utility function estimation the entropy approach abstract the maximum entropy principle can be used to assign utility values when only partial information is available about the decision maker s preferences in order to obtain such utility values it is necessary to establish an analogy between probability and utility through the notion of a utility density function in this paper we explore the maximum entropy principle to estimate the utility function of a risk averse decision maker

a simple augmented constraint method for multi objective mathematical integer programming problems abstract a simple augmented constraint saugmecon method is put forward to generate all non dominated solutions of multi objective integer programming moip problems the saugmecon method is a variant of the augmented constraint augmecon method proposed in 2009 and improved in 2013 by mavrotas et al however with the saugmecon method all non dominated solutions can be found much more efficiently thanks to our innovations to algorithm acceleration these innovative acceleration mechanisms include 1 an extension to the acceleration algorithm with early exit and 2 an addition of an acceleration algorithm with bouncing steps the same numerical example in lokman and koksalan 2012 is used to illustrate workings of the method then comparisons of computational performance among the method proposed by ozlen and azizog lu 2009 ozlen et al 2013 the method developed by lokman and koksalan 2012 and the saugmecon method are made by solving randomly generated general moip problem instances as well as special moip problem instances such as the mokp and mosp problem instances presented in table 4 in lokman and koksalan 2012 the experimental results show that the saugmecon method performs the best among these methods more importantly the advantage of the saugmecon method over the method proposed by lokman and koksalan 2012 turns out to be increasingly more prominent as the number of objectives increases

interactive group decision making procedure under incomplete information this paper deals with multiple criteria decision making problem with incomplete information when multiple decision makers multiple criteria group decision making mcgdm are involved usually decision makers dms are willing or able to provide only incomplete information because of time pressure lack of knowledge or data and their limited expertise related with problem domain there have been just a few studies considering incomplete information in group settings this incompletely specified information constructs region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable nonlinear programmings hence to handle this difficulty we suggest a method utilizing individual decision results to form group consensus final group consensus ranking toward more agreement of participants can be built through solving a series of linear programmings using individual decision results under group members possibly different weight constraints

two stage lotteries without the reduction axiom preference relations over two stage lotteries are analyzed empirical evidence indicates that decisionmakers do not always behave in accordance with the reduction of compound lotteries axiom but they seem to satisfy a compound independence axiom although the reduction and the compound independence axioms together with continuity imply expected utility theory each of them by itself is compatible with all possible preference relations over simple lotteries using these axioms the author analyzes three different versions of expected utility for two stage lotteries the author suggests several different compound dominance axioms as possible replacements of the reduction axiom which are strictly weaker than the reduction of compound lotteries axiom copyright 1990 by the econometric society

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

judgemental modelling based on geometric least square abstract the analytic hierarchy process developed by t l saaty has received widespread attention in the literature however this has not been without some criticisms including the problems of meaning of consistency and large data requirements this paper addresses the last two problems and presents a new method of calculating preference vectors to the user the procedure is essentially the same but the data requirements can be made less onerous and at the same time feedback is provided permitting a greater understanding of the data inputs preliminary results indicate the acceptability of the proposed methodology

ranking with partial information a method and an application a method is presented for ranking multiattributed alternatives using a weighted additive evaluation function with partial information about the weighting scaling constants the method is applied to evaluate materials for use in nuclear waste containment the paper derives conditions to determine whether a pair of alternatives can be ranked given the partial information about weighting constants and presents an algorithm that partially rank orders the complete set of alternatives based on the pairwise ranking information

mappac as a compromise between outranking methods and maut abstract this article shows that the bicriteria preference indices of the mappac method may be classified in two categories those of a compensatory type in cases of discordant evaluations methodologically in line with the maut approach and those which underline partial dominance relations in cases of concordant evaluations in analogy with noncompensatory outranking methods and with the electre methods in particular mappac may therefore be considered a mixed or intermediate method a sort of compromise between the approaches mentioned above it will also be shown that the aggregated index of mappac is a function not only of the weight of the criteria and of the entity of the difference in evaluation but also all other conditions remaining unvaried of the number of criteria according to which one action is preferred or indifferent with respect to another it is possible to note a number of similarities and differences between the indices of this method and the concordance indices of the electre methods

