an o n log log n time algorithm for triangulating a simple polygon given a simple n vertex polygon the triangulation problem is to partition the interior of the polygon into n 2 triangles by adding n 3 nonintersecting diagonals we propose an o n log log n time algorithm for this problem improving on the previously best bound of o n log n and showing that triangulation is not as hard as sorting improved algorithms for several other computational geometry problems including testing whether a polygon is simple follow from our result

ordinal regression revisited multiple criteria ranking using a set of additive value functions abstract we present a new method called utagms for multiple criteria ranking of alternatives from set a using a set of additive value functions which result from an ordinal regression the preference information provided by the decision maker is a set of pairwise comparisons on a subset of alternatives ar a called reference alternatives the preference model built via ordinal regression is the set of all additive value functions compatible with the preference information using this model one can define two relations in the set a the necessary weak preference relation which holds for any two alternatives a b from set a if and only if for all compatible value functions a is preferred to b and the possible weak preference relation which holds for this pair if and only if for at least one compatible value function a is preferred to b these relations establish a necessary and a possible ranking of alternatives from a being respectively a partial preorder and a strongly complete relation the utagms method is intended to be used interactively with an increasing subset ar and a progressive statement of pairwise comparisons when no preference information is provided the necessary weak preference relation is a weak dominance relation and the possible weak preference relation is a complete relation every new pairwise comparison of reference alternatives for which the dominance relation does not hold is enriching the necessary relation and it is impoverishing the possible relation so that they converge with the growth of the preference information distinguishing necessary and possible consequences of preference information on the complete set of actions utagms answers questions of robustness analysis moreover the method can support the decision maker when his her preference statements cannot be represented in terms of an additive value function the method is illustrated by an example solved using the utagms software some extensions of the method are also presented

set choice problems with incomplete information about the preferences of the decision maker we consider the problem of selecting a predetermined number of objects from a given finite set it is assumed that the preferences of the decision maker on this set are only partially known our solution approach is based on the notions of optimal and non dominated subsets the properties of such subsets and the objects they contain are investigated the implementation of the developed approach is discussed and illustrated by various examples

robustness and information levels in case based multiple criteria sorting abstract case based preference elicitation methods for multiple criteria sorting problems have the advantage of posing rather small cognitive demands on a decision maker but they may lead to ambiguous results when preference parameters are not uniquely determined we use a simulation approach to determine the extent of this problem and to study the impact of additional case information on the quality of results our experiments compare two decision analysis tools case based distance sorting and the simple additive weighting method in terms of the effects of additional case information on sorting performance depending on problem dimension number of groups number of criteria etc our results confirm the expected benefit of additional case information on the precision of estimates of the decision maker s preferences problem dimension however has some unexpected effects

non dominance and potential optimality for partial preference relations abstract in this paper we obtain new theoretical results relating the notions of potential optimality and non dominance without an assumption that a value function exists in particular we investigate a decision problem involving the choice of single or multiple best objects our results show that the notions of potential optimality and non dominance are equivalent in a special case of preferences of the decision maker expressed by partial quasi orders

brief paper a new concept of invariance for saturated systems in this paper the notions of sns invariance and sns domain of attraction are introduced the sns domain of attraction serves as an estimation of the domain of attraction of a saturated system it is shown that in the case of single input saturated systems any contractive set is contained in the sns domain of attraction another important characteristic of the sns domain of attraction is that it contains any estimation obtained by means of a linear difference inclusion of the saturated system a simple algorithm that converges to the sns domain of attraction is presented an illustrative example is given

the aspiration level interactive method aim reconsidered robustness of solutions abstract in this paper we explore theory and practice for the aspiration level interactive model aim a useful decision tool that takes advantage of the concepts of satisficing as well as other concepts of multiple criteria decision making mcdm we examine the relationship between aspiration levels and their mapped to solutions in the mcdm context using aim we extend the concept of robustness in decision making by defining a solution to be robust if many suitably defined aspiration levels map to it we use simulation to help explore robustness by generating three groups of random test problems each problem has twenty alternatives for each group of problems the top 5 most mapped to alternatives out of 20 are mapped to by at least 50 of the aspiration levels we also relate the concept of robustness in decision making to the ideas of simply ranking alternatives using equal weights there is a strong correlation between the robustness ranking and the equal weights ranking based on our analyses we then randomly generate additional problems to explore certain other factors we also discuss practical aspects of robustness

