily imply a concave utility function the latter does follow if the weighting functions are continuous by investigating the exact relationship between loss aversion and strong risk aversion a natural index for the degree of loss aversion is derived

probability weighting and l moments abstract several popular generalizations of expected utility theory cumulative prospect theory rank dependent utility and yaari s dual model allow for non linear transformation of de cumulative probabilities this paper shows an unexpected connection between probability weighting and the statistical theory of l moments specifically cubic probability weighting results in a linear tradeoff between the expected value the first l moment gini 1912 mean difference statistic the second l moment also known as l scale and the third l moment measuring skewness inverse s shaped probability weighting function crossing the 45 line at a probability 0 5 reflects an aversion to the dispersion of outcomes and an attraction to positively skewed distributions

a behavioral foundation for fuzzy measures in savage 41 a behavioral foundation was given for subjective probabilities to be used in the maximization of expected utility this paper analogously gives a behavioral foundation for fuzzy measures to be used in the maximization of choquet expected utility this opens the way to empirical verification or falsification of fuzzy measures and frees them of their ad hoc character

orienting cayley graphs generated by transposition trees day and tripathi k day a tripathi unidirectional star graphs inform process lett 45 1993 123 129 proposed an assignment of directions on the star graphs and derived attractive properties for the resulting directed graphs cheng and lipman e cheng m j lipman on the day tripathi orientation of the star graphs connectivity inform process lett 73 2000 5 10 e cheng m j lipman connectivity properties of unidirectional star graphs congr numer 150 2001 33 42 studied the connectivity properties of these unidirectional star graphs the class of star graphs is a special case of cayley graphs generated by transposition trees in this paper we give directions on these graphs and study the connectivity properties of the resulting unidirectional graphs

choquet based optimisation in multiobjective shortest path and spanning tree problems this paper is devoted to the search of choquet optimal solutions in finite graph problems with multiple objectives the choquet integral is one of the most sophisticated preference models used in decision theory for aggregating preferences on multiple objectives we first present a condition on preferences name hereafter preference for interior points that characterizes preferences favouring compromise solutions a natural attitude in various contexts such as multicriteria optimisation robust optimisation and optimisation with multiple agents within choquet expected utility theory this condition amounts to using a submodular capacity and a convex utility function under these assumptions we focus on the fast determination of choquet optimal paths and spanning trees after investigating the complexity of these problems we introduce a lower bound for the choquet integral computable in polynomial time then we propose different algorithms using this bound either based on a controlled enumeration of solutions ranking approach or an implicit enumeration scheme branch and bound finally we provide numerical experiments that show the actual efficiency of the algorithms on multiple instances of different sizes

temporal resolution of uncertainty and recursive non expected utility models if an agent weakly prefers early resolution of uncertainty then the recursive forms of both the most commonly used non expected utility models betweenness and rank dependence almost reduce to kreps porteus s 1978 recursive expected utility

from fuzzy set theory to non additive probabilities how have economists reacted abstract in this paper we are going to try to conduct a comparative review of the two programmes devoted to the application of fuzzy sets theory in economics for the first and to nonadditive probabilities for the second while putting forward some explanations and conjecture as to their development and their future in section 1 we defend the thesis which claims that the first programme has only had a global focus on the approach in terms of generalization and we shall go deeper into the analysis of the particular area of general equilibrium as it is the programme on which ponsard worked the most in section 2 we shall seek to show that the second programme devoted to the introduction of nonadditive probabilities in decision theory on the contrary has attempted to come up with independent findings this would explain why this last programme has managed to fit into topics at a standstill or in crisis easily which is undeniably the case of the standard theory of decision making while the first programme was only envisaged as a kind of mathematical game involving the application of new rules to an old model in the case of the first programme one might thus speak of an extension principle and in the second case of a resolution principle

optimization with stochastic preferences based on a general class of scalarization functions it is of crucial importance to develop risk averse models for multicriteria decision making under uncertainty a major stream of the related literature studies optimization problems that feature multivariate stochastic benchmarking constraints these problems typically involve a univariate stochastic preference relation often based on stochastic dominance or a coherent risk measure such as conditional value at risk which is then extended to allow the comparison of random vectors by the use of a family of scalarization functions all scalarized versions of the vector of the uncertain outcomes of a decision are required to be preferable to the corresponding scalarizations of the benchmark outcomes while this line of research has been dedicated almost entirely to linear scalarizations the corresponding deterministic literature uses a wide variety of scalarization functions that among other advantages offer a high degree of modeling flexibility in this paper we aim to incorporate these scalarizations i