how to select and how to rank projects the promethee method abstract in this paper we present the promethee methods a new class of outranking methods in multicriteria analysis their main features are simplicity clearness and stability the notion of generalized criterion is used to construct a valued outranking relation all the parameters to be defined have an economic signification so that the decision maker can easily fix them two ways of treatment are proposed it is possible to obtain either a partial preorder promethee i or a complete one promethee ii both on a finite set of feasible actions a comparison is made with the electre iii method the stability of the results given by the two methods is analysed numerical applications are given in order to illustrate the properties of the new methods and some further problems are discussed

risk return and utility expected utility theory is widely acknowledged to be a rational approach to making decisions involving risk yet the methodology gives no explicit role to measures of risk and return in this paper we identify those families of utility functions that are compatible with a risk return interpretation from these families we deduce utility compatible measures of risk

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

an experimental comparison of different approaches to determining weights in additive utility models several studies this past decade have examined differences between holistic and decomposed approaches to determining weights in additive utility models some have argued that it matters little which procedure is used whereas others strongly favored particular methods in this paper we address this controversy experimentally by comparing five conceptually different approaches in terms of their weights and predictive ability the five methods are 1 multiple linear and non linear regression analyses of ten and fifteen holistic assessments 2 direct decomposed tradeoffs as proposed by keeney and raiffa keeney r l h raiffa 1977 decisions with multiple objectives wiley new york 3 a recent eigen vector technique of saaty saaty t l 1977 a scaling method for priorities in hierarchical structures j math psych 15 3 234 281 involving redundant pairwise comparisons of attributes 4 a straightforward allocation of hundred importance points and 5 unit weighting i e equal weighting after standardizing the attributes the decision task involved college admissions subjects were asked to evaluate hypothetical college applicants on the basis of verbal sat quantitative sat high school grade point average and a measure of extra curricular activity linear as well as nonlinear attribute utility functions were used in constructing the additive models the nonlinear functions were specified graphically by the subjects through selection from five different shapes i e one per attribute to test the predictive ability of the various models each subject made twenty separate pairwise comparisons of alternatives including direction and strength of preference the prediction criteria were percentage correct predictions as well as correlations using these twenty pairs seventy subjects were tested using an order controlled within subject design in comparing the different methods of weight determination monetary incentives were used to enhance motivation in terms of findings the methods generally differed systematically concerning the weights given to the various attributes as well as the variances of the resulting predictions on average however the methods predicted about equally well except for unit weighting which was clearly inferior the findings differ in this regard from the general literature furthermore nonlinear models were found to be inferior to linear ones finally subjects judged the methods to differ significantly in difficulty and trustworthiness which were found to correlate inversely the overall results raise various applied and theoretical issues which are discussed

preference ranking global frequencies in multicriterion analysis pragma abstract this paper presents an mcdm method known as pragma which provides the ranking frequencies of feasible actions the method is based on the comparison of the partial profiles of each alternative with reference to all the possible pairs of criteria considered the global frequencies are obtained as the weighted sum of the corresponding partial ranking frequencies the information supplied by this method is valuable in solving discrete multiple criteria choice problems and in particular in building complete and partial preoders of feasible actions pragma is a useful complement to the mappac method being instrumentally based on the same fundamental preference indices

generalized transitivity and preferences modelling the concept of hyper order abstract a relational system of preferences hyper order based on a generalization of the property of transitivity is proposed avoiding some shortcomings of previous contributions to model the prefenreces of decision makers the purpose of this contribution is enlarging the spectrum of existing theoretical frameworks to support decision aid methodes based on pairwise comparisons an application to a real case study and a computational implementation are also presented herein

l p bounds for the beurling ahlfors transform let b denote the beurling ahlfors transform defined on l p c 1 p 00 the celebrated conjecture of t iwaniec states that its l p norm b p p 1 1 where p max p p p 1 in this paper the new upper estimate b p 1 575 p 1 1 p is found