deriving rankings from incomplete preference information a comparison of different approaches abstract volume based methods for decision making under incomplete information like the smaa family of methods provide rich probabilistic information to support decision making however they usually do not directly generate a unique ranking of alternatives methods to create such a unique ranking from incomplete preference information typically select one parameter vector either by mathematical programming approaches or by averaging and then apply a preference model using this parameter vector in the present paper we develop several models to infer a complete ranking or a complete preorder of alternatives directly from the probabilistic information provided by volume based methods without singling out a specific parameter vector we compare the results obtained by these models to those obtained with a single parameter approach in a computational study results indicate small but significant differences in the performance of methods as well as in the probability that additional preference information might worsen rather than improve the results

decision network polynomials and the sensitivity of decision support models abstract decision makers benefit from the utilization of decision support models in several applications obtaining managerial insights is essential to better inform the decision process this work offers an in depth investigation into the structural properties of decision support models we show that the input output mapping in influence diagrams decision trees and decision networks is piecewise multilinear the conditions under which sensitivity information cannot be extracted through differentiation are examined in detail by complementing high order derivatives with finite change sensitivity indices we obtain a systematic approach that allows analysts to gain a wide range of managerial insights a well known case study in the medical sector illustrates the findings

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

the utility efficient set and its interactive reduction we assume a decision situation under risk with incomplete information on preferences modelled as a vector utility function we consider an additive aggregation of its components and partial information on the scaling constants we develop the concept of utility efficiency to identify efficient strategies in discrete problems when the information about the scaling constants of the decision maker is in the form of a polyhedral cone a characterization of the utility efficient set provides a practical way to compute such efficient strategies we then discuss an interactive method based on the assessment of the scaling constants via an interactive paired comparison with its convergence the method is complemented by a procedure to reduce the utility efficient set to aid in the process of reaching a final strategy

an aggregation disaggregation approach to obtain robust conclusions with electre tri electre tri is a well known method to assign a set of alternatives to a set of predefined categories considering multiple criteria using this method requires setting many parameters which is often a difficult task we consider the case where the decision makers dms in the decision process are unsure of which values should each parameter take which may result from uncertain imprecise or inaccurately determined information as well as from lack of consensus among them this paper discusses the synergy between two approaches developed independently to deal with this difficulty the first approach infers the value of parameters from assignment examples provided by the dms as an elicitation aid each assignment example originates mathematical constraints that the parameter values should satisfy the second approach considers a set of constraints on the parameter values reflecting the imprecise information that the dms are able to provide then it computes the best and worst categories for each alternative compatible with constraints in order to present robust conclusions both approaches avoid asking for precise values for the parameters rather they proceed to solve the problem in a way that requires from the dms much less effort by integrating these two approaches this paper proposes a new interactive approach where the insight obtained during robustness analyses guides the dms during the elicitation phase

a unified lyapunov approach to analysis of oscillations and stability for systems with piecewise linear elements this technical note develops a unified lyapunov approach to analysis of self induced oscillations and stability for systems with piecewise linear elements for self induced oscillation within a global or regional attractor invariant level sets of a piecewise quadratic lyapunov function are obtained to bound the attractor via linear matrix inequality based optimization the analysis results for self induced oscillations are easily adapted to global or regional stability analysis

an optimal algorithm for detecting weak visibility of a polygon notation and a theorem are presented which using a result of b chazelle and l j guibas 1985 enable the authors to design an o n log n algorithm for reporting all visibility edges of a given n vertex polygon improving on this bound to o n is presently focused upon this problem is solved for polygons with at least one given visibility edge it is assumed that both endpoints of this edge are convex vertices subsequently it is shown how to drop this restriction the general case of detecting weak edge visibility of an arbitrary simple polygon is dealt with

decision theory and strict ranking of probabilities abstract this paper is concerned with the derivation of guides to decision making in a set of circumstances intermediate between the classic extremes of pure risk and pure uncertainty it is assumed that the decision maker can specify a subjective strict ranking of the probabilities of states of nature in which case given knowledge of the payoffs of a strategy it is possible to find in a straightforward fashion maximum and minimum expected payoffs for the strategy if the information contained in the strict ranking is available to the decision maker then to fail to take it into account must adversely affect the quality of decision making the paper discusses both the interpretation and the possible practical uses of extreme expected values in decision making and includes a numerical example based on an investment decision problem to demonstrate the ease of use of the results obtained