a genuine rank dependent generalization of the von neumann morgenstern expected utility theorem this paper uses revealed probability trade offs to provide a natural foundation for probability weighting in the famous von neumann and morgenstern axiomatic set up for expected utility in particular it shows that a rank dependent preference functional is obtained in this set up when the independence axiom is weakened to stochastic dominance and a probability trade off consistency condition in contrast with the existing axiomatizations of rank dependent utility the resulting axioms allow for complete flexibility regarding the outcome space consequently a parameter free test elicitation of rank dependent utility becomes possible the probability oriented approach of this paper also provides theoretical foundations for probabilistic attitudes towards risk it is shown that the preference conditions that characterize the shape of the probability weighting function can be derived from simple probability trade off conditions

fuzzy sets spl minus a convenient fiction for modeling vagueness and possibility this paper is a reply to laviolette and seaman s critical discussion of fuzzy set theory rather than questioning the interest of the bayesian approach to uncertainty some reasons why bayesian find the idea of a fuzzy set not palatable are laid bare some links between fuzzy sets and probability that laviolette and seaman seem not to be aware of are pointed out these links suggest that contrary to the claim sometimes found in the literature probability theory is not a special case of fuzzy set theory the major objection to laviolette and seaman is that they found their critique on as very limited view of fuzzy sets including debatable papers while they fail to account for significant works pertaining to axiomatic derivation of fuzzy set connectives possibility theory fuzzy random variables among others

generalized evaluation in decision analysis the paper presents a discussion on evaluation methods in decision analysis the presentation begins with the discussion of the expected value rule for selection amongst a number of available courses of action then a number of other evaluation rules to either replace or supplement the expected value are presented they are discussed from a choice rather than preference view to improve the expected value rule or any other similar rule it is suggested that it should be supplemented with other qualitative rules rather than engaging in further modifications in pursuit of the perfect rule a characteristic of qualitative rules is that they do not rely on multiplying probabilities and values but treat them as separate numeric entities once a rule has been agreed upon it can be applied to all the alternatives provided there is a computational procedure for evaluating the alternatives under that rule delta dominance is introduced as a unifying concept for many of the dominance rules in current use dominance and threshold methods are discussed and the kinship between them is pointed out

a kind of conditional vertex connectivity of cayley graphs generated by 2 trees let g be a graph then t v g is called an r k vertex cut if g t is disconnected and each vertex in v g t has at least k neighbors in g t the size of a smallest r k vertex cut is the r k vertex connectivity of g and is denoted by k k g in this paper we determine the numbers k 1 and k 2 for cayley graphs generated by 2 trees including the popular alternating group graphs

comonotonicity and choquet integrals of hermitian operators and their applications in a quantum system with d dimensional hilbert space the q function of a hermitian positive semidefinite operator is defined in terms of the d 2 coherent states in this system the choquet integral of the q function of is introduced using a ranking of the values of the q function and mobius transforms which remove the overlaps between coherent states it is a figure of merit of the quantum properties of hermitian operators and it provides upper and lower bounds to various physical quantities in terms of the q function comonotonicity is an important concept in the formalism which is used to formalize the vague concept of physically similar operators comonotonic operators are shown to be bounded with respect to an order based on choquet integrals applications of the formalism to the study of the ground state of a physical system are discussed bounds for partition functions are also derived

mixture symmetry and quadratic utility the independence axiom of expected utility theory has recently been weakened to the betweenness axiom in this paper an even weaker axiom called mixture symmetry is presented the corresponding functional structure is such that utility is a betweenness functional on part of its domain and quadratic in probabilities elsewhere the experimental evidence against betweenness provides one motivation for the more general theory presented here another advantage of the mixture symmetric class of utility functions is that it is sufficiently flexible to permit the disentangling of attitudes towards risk and towards randomization

extraconnectivity of k ary n cube networks given a graph g and a non negative integer g the g extraconnectivity of g is the minimum cardinality of a set of vertices in g if such a set exists whose deletion disconnects g and leaves every remaining component with more than g vertices this study shows that the 2 extraconnectivity of a k ary n cube q n k for k 4 and n 5 is equal to 6n 5

equilibrium routing under uncertainty we provide a brief introduction to the basic models used to describe traffic on congested networks both in urban transport and telecommunications we discuss traffic equilibrium models covering atomic and non atomic routing games with emphasis on situations where the travel times are subject to random fluctuations we use convex optimization to present the models in a unified framework that stresses the common underlying structures as a prototypical example of traffic equilibrium with elastic demands we discuss some models for routing and congestion control in telecommunications we also describe a class of stochastic dynamics that model the adaptive behavior of agents and which provides a plausible micro foundation for the equilibrium finally we present some recent ideas on how risk averse behavior might be incorporated in the equilibrium models