a note on a minimax rule for portfolio selection and equilibrium price system this paper concerns a minimax model to investigate the optimal portfolio selection problem without riskless assets and with or without short sale restriction a numerical solution to the problem with short sale restriction is obtained by using the maximum entropy algorithm for the problem without short sale restriction we derive a analytical expression for the optimal solution a sufficient condition for the existence and uniqueness of a nonnegative equilibrium price system and an explicit formula for the price system furthermore a numerical example is given to show the validity of the method

parameter free elicitation of utility and probability weighting functions this paper proposes a two step method to successively elicit utility functions and decision weights under rank dependent expected utility theory and its more descriptive version cumulative prospect theory the novelty of the method is that it is parameter free and thus elicits the whole individual preference functional without imposing any prior restriction this method is used in an experimental study to elicit individual utility and probability weighting functions for monetary outcomes in the gain and loss domains concave utility functions are obtained for gains and convex utility functions for losses the elicited weighting functions satisfy upper and lower subadditivity and are consistent with previous parametric estimations the data also show that the probability weighting function for losses is more elevated than for gains

relative risk value models in this paper we propose a relative risk value model and derive a relative measure of risk for lotteries with positive outcomes under a condition called relative risk independence a decision could be made by explicitly trading off between the relative measure of risk and a measure of value which can either be consistent with some expected utility models or represent nonexpected utility preferences specifically this type of risk value model is associated with power or linear plus power and logarithmic or linear plus logarithmic functions we address some prescriptive and descriptive implications of our relative risk value framework and show that our generalized relative risk value model is very flexible for modeling individuals preferences and can explain many decision paradoxes

the probability weighting function a probability weighting finction w p is a prominent feature of several non expected utility theories including prospect theoiy and rank dependent models empirical esti mates indicate that w p is regressive first w p p then iv p p s shaped first concave then convex and asymmetrical intersecting the diagonal at about 1 3 the paper states axioms for several w p forms including the compound invariant w p exp ln p 1 0 a 1 which is regressive s shaped and with an invariant fixed point and inflection point at i e 37 the common ratio effect allais 1953 refers to the obselvation that the more risky of two simple prospects becomes relatively more attractive when the probability of winning is reduced by equal proportion in both prospects thus a person who prefers a sure gain of 100 000 over a coin toss for 300 000 or nothing might also prefer a one in a million lottery ticket for 300 000 over a two in a million lottery ticket for 100 000 this contradicts expected utility but not common sense there is a world of difference between certainty and a 50 50 shot the difference between one or two chances in a million is negligible the example has all the force and simplicity of classical arguments for nonlinear utility where the utility interval from say 10 and 20 is taken as self evidently greater than the utility interval from 1 000 010 and 1 000 020 both arguments appeal directly to our intuitions about numbers a major point of difference is that the money argument involves a constant money intelval and the probability argument a constant probability ratio a minor difference is that in the money domain a constant interval has less impact as the numbers get larger while in the probability domain a constant ratio has less impact as the numbers get smaller putting the two demonstrations side by side like this raises an interesting question namely whether an account of nonlinearity in probabilities can be somehow adapted from classical utility theory modulo a log transformation converting statements about probability ratios into statements about utility intervals indeed in their seminal paper on prospect theory kahneman and tversky 1979 explained the common ratio effect by means of a nonlinear transformation of probabilities into decision weights p w p with log w