establishing dominance between alternatives with incomplete information in a hierarchically structured attribute tree abstract a model for establishing dominance with incomplete information is proposed in a hierarchically structured attribute tree the linear additive value function under certainty is used in the model the model allows the decision maker to provide any type of linear partial information on the attribute weights and the alternative values the incompletely specified information constructs a feasible region of linear constraints and therefore pairwise dominance relationship between alternatives reduces to intractable non linear programming hence to handle this difficulty we propose a solution technique also to handle the tree structure we break down the attribute tree into sub trees due to the recursive structure of the solution technique the optimization results from sub trees can be utilized in computing the value interval on the topmost attribute based on the solution technique an algorithm for obtaining the value interval is proposed and dominance relation is established

hierarchical multi objective decision making this paper proposes a hierarchical procedure for solving decision problems with multiple objectives the procedure consists of two levels a top and a base level the main idea is that the top level only provides general preference information taking this information into account the base level then determines a compromise solution for a multi objective linear program it will be shown how such a hierarchical procedure can be structured by deriving weight restrictions from the general preference information of the top level and by using the interactive modm procedure of zionts and wallenius on the base level

assessing non additive utility for multicriteria decision aid abstract in the framework of multi attribute utility theory maut several methods have been proposed to build a decision maker s dm utility function representing his her preferences among such methods the uta method infers an additive utility function from a set of exemplary decisions using linear programming however the uta method does not guarantee to find a utility function which is coherent with the available information this drawback is due to the underlying utility model of uta viz the additive one which does not allow to include additional information such as an interaction among criteria in this paper we present a methodology for building a non additive utility function in the framework of the so called fuzzy integrals which permits to model preference structures with interaction between criteria like in the uta method we aim at searching a utility function representing the dm s preferences but unlike uta the functional form is a specific fuzzy integral choquet integral as a result we obtain weights which can be interpreted as the importance of coalitions of criteria exploiting the potential interaction between criteria as already proposed by other authors however within the same framework we obtain also the marginal utility functions relative to each one of the considered criteria that are evaluated on a common scale as a consequence of the implemented methodology finally we illustrate our approach with an example

linear systems with state and control constraints the theory and application of maximal output admissible sets the initial state of an unforced linear system is output admissible with respect to a constraint set y if the resulting output function satisfies the pointwise in time condition y t in y t or 0 the set of all possible such initial conditions is the maximal output admissible set o sub infinity the properties of o sub infinity and its characterization are investigated in the discrete time case it is generally possible to represent o sub infinity or a close approximation of it by a finite number of functional inequalities practical algorithms for generating the functions are described in the continuous time case simple representations of the maximal output admissible set are not available however it is shown that the discrete time results may be used to obtain approximate representations

on a convex hull algorithm for polygons and its application to triangulation problems abstract a frequently used algorithm for finding the convex hull of a simple polygon in linear running time has been recently shown to fail in some cases due to its simplicity the algorithm is nevertheless attractive in this paper it is shown that the algorithm does in fact work for a family of simple polygons known as weakly externally visible polygons some application areas where such polygons occur are briefly discussed in addition it is shown that with a trivial modification the algorithm can be used to internally and externally triangulate certain classes of polygons in 0 n time

brief paper convex invariant sets for discrete time lur e systems in this paper a method to estimate the domain of attraction of a class of discrete time lur e systems is presented a new notion of invariance denoted lnl invariance is introduced an algorithm to determinate the largest lnl invariant set for this class of systems is proposed moreover it is proven that the lnl invariant sets provided by this algorithm are polyhedral convex sets and constitute an estimation of the domain of attraction of the non linear system it is shown that any contractive set for the lur e system is contained in the lnl invariant set obtained applying the results of this paper two illustrative examples are given

sensitivity analysis of additive multiattribute value models we present two simple computational procedures for sensitivity analysis of additive multiattribute value models that yield variations in attribute weights scaling constants for the first or entropy based procedure the point of departure is the concept of equal weights for all attributes for the second or least squares procedure the point of departure is a set of arbitrary weights for attributes in each procedure we either a calculate the closest set of weights that equates the multiattribute value for a pair of alternatives that alternative whose overall value is optimal for the original attribute weights and any other specific nondominated alternative or b calculate the closest set of weights required for the specific alternative to exceed the optimal alternative by a specified amount