additivizations of nonadditive measures the concept of an additivization of a nonadditive probability measure is introduced and studied the relation to cooperative game theory is explored and it is shown that in many cases of interest additivizations may be considered as a special type of semivalues

additive consistency of risk measures and its application to risk averse routing in networks we investigate the use of risk measures and theories of choice to model risk averse routing and traffic equilibrium on networks with random travel times we interpret the postulates of these theories in the context of routing identifying additive consistency as a plausible condition that allows to reduce risk averse route choice to a standard shortest path problem within the classical theories of choice we show that the only preferences that satisfy this condition are the ones induced by the entropic risk measures

unbounded utility for savage s foundations of statistics and other models a general procedure for extending finite dimensional additive like representations for binary relations to infinite dimensional integral like representations is developed by means of a condition called truncation continuity the restriction of boundedness of utility met throughout the literature can now be dispensed with and for instance normal distributions or any other distribution with finite first moment can be incorporated classical representation results of expected utility such as savage 1954 von neumann and morgenstern 1944 anscombe and aumann 1963 de finetti 1937 and many others can now be extended the results are generalized to schmeidler s 1989 approach with nonadditive measures and choquet integrals and quiggin s 1982 rank dependent utility the different approaches have been brought together in this paper to bring to the fore the unity in the extension process

common mathematical foundations of expected utility and dual utility theories we show that the main results of the expected utility and dual utility theories can be derived in a unified way from two fundamental mathematical ideas the separation principle of convex analysis and integral representations of continuous linear functionals from functional analysis our analysis reveals the dual character of utility functions we also derive new integral representations of dual utility models

new models of decision under uncertainty an interpretative essay the theory of decision under risk and uncertainty has taken a new course in the last ten years the present paper puts these developments into perspective it briefly recalls the experimental results obtained and sketches some of the most important alternative models suggested to fit these results finally a tentative interpretation of all this research movement is offered

what determines the shape of the probability weighting function under uncertainty decision weights are an important component in recent theories of decision making under uncertainty to better explain these decision weights a two stage approach has been proposed first the probability of an event is judged and then this probability is transformed by the probability weighting function known from decision making under risk we extend the two stage approach by allowing the probability weighting function to depend on the type of uncertainty using this more general approach properties of decision weights can be attributed to properties of probability judgments and or to properties of probability weighting we present an empirical study that shows that it is indeed necessary to allow the probability weighting function to be source dependent the analysis includes an examination of properties of the probability weighting function under uncertainty that have not been considered yet

a unified approach to the monotone integral based premium principles under the cpt theory abstract we consider the relationship between different types of the monotone integral based premium principles as a common frame for the cpt premium principle and the mean premium principle the cpt like integral based premium principle is introduced and characterized the jensen type inequalities for the choquet integral and the cpt like premium principle on the class of non negative risks are proven we establish conditions under which the jensen steffensen type inequalities for the cpt premium principle and the cpt like premium principle hold for risks with finite range

fault tolerance and diagnosability of burnt pancake networks under the comparison model processor fault diagnosis plays an important role in measuring the reliability of a multiprocessor system and the diagnosabilities of many well known multiprocessor systems have been investigated the conditional diagnosability has been widely accepted as a new measure of diagnosability by assuming an additional condition that any faulty set can t contain all the neighbors of any node in a multiprocessor system in this paper we explore algebraic and combinatorial properties of burnt pancake networks and investigate the structural vulnerability as well as super and extra connectivities furthermore we show that the classic diagnosability and the conditional diagnosability of n dimensional burnt pancake network bp n n 4 are n and 3 n 4 respectively algebraic and combinatorial properties of burnt pancake networks are established the structural vulnerability as well as super and extra connectivities are explored the classic and conditional diagnosabilities under the comparison model are derived

a family of transformed copulas with a singular component abstract in this paper we present a family of bivariate copulas obtained by transforming a given copula function by means of two increasing functions named as transformed copula one distinctive characteristic of the transformed copula is its singular component along the main diagonal conditions guaranteeing the transformed function to be a copula function are provided and several classes of the transformed copulas are given the singular component along the main diagonal of the transformed copula is verified and the tail dependence coefficients of transformed copulas are obtained some properties of the transformed copula are discussed such as the total positivity of order 2 and the concordance order finally conditions for the proposed transformation being invariant are given sufficient conditions guaranteeing that the iterative transformation is a copula function are provided and the convergence of the iterative transformation is proved under some conditions