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

testing and characterizing properties of nonadditive measures through violations of the sure thing principle in expected utility theory risk attitudes are modeled entirely in terms of utility in the rank dependent theories a new dimension is added chance attitude modeled in terms of nonadditive measures or nonlinear probability transformations that are independent of utility most empirical studies of chance attitude assume probabilities given and adopt parametric fitting for estimating the probability transformation only a few qualitative conditions have been proposed or tested as yet usually quasi concavity or quasi convexity in the case of given probabilities this paper presents a general method of studying qualitative properties of chance attitude such as optimism pessimism and the inverse s shape pattern both for risk and for uncertainty these qualitative properties can be characterized by permitting appropriate relatively simple violations of the sure thing principle in particular this paper solves a hitherto open problem the preference axiomatization of convex pessimistic or uncertainty averse nonadditive measures under uncertainty the axioms of this paper preserve the central feature of rank dependent theories i e the separation of chance attitude and utility

preference ranking of discrete multiattribute instances abstract this paper presents a procedure for preference ranking of discrete multiattribute instances based on the observations that 1 a difficult question could be answered in terms of answers to a sequence of easier ones 2 in general the decision maker s preferences can easily be expressed only relative to pairs of instances that differ over one attribute and 3 the decision maker is able and willing to express his uncertainty regarding a quantity via a subjective probability distribution the procedure is illustrated through a hypothetical situation

solving the discrete multiple criteria problem using convex cones an interactive method employing pairwise comparisons of attainable solutions is developed for solving the discrete deterministic multiple criteria problem assuming a single decision maker who has an implicit quasi concave increasing utility or value function the method chooses an arbitrary set of positive multipliers to generate a proxy composite linear objective function which is then maximized over the set of solutions the maximizing solution is compared with several solutions using pairwise judgments asked of the decision maker responses are used to eliminate alternatives using convex cones based on expressed preferences and then a new set of weights is found that satisfies the indicated preferences the requisite theory and proofs as well as a detailed numerical example are included in addition the results of some computational experiments to test the effectiveness of the method are described

deciding game invariance abstract in a previous paper duchene and rigo introduced the notion of invariance for take away games on heaps roughly speaking these are games whose rulesets do not depend on the position given a sequence s of positive tuples of integers the question of whether there exists an invariant game having s as set of p positions is relevant in particular it was recently proved by larsson et al that if s is a pair of complementary beatty sequences then the answer to this question is always positive in this paper we show that for a fairly large set of sequences expressed by infinite words the answer to this question is decidable

methods for decision making with cardinal numbers and additive aggregation abstract for multi attribute decision making with cardinal numbers and additive aggregation the methods additive aggregation and outranking for crisp and fuzzy numbers are connected with the concept of linguistic variables preference ranking a generalization of outranking and preference ranking organization methods such as electre and promethee can be divided into three phases where each of them is defined completely by linguistic variables the derived method preference ranking with additive weighting and individual fuzziness has an improved selectivity or discrimination compared to conventional methods moreover the method fulfils four important requirements preference only for sufficiently large weights considering evaluation differences outside of thresholds and regarding aggregational and substitutional properties the simplified method preference ranking with additive weighting and general fuzziness allows a reduction of computational resources

resource allocation to interrelated risky projects using a multiattribute utility function two major contributions are made to the problem of resource allocation to indivisible projects with uncertain outcomes the concepts of preferential independence and utility independence for the space of discrete projects are defined and a multiattribute utility theory is linked with mathematical programming for allocation the utility function as shown by keeney can be either multiplicative or additive an overall procedure for structuring the model is outlined a branch and bound algorithm for solving the multiplicative model is developed and a numerical example is presented

the use of domains in multicriteria decision making abstract this paper describes a domain criterion for a multicriteria problem given decision maker it then outlines possibilities for aggregating individual preference structures in the case of multiple decision makers

screening discrete alternatives with imprecisely assessed additive multi attribute functions abstract the classical problem of ranking alternatives when there exists partial information on the scaling constants for additive multi attribute utility functions maufs is reexamined most approaches assume that the unknown scaling constants can be precisely known in this paper we argue that this assumption may not be realistic and we develop a new approach based on an assumption that is less restrictive and does not require that the decision maker be consistent over the given partial information regarding the unknown scaling constants definitions and computationally efficient procedures are developed to identify nondominated alternatives with respect to partial information on the scaling constants which is called utility nondominancy the concepts and procedures developed demonstrate through two tests solving two linear programming problems whether or not the set of alternatives can be further screened finding the best alternative via an interactive method in which the proportion of alternatives screened may be changed is discussed the approach is generalized and related to other mauf structures such as multilinear quasi concave and quasi convex it is demonstrated that linear programming is sufficient to solve all ensuing problems some examples are provided