absolute stability with a generalized sector condition this paper generalizes the linear sector in the classical absolute stability theory to a sector bounded by concave convex functions this generalization allows more flexible or more specific description of the nonlinearity and will thus reduce the conservatism in the estimation of the domain of attraction we introduce the notions of generalized sector and absolute contractive invariance for estimating the domain of attraction of the origin necessary and sufficient conditions are identified under which an ellipsoid is absolutely contractively invariant in the case that the sector is bounded by piecewise linear concave convex functions these conditions can be exactly stated as linear matrix inequalities moreover if we have a set of absolutely contractively invariant aci ellipsoids then their convex hull is also aci and inside the domain of attraction we also present optimization technique to maximize the absolutely contractively invariant ellipsoids for the purpose of estimating the domain of attraction the effectiveness of the proposed method is illustrated with examples

generalized chebychev inequalities theory and applications in decision analysis in many decision analysis problems we have only limited information about the relevant probability distributions in problems like these it is natural to ask what conclusions can be drawn on the basis of this limited information for example in the early stages of analysis of a complex problem we may have only limited fractile information for the distributions in the problem what can we say about the optimal strategy or certainty equivalents given these few fractiles this paper describes a very general framework for analyzing these kinds of problems where given certain moments of a distribution we can compute bounds on the expected value of an arbitrary objective function by suitable choice of moment and objective functions we can formulate and solve many practical decision analysis problems we describe the general framework and theoretical results discuss computational strategies and provide specific results for examples in dynamic programming decision analysis with incomplete information bayesian statistics and option pricing

rough sets and intelligent data analysis rough set based data analysis starts from a data table called an information system the information system contains data about objects of interest characterized in terms of some attributes often we distinguish in the information system condition and decision attributes such information system is called a decision table the decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table with every decision table a set of decision rules called a decision algorithm can be associated it is shown that every decision algorithm reveals some well known probabilistic properties in particular it satisfies the total probability theorem and the bayes theorem these properties give a new method of drawing conclusions from data without referring to prior and posterior probabilities inherently associated with bayesian reasoning

rough sets decision algorithms and bayes theorem abstract rough set based data analysis starts from a data table called an information system the information system contains data about objects of interest characterized in terms of some attributes often we distinguish in the information system condition and decision attributes such information system is called a decision table the decision table describes decisions in terms of conditions that must be satisfied in order to carry out the decision specified in the decision table with every decision table a set of decision rules called a decision algorithm can be associated it is shown that every decision algorithm reveals some well known probabilistic properties in particular it satisfies the total probability theorem and bayes theorem these properties give a new method of drawing conclusions from data without referring to prior and posterior probabilities inherently associated with bayesian reasoning

extended methods for identifying dominance and potential optimality in multi criteria analysis with imprecise information abstract many of the recent prescriptive approaches to multi attribute decision analysis have dealt with situations in which trade off weights are known imprecisely while marginal values are known exactly a way to handle such problems is to utilize a linear programming technique from which non dominated and or potentially optimal score vectors can be obtained in some attributes however it is not easy for decision makers to provide the marginal value functions that are explicit and exact the purpose of this paper is to address problems such that the both attribute weights and marginal values are known imprecisely we then assume without loss of generality that these imprecise information on both weights and values are in the form of inequalities and or equalities such as rankings and bounds the first formulations for checking dominance and potential optimality become non linear programming problems hard to be solved generally we thus present how these non linear problems are reduced to linear programming equivalents

brief piecewise affine lyapunov functions for discrete time linear systems with saturating controls this paper is concerned with piecewise affine pwa functions as lyapunov function candidates for stability analysis of time invariant discrete time linear systems with saturating closed loop control inputs using a pwa model of saturating closed loop system new necessary and sufficient conditions for a pwa function be a lyapunov function are presented based on linear programming formulation of these conditions an effective algorithm is proposed for construction of such lyapunov functions for estimation of the region of local asymptotic stability compared to piecewise linear functions like minkowski functions pwa functions are more adequate to capture the dynamical effects of saturation nonlinearities giving strictly less conservative results the complexity of the proposed approach is polynomial in state dimension and exponential in saturating control dimension being hence appropriate for problems with large state dimension but with few saturating inputs