on the sequentiality of the successor function abstract letube a strictly increasing sequence of integers by a greedy algorithm every nonnegative integer has a greedyu representation the successor function maps the greedyu representation ofnonto the greedyu representation ofn 1 we characterize the sequencesusuch that the successor function associated withuis a left resp a right sequential function we also show that the odometer associated touis continuous if and only if the successor function is right sequential

the midweight method to measure attitudes toward risk and ambiguity this paper introduces a parameter free method for measuring the weighting functions of prospect theory and rank dependent utility these weighting functions capture risk attitudes subjective beliefs and ambiguity attitudes our method called the midweight method is based on a convenient way to obtain midpoints in the weighting function scale it can be used both for risk known probabilities and for uncertainty unknown probabilities the resulting integrated treatment of risk and uncertainty is particularly useful for measuring ambiguity i e the difference between uncertainty and risk compared to existing methods to measure weighting functions and attitudes toward uncertainty and ambiguity our method is more efficient and can accommodate violations of expected utility under risk an experiment demonstrates the tractability of our method yielding plausible results such as ambiguity aversion for moderate and high likelihoods but ambiguity seeking for low likelihoods as predicted by ellsberg this paper was accepted by george wu decision analysis

co plot a graphic display method for geometrical representations of mcdm abstract a relatively new multivariate analysis method called co plot is shown to be highly efficient for the geometrical representation of multicriteria decision problems co plot a two dimensional graphic display technique is designed for multicriteria analysis its main feature is the simultaneous analysis of actions e g observations and criteria e g variables in a simple way the method produces three results 1 similarity among actions by the composite of all criteria involved 2 the structure of correlations among the criteria and 3 the mutual relationships between the actions and the criteria the method is demonstrated on two numerical applications previously analyzed by mareschal and brans b mareschal j p brans european journal of operational research 34 1988 69 77 using the promethee methods and principal component analysis

decompositions of multiattribute utility functions based on convex dependence we describe a method of assessing von neumann morgenstern utility functions on a two attribute space and its extension to n attribute spaces first we introduce the concept of convex dependence between two attributes where we consider the change of shapes of conditional utility functions then we establish theorems which show how to decompose a two attribute utility function using the concept of convex dependence this concept covers a wide range of situations involving trade offs the convex decomposition includes as special cases keeney s additive multiplicative decompositions fishburn s bilateral decomposition and bell s decomposition under the interpolation independence moreover the convex decomposition is an exact grid model which was axiomatized by fishburn and farquhar finally we extend the convex decomposition theorem from two attributes to an arbitrary number of attributes

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

cost conscious comparison of supervised learning algorithms over multiple data sets in the literature there exist statistical tests to compare supervised learning algorithms on multiple data sets in terms of accuracy but they do not always generate an ordering we propose multi 2test a generalization of our previous work for ordering multiple learning algorithms on multiple data sets from best to worst where our goodness measure is composed of a prior cost term additional to generalization error our simulations show that multi 2test generates orderings using pairwise tests on error and different types of cost using time and space complexity of the learning algorithms

multicriteria analysis survey and new directions abstract before the advent of multicriteria analysis decision problems often took the form of the optimization of an objective function or a utility function this approach has the advantage of resulting in well defined mathematical problems but is not always representative of reality in fact the comparison of several possible decisions is rarely made according to a single point of view and the preferences on a point of view are in many cases only modelled with difficulty by a function the aim of this paper is to survey the different directions in which multicriteria analysis has developed multiattribute utility theory outranking relations interactive methods the methodology recently proposed by b roy is also presented

deterministic synchronization of automations with bounded delay resume nous montrons qu un automate a delai borne sous sequentiel i e deterministe sur les entrees est equivalent a un automate en ligne c est a dire lettre a lettre apres une periode transitoire fixe ou l automate lit le debut de l entree sans rien sortir et sous sequentiel les resultats de synchronisation etablis anterieurement pour les automates a delai borne ne preservaient pas la sous sequentialite

estimating aspiration levels from discrete choices computational techniques and experiences abstract this paper discusses the problem of estimating aspiration or reference levels in criteria space from choices between alternatives characterized by multiple criteria several methods for such estimations are developed and compared taking into account both solution quality and computational efficiency methods based on mixed integer linear programming which provide optimal solutions require unacceptable computing times for application in interactive systems an alternative method based on a direct search algorithm is shown to be an effective way of generating high quality estimates with small computational effort

remarks on a measure of risk and a decision making model based on expected utility and entropy by jiping yang and wanhua qiu ejor 164 2005 792 799 abstract yang and qiu yang j qiu w 2005 a measure of risk and a decision making model based on expected utility and entropy european journal of operational research 164 792 799 suggest a new concept for decision making under risk this concept relies on a combination of the well known expected utility criterion and the so called entropy the authors claim that the approach might be used as a descriptive as well as a normative decision model in this paper the theoretical soundness of the concept of entropy is critically examined the analysis is underpinned by a discussion of the properties of the respective entropy function furthermore normative and descriptive features of the concept are discussed and it is shown that the usefulness with respect to both aspects is questionable

a generalized decomposable multiattribute utility function in this paper a generalized decomposable multiattribute utility function mauf is developed it is demonstrated that this new mauf structure is more general than other well known mauf structures such as additive multiplicative and multilinear therefore it is more flexible and does not require that the decision maker be consistent with restrictive assumptions such as preferential independence conditions about his her preferences we demonstrate that this structure does not require any underlying assumption and hence solves the interdependence among attributes hence there is no need for verification of its structure several useful extensions and properties for this generalized decomposable mauf are developed which simplify its structure or assessment the concept of utility efficiency is developed to identify efficient alternatives when there exists partial information on the scaling constants of an assumed mauf it is assumed that the structure decomposition of the mauf is known and the partial information about the scaling constants of the decision maker is in the form of bounds or constraints for the generalized decomposable structure linear programming is sufficient to solve all ensuing problems some examples are provided

multicriterion analysis of preferences by means of pairwise actions and criterion comparisons mappacc this paper presents a method for solving discrete choice problems characterized by multiple evaluative criteria the proposed method known as mappac is based on a pairwise comparison of alternatives relative to each pair of criteria defining the two relations p preference and i indifference which constitute a complete preorder moreover by aggregating these preferences it is possible to obtain a variety of relations on a set of feasible actions

a decision model based on expected utility entropy and variance abstract a decision model the expected utility entropy and variance eu ev model is proposed where the decision criterion depends on the uncertainty risk factors entropy and variance and on the subjective expected utility the eu ev model is applied to decision problems existing in the literature and it is shown that they can be well explained with this model

finite degree utility independence when u is a von neumann morgenstern utility function on x y y is utility independent of x if u can be written as ux y fxgy ax with f positive this paper introduces a fundamental extension of utility independence that is based on induced indifference relations over gambles on one factor when the level of the other factor is fixed it is proved that y is degree n utility independent of x if and only if u can be written as ux y ftxgty fnxgny ax and cannot be written in a similar way with fewer than n products of single factor functions a similar theorem holds when the roles of y and x are interchanged it follows that if y is degree n utility independent of x then x is degree m utility independent of y for some m n 1 n n 1 it is then shown that u can be represented in terms of n conditional utility functions on y m conditional utility functions on x and at most n 1m 1 scaling constants