ultimate boundedness control for uncertain discrete time systems via set induced lyapunov functions in this note linear discrete time systems affected by both parameter and input uncertainties are considered the problem of the synthesis of a feedback control assuring that the system state is ultimately bounded within a given compact set containing the origin with an assigned rate of convergence is investigated it is shown that the problem has a solution if and only if there exists a certain lyapunov function which does not belong to a preassigned class of functions e g the quadratic ones but it is determined by the target set in which ultimate boundedness is desired one of the advantages of this approach is that we may handle systems with control constraints no matching assumptions are made for systems with linearly constrained uncertainties it is shown that such a function may be derived by numerically efficient algorithms involving polyhedral sets the resulting compensator may be implemented as a linear variable structure control

robust ordinal regression for value functions handling interacting criteria we present a new method called utagms int for ranking a finite set of alternatives evaluated on multiple criteria it belongs to the family of robust ordinal regression ror methods which build a set of preference models compatible with preference information elicited by the decision maker dm the preference model used by utagms int is a general additive value function augmented by two types of components corresponding to bonus or penalty values for positively or negatively interacting pairs of criteria respectively when calculating value of a particular alternative a bonus is added to the additive component of the value function if a given pair of criteria is in a positive synergy for performances of this alternative on the two criteria similarly a penalty is subtracted from the additive component of the value function if a given pair of criteria is in a negative synergy for performances of the considered alternative on the two criteria the preference information elicited by the dm is composed of pairwise comparisons of some reference alternatives as well as of comparisons of some pairs of reference alternatives with respect to intensity of preference either comprehensively or on a particular criterion in utagms int ror starts with identification of pairs of interacting criteria for given preference information by solving a mixed integer linear program once the interacting pairs are validated by the dm ror continues calculations with the whole set of compatible value functions handling the interacting criteria to get necessary and possible preference relations in the considered set of alternatives a single representative value function can be calculated to attribute specific scores to alternatives it also gives values to bonuses and penalties utagms int handles quite general interactions among criteria and provides an interesting alternative to the choquet integral

local attribute reductions for decision tables abstract attribute reduction is among the most important areas of research in rough sets this paper investigates the types of local attribute reduction for decision tables we propose the concepts of lth decision class lower approximation reduction lth decision class reduction and lth decision class reduction for decision tables and provide their corresponding reduction algorithms via discernibility matrices we also establish the relationship between positive region reduction and the lth decision class reduction and report a case study using the university of california irvine dataset to verify the theoretical results

brief paper on the computation of convex robust control invariant sets for nonlinear systems in this paper we provide a method to compute robust control invariant sets for nonlinear discrete time systems a simple criterion to evaluate if a convex set in state space is a robust control invariant set for a nonlinear uncertain system is presented the criterion is employed to design an algorithm for computing a polytopic robust control invariant set the method is based on the properties of dc functions i e functions which can be expressed as the difference of two convex functions since the elements of a wide class of nonlinear functions have dc representation or at least admit an arbitrarily close approximation the method is quite general the algorithm requires relatively low computational resources

on the computation of set induced control lyapunov functions for continuous time systems the paper presents a computation oriented method for characterizing and obtaining local control lyapunov functions induced by particular star shaped nonconvex sets for continuous time nonlinear systems with bounded inputs for a given set the necessary and sufficient conditions for the induced function to be a nonconvex local control lyapunov function are provided the related convex problems for computing the exact region in which the function is decreasing and the optimal control input are presented the results are applied to the brockett integrator

ranking and selection for multiple performance measures using incomplete preference information abstract this paper presents two new procedures for ranking and selection r s problems where the best system designs are selected from a set of competing ones based on multiple performance measures evaluated through stochastic simulation in the procedures the performance measures are aggregated with a multi attribute utility function and incomplete preference information regarding the weights that reflect the relative importance of the measures is taken into account a set of feasible weights is determined according to preference statements that are linear constraints on the weights given by a decision maker non dominated designs are selected using two dominance relations referred to as pairwise and absolute dominance based on estimates for the expected utilities of the designs over the feasible weights the procedures allocate a limited number of simulation replications among the designs such that the probabilities of correctly selecting the pairwise and absolutely non dominated designs are maximized the new procedures offer ease of eliciting the weights compared with existing r s procedures that aggregate the performance measures using unique weights moreover computational advantages are provided over existing procedures that identify non dominated designs based on the expected values of the performance measures the new procedures allow to obtain a smaller number of non dominated designs they also identify these designs correctly with a higher probability or require a smaller number of replications for correct selection finally the new procedures allocate a larger number of replications to the non dominated designs that are therefore evaluated with greater accuracy these computational advantages are illustrated through several numerical experiments