risk attributes theory decision making under risk in this paper some limitations in the conventional theories and models of the decision making under risk are presented from a new angle to eliminate those limitations a theoretical framework is proposed in which the risk preference relation is constructed on a set of risk attributes instead of risky prospects the axioms are presented to ensure the existence of the representation function for this risk preference relation through employing the multi attribute utility theory maut in our framework we construct a risk decision model with four risk attributes one of these attributes measured by a newly defined attribute measurement the relative maximum absolute value rmav can be employed in our model to explain the experimental result more intuitively compared with the overweighting of small probability proposed by kahneman and tversky in their prospect theory in addition the validity of the model is testified by applying it to explain the allais paradox and the fourfold pattern of risk attitudes the advantages of our theory are summarized to complete this paper since our model is based on an axiomatized preference relation and has a good descriptive ability it can either serve as a normative or a descriptive decision model under risk

on the bellman function of nazarov treil and volberg we give an explicit formula for the bellman function associated with the dual bound related to the unconditional constant of the haar system

relational systems of preference with one or more pseudo criteria some new concepts and results this paper proposes new concepts and new results which could lead to a more realistic preference modeling than in classical decision theory sections 1 3 present four fundamental situations of preferences their combinations and the concept of relational system of preferences in 4 a particular case of relational system of preference is studied it is associated with the concept of pseudo criterion derived from the classical concept of criterion by adjunction of two thresholds some results are given generalizing the properties of such well known structures as complete preorders and semiorders sections 5 and 6 emphasize the possibilities given by the preceding concepts to take the imprecisions irresolutions and incomparabilities appearing in every concrete problem where several criteria must be considered into account

a measure of risk and a decision making model based on expected utility and entropy abstract in this paper we extend the classical decision model under risk to a more general case in which the state of nature corresponding to each risky action may have its own distribution more specifically we propose an expected utility entropy eu e measure of risk and a decision making model based on expected utility and entropy the eu e measure of risk reflects an individual s intuitive attitude toward risk the decision model incorporates the expected utility decision criterion as a special case using this decision model a class of decision problems which cannot be dealt with the expected utility or mean variance criterion reasonably can be solved besides some famous decision paradoxes can be interpreted this decision model can either serve as a descriptive or a normative decision model involving risk

curvature of the probability weighting function when individuals choose among risky alternatives the psychological weight attached to an outcome may not correspond to the probability of that outcome in rank dependent utility theories including prospect theory the probability weighting function permits probabilities to be weighted nonlinearly previous empirical studies of the weighting function have suggested an inverse s shaped function first concave and then convex however these studies suffer from a methodological shortcoming estimation procedures have required assumptions about the functional form of the value and or weighting functions we propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function empirical tests of these conditions are independent of the form of the value function we test these conditions using preference ladders a series of questions that differ only by a common consequence the concavity convexity ladders validate previous findings of an s shaped weighting function concave up to p 0 40 and convex beyond that probability the tests also show significant nonlinearity away from the boundaries 0 and 1 finally we fit the ladder data with weighting functions proposed by tversky and kahneman tversky amos daniel kahneman 1992 advances in prospect theory cumulative representation of uncertainty j risk and uncertainty5 297 323 and prelec prelec dra en 1995 the probability weighting function unpublished paper

multiattribute nonlinear utility theory independence axioms similar to those proposed for multiattribute von neumann morgenstern linear utility theory are examined in the context of new nonlinear utility theories developed by chew and maccrimmon and fishburn these new theories weaken the independence axiom of von neumann and morgenstern and fishburn s theory does not require preferences to be transitive the paper shows that axioms for independence between attributes lead to decompositions of utility for the nonlinear theories that are related to standard decompositions for linear utility

risk attitudes and decision weights to accommodate the observed pattern of risk aversion and risk seeking as well as common violations of expected utility e g the certainty effect we introduce and characterize a weighting function according to which an event has greater impact when it turns impossibility into possibility or possibility into certainty than when it merely makes a possibility more or less likely we show how to compare such weighting functions of different individuals with respect to the degree of departure from expected utility and we present a method for comparing an individual s weighting functions for risk and for uncertainty

numeration systems linear recurrences and regular sets a numeration system based on a strictly increasing sequence of positive integers u0 1 u1u2 expresses a non negative integer n as a sum n j 0 i ajuj in this case we say the string a i a i 1 a1 a0 is a representation for n