comparison of weighting judgments in multiattribute utility measurement this paper compares four weighting methods in multiattribute utility measurement the ratio method the swing weighting method the tradeoff method and the pricing out method 200 subjects used these methods to weight attributes for evaluating nuclear waste repository sites in the united states the weighting methods were compared with respect to their internal consistency convergent validity and external validity internal consistency was measured by the degree to which ordinal and cardinal or ratio responses agreed within the same weighting method convergent validity was measured by the degree of agreement between the weights elicited with different methods external validity was determined by the degree to which weights elicited in this experiment agreed with weights that were elicited with managers of the department of energy in terms of internal consistency the tradeoff method fared worst in terms of convergent validity the pricing out method turned out to be an outlier in terms of external validity the pricing out method showed the best results while the ratio and swing methods are quite consistent and show a fair amount of convergent validity their external validity problems cast doubt on their usefulness the main recommendation for applications is to improve the internal consistency of the tradeoff method by careful interactive elicitation and to use it in conjunction with the pricing out method to enhance its external validity

parametric absolute stability of lur e systems the concept of parametric stability is extended to include lur e type nonlinear control systems with uncertain parameters and constant reference inputs conditions for parametric absolute stability are derived which guarantee that the system remains stable despite uncertainty of equilibrium location caused by parametric uncertainties and values of the reference input the conditions can be tested by computing value sets using the polygon interval arithmetic algorithm

efficient updating rough approximations with multi dimensional variation of ordered data ordered data widely exists in practical problems dominance based rough set approach drsa is an effective mathematical tool to obtain approximations of concepts and discovery knowledge from ordered data in this paper we focus on the dynamic drsa for the multi dimensional variation of an ordered information system and propose a novel incremental simplified algorithm which can efficiently update approximations of drsa when objects and attributes increase simultaneously most of existing algorithms can efficiently deal with the single dimensional variation of an information system however multi dimensional variations often occur in real dynamic data that is the object set the attribute set or attribute values of an information system often vary simultaneously although we can directly use the definitions of approximations or integrate some single dimensional incremental algorithms to cope with multi dimensional variations this always results in complex algorithm architectures and a large amount of inefficient computation in our works by simplifying traditional definitions of drsa and employing the incremental learning strategy we develop an algorithm to neglect unnecessary parameters and avoid much redundant computation then we present two different storage schemes for our proposed algorithm to solve the problem of memory consumption finally a series of experiments are conducted to evaluate its efficiency experimental results clearly show that for the two dimensional variation of objects and attributes in an ordered information system our proposed algorithm is much faster not only than the non incremental algorithm based on traditional definitions but also than the integration of two single dimensional incremental algorithms

the magnitude of errors in proximal multiattribute decision analysis with probabilistically dependent attributes this paper investigates the accuracy of an approximation procedure for evaluating alternatives under uncertainty with multiple evaluation attributes this approximation uses only the first two moments of the probability distributions for the alternatives and hence it can substantially reduce the amount of information which must be collected in order to evaluate alternatives when evaluation attributes are probabilistically dependent the accuracy of the approximation is investigated by comparing results from using it with exact calculations for a variety of situations representative of those found in decision analysis practice this investigation shows that the approximation is accurate for situations representative of many decision analysis applications however caution is needed in applying the approximation in some situations where it may give inaccurate results characteristics of cases where the approximation is less accurate are presented

decision making with incomplete information abstract decision situations with incomplete information are characterized by a decision maker without a precisely defined stable preference structure by probability distributions not known completely or by an inexact evaluation of consequences within the paper a general framework for decision making with incomplete information is presented which shows how to solve problems from descriptive as well as prescriptive decision theory based on this framework an overview of existing methods which are particularly suitable for handling incomplete information is given

rough sets theory for multicriteria decision analysis the original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation it operates on a data table composed of a set u of objects actions described by a set q of attributes its basic notions are indiscernibility relation on u lower and upper approximation of either a subset or a partition of u dependence and reduction of attributes from q and decision rules derived from lower approximations and boundaries of subsets identified with decision classes the original rough set idea is failing however when preference orders of attribute domains criteria are to be taken into account precisely it cannot handle inconsistencies following from violation of the dominance principle this inconsistency is characteristic for preferential information used in multicriteria decision analysis mcda problems like sorting choice or ranking in order to deal with this kind of inconsistency a number of methodological changes to the original rough sets theory is necessary the main change is the substitution of the indiscernibility relation by a dominance relation which permits approximation of ordered sets in multicriteria sorting to approximate preference relations in multicriteria choice and ranking problems another change is necessary substitution of the data table by a pairwise comparison table where each row corresponds to a pair of objects described by binary relations on particular criteria in all those mcda problems the new rough set approach ends with a set of decision rules playing the role of a comprehensive preference model it is more general than the classical functional or relational model and it is more understandable for the users because of its natural syntax in order to workout a recommendation in one of the mcda problems we propose exploitation procedures of the set of decision rules finally some other recently obtained results are given rough approximations by means of similarity relations rough set handling of missing data comparison of the rough set model with sugeno and choquet integrals and results on equivalence of a decision rule preference model and a conjoint measurement model which is neither additive nor transitive

preference programming with incomplete ordinal information abstract this paper extends possibilities for analyzing incomplete ordinal information about the parameters of an additive value function such information is modeled through preference statements which associate sets of alternatives or attributes with corresponding sets of rankings these preference statements can be particularly helpful in developing a joint preference representation for a group of decision makers who may find difficulties in agreeing on numerical parameter values because these statements can lead to a non convex set of feasible parameters a mixed integer linear formulation is developed to establish a linear model for the computation of decision recommendations this makes it possible to complete incomplete ordinal information with other forms of incomplete information

brief paper ultimate bounded stability and stabilization of linear systems interconnected with generalized saturated functions this paper proposes some ultimate bounded stability analysis and stabilization conditions for systems involving actuators with different nonlinear elements like for instance both saturation and dead zone or both saturation and stick slip results are based on the use of a convex differential inclusion approach indeed an adequate property allowing to upper bound some product terms related to the nonlinearity is provided thus constructive conditions associated to convex optimization schemes are developed to determine suitable regions of the state space in which the closed loop trajectories can be captured

partial information dominance and potential optimality in multiattribute utility theory when a multiattribute utility function is only partially specified by prior preference statements what can be said about the relative desirability of actual alternatives this question is addressed for the cases of additively separable cardinal utility with unknown scaling constants multiplicatively separable cardinal utility with unknown scaling constants and additively separable ordinal utility we review previous approaches and treat issues of consistency is the prior information consistent dominance does the prior preference information imply that one outcome is preferred to another and potential optimality are there utility functions of the given form consistent with prior preference information under which a particular outcome is preference optimal in the additive cases a key relationship between dominance and potential optimality may be derived the paper concludes by presenting an example application to a well known nuclear siting study

decision quality using ranked attribute weights three published approximation formulae for selecting the best multiattribute alternative based on rank ordered weights are evaluated all formulae are surprisingly efficacious in determining the best multiattribute alternative rank order centroid roc weights are more accurate than the other rank based formulae furthermore the roc formula generalizes to incorporate both other forms of partial information about attribute weights and partial rank order information as well because a roc based analysis is so straightforward and efficacious it provides an appropriate implementation tool

invariant sets computation for convex difference inclusions systems in this paper we introduce the convex difference inclusion cdi systems as a modeling framework useful to analyze set theory and invariance related issues for nonlinear and uncertain systems the dynamics of a cdi system is given by a set valued map whose values are convex compact subsets of the space and are determined by convex bounding functions necessary and sufficient boundary type conditions for invariance and contractiveness characteristic of the linear systems are given for the cdi systems lyapunov functions are proved to be induced by contractive sets for cdi systems as in the linear context a computational procedure for obtaining polytopic invariant and contractive sets for nonlinear systems based on the properties of the cdi systems is presented

a nearly optimal sensor placement algorithm for boundary coverage locating visual sensors in 2d can be often modeled as an art gallery problem tasks such as surveillance require observing or covering the interior of a polygon with a minimum number of sensors or guards for other tasks such as inspection and image based rendering observing the boundaries of the environment is sufficient as interior covering ic also edge covering ec is np hard and no finite algorithm is known for its exact solution approximate ec solutions are provided by many heuristic algorithms but their performances with respect to optimality minimum number of sensors is unknown in this paper we propose a new ec sensors location technique the algorithm is incremental and converges toward the optimal solution it refines an initial approximation provided by an integer covering algorithm iec where each edge is observed entirely by at least one sensor a lower bound for the number of sensors specific of the polygon considered is used at each step for evaluating the quality of the current solution and a set of rules are provided for performing a local refinement to reduce the computational burden the algorithm has been implemented and tests over hundreds of random polygons show that it supplies solutions very close to and often coincident with the lower bound and then suboptimal or optimal in addition the approximate starting solutions provided by the iec algorithms are on the average close to optimum the tight lower bound can also be used for testing other ec sensor location algorithms running times allow dealing with polygons with up to a few hundreds of edges which appears adequate for many practical cases an enhanced version of the algorithm also taking into account range and incidence constraints has also been implemented and tested

survey paper set invariance in control the properties of positively invariant sets are involved in many different problems in control theory such as constrained control robustness analysis synthesis and optimization in this paper we provide an overview of the literature concerning positively invariant sets and their application to the analysis and synthesis of control systems

evidential weights of multiple preferences for competitiveness the alternative selections or feasible sets in multi attribute utility theory usually face problems of inaccuracy or inconsistency in weighting evidential weight and weight of evidence still have not resolved these problems in an efficient manner this research proposes evidential weights of multiple preferences by using evidence and inference based on the rough set theory an evidential probability is constructed to resolve this weight technically the evidential probability is required to satisfy the following conditions uniqueness independence and consistency to identify various evidence and noise and to provide quantities of certain evidence to resolve weights empirically the resolved weights are fused into competitiveness utility for verification a practical case successfully classifies dominating nations of world competitiveness yearbook another case analyzes the competitiveness trends of china during 1997 to 2012 predicting china will continue rising in near future

effects of imprecise weighting in hierarchical preference programming abstract preference programming is a general term for multi criteria decision analytical approaches allowing incomplete preference information in the pairs method interval judgments are assigned to weight ratios between attributes to model imprecision in multi attribute value trees this paper studies the effects of a hierarchical model structure on the overall imprecision as the form of the hierarchy also affects the form of imprecision that can be assigned to the model the aim is to find out good procedural practices for reducing overall imprecision descending inherently from the model structure the study provides simulation results about the ability of various weighting schemes to identify dominated alternatives which are discussed with respect to other issues related to the weighting process according to the results a hierarchical model is structurally somewhat more unable to identify dominances than a corresponding nonhierarchical model but its cognitive advantages often cancel out this the results also suggest paying reasonable attention to the precision of the lower level judgments and to identifying possible correlations between the criteria

multi criteria analysis with partial information about the weighting coefficients abstract in this paper we address the problem of ranking a set of alternatives with partial information about the weighting coefficients we introduce a family of quasiorders that are easily interpretable and manageable which includes among others the natural quasiorder in r n and other well known preference structures in the literature the enrichment of the preference structure with respect to the natural quasiorder is measured by means of an absolute measure we introduce

differential characterizations of nonconical dominance in multiple objective decision making suppose a decision maker s preferences are represented by an unknown value function v prior information concerning v in the form of structural assumptions or revealed preferences may serve to restrict v to some class v of value functions an alternative y is dominated by an alternative z if v y v z for almost every v v in which case we write y v z continuous variable problems are considered in which alternatives are sought which are undominated under v for these problems we derive necessary and sufficient differential optimality conditions of the kuhn tucker type an example is presented in which v is a class of measurable value functions of the multiplicative form introduced by dyer and sarin since v may be a nonconical order these results are not subsumed by conventional vector optimization

brief input to state stability for a class of lurie systems we analyze input to state stability iss for the feedback interconnection of a linear block and a nonlinear element this study is of importance for establishing robustness against actuator nonlinearities and disturbances in the absolute stability framework we prove iss from a positive real property of the linear block by restricting the sector nonlinearity to grow unbounded as its argument tends to infinity when this growth condition is violated examples show that the iss property is lost the result is used to give a simple proof of boundedness for negative resistance oscillators such as the van der pol oscillator in a separate application we relax the minimum phase assumption of an earlier boundedness result for systems with nonlinearities that grow faster than linear