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

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

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

decision making under uncertainty with unknown utility function and rank ordered probabilities abstract we consider the ranking of decision alternatives in decision analysis problems under uncertainty under very weak assumptions about the type of utility function and information about the probabilities of the states of nature namely the following two assumptions are required for the suggested method the utility function is in the class of increasing continuous functions and the probabilities of the states of nature are rank ordered we develop a simple analytical method for the partial ranking of decision alternatives under the stated assumptions this method does not require solving optimization programs and is free of the rounding errors

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

tools for interactive multiattribute decisionmaking with incompletely identified information abstract the aim of this paper is to present tools or techniques for an interactive multiattribute decisionmaking with the decision maker s incomplete information that is 1 we formally describe mathematical models under certainty and uncertainty for establishing pairwise dominance where the incomplete information becomes the set of constraints in the model 2 we present a description on styles of incomplete parameter value information 3 the characteristic of a weak dominance is described when the decision maker is not willing or able to provide more information on parameters the weak dominance technique is useful for a final choicemaking 4 we propose a dominance graph and also present an algorithm of generating the dominance graph based on the information of pairwise dominance the dominance graph compactly displays the dominance structure of all alternatives thus it can be used for aiding the selection of preferable alternatives

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

rank inclusion in criteria hierarchies this paper presents a method called rank inclusion in criteria hierarchies rich for the analysis of incomplete preference information in hierarchical weighting models in rich the decision maker is allowed to specify subsets of attributes which contain the most important attribute or more generally to associate a set of rankings with a given set of attributes such preference statements lead to possibly non convex sets of feasible attribute weights allowing decision recommendations to be obtained through the computation of dominance relations and decision rules an illustrative example on the selection of a subcontractor is presented and the computational properties of rich are considered

on the normalizers of f residuals of all subgroups of a finite group abstract let f be a non empty formation and g be a finite group we define the subgroup n f g to be the intersection of the normalizers of the f residuals of all subgroups of g set n f 0 g 1 and define n f i 1 g n f i g n f g n f i g for i 1 by n f g denote the terminal term of this ascending series let f nf be the class of all groups whose f residuals are nilpotent in this paper we release several deep relationships between g n f g and g f we characterize the formations f such that g f would imply that g n f g and the formations f such that g n f g would imply that g f we also study the relationship between n f g and int f g the intersection of all f maximal subgroups of g we characterize the formations f such that n f g is contained in int f g for each group g and the formations f such that n f g coincides with int f g for each group g moreover for an arbitrary non empty formation f the properties of n f g are investigated provided that g is p soluble some recent results are generalized

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

algebraic shift equivalence and primitive matrices motivated by symbolic dynamics we study the problem given a unital subring s of the reals when is a matrix a algebraically shift equivalent over s to a primitive matrix we conjecture that simple necessary conditions on the nonzero spectrum of a are sufficient and establish the conjecture in many cases if s is the integers we give some lower bounds on sizes of realizing primitive matrices for dedekind domains we prove that algebraic shift equivalence implies algebraic strong shift equivalence

preference assessment by imprecise ratio statements the pairs method developed in this paper introduces imprecise preference statements into value trees the assessment of attribute weights in pairs extends the well known smart technique so that in addition to exact statements the decision maker can enter interval judgments which indicate ranges for the relative importance of the attributes the interval judgments and the possibly range valued information about the outcomes of the alternatives are processed with linear programming into value intervals and dominance relations as the decision maker refines the description of his preferences either by entering new statements or by tightening his earlier judgments these results become more detailed and convey more information about which alternatives are preferred throughout the interactive refinement process pairs supports the decision maker by deriving and displaying the consequences of his earlier judgments

multi attribute decision aid under incomplete information and hierarchical structure abstract this paper presents methods for dealing with incomplete information about both attribute weights and values under a hierarchically structured value tree incomplete information in this paper covers arbitrary linear inequalities and is hence to treat a more general situation than a previous restrictive definition of incomplete information that typically includes interval judgment this may give decision makers chances that is enhanced freedom of choice and comforts of specification we propose two techniques for prioritizing alternatives by strict dominance relationship one is the extension of a previous method for operating flat structured value trees to hierarchical ones the other approach propagates pairwise dominance values from leaf nodes to topmost node consecutively which is also an extension of a previous method because the strict dominance rule fails to fully prioritize alternatives as is usual the case under incomplete information we suggest a new method a measure of preference strength which can provide decision makers with a single optimal alternative or full rank of alternatives without any further interaction with decision makers

eventual finite order generation for the kernel of the dimension group representation the finite order generation problem fog in symbolic dynamics asks whether every element in the kernel of the dimension group representation of a subshift of finite type xa aa is a product of elements of finite order in the group aut aa of homeomorphisms of xa commuting with ca we study the space of strong shift equivalences over the nonnegative integers and the first application is to prove eventual fog which says that every inert symmetry of ca is a product of finite order homeomorphisms of xa commuting with sufficiently high powers of ca then we discuss the relation of fog to williams lifting problem lift for symmetries of fixed points in particular either fog or lift is false finally we also discuss p adic convergence and other implications of eventual fog for gyration numbers

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

establishing performance evaluation structures by fuzzy relation based cluster analysis the purpose of this study is to establish hierarchical structures for the performance evaluation of vague humanistic complicated systems to overcome the difficulties due to partial information and the vagueness of human knowledge and recognition a fuzzy relation based clustering method is proposed to model this evaluation first the effects of different max t i compositions on the formation of clusters are discussed then an improved clustering algorithm is developed to produce several partition trees with different levels and clusters according to different t i norm compositions to demonstrate the usefulness of the proposed algorithm the academic departments of higher education were considered using actual engineering school data in taiwan three performance evaluation structures are established by using max t 1 max t 2 and max t 3 compositions the results show that the proposed fuzzy hierarchical approach is useful and practical for performance evaluations of complicated humanistic systems

recovery of the absorption coefficient from diffused reflected light using a discrete diffusive model an algorithm based on a discrete model for photon migration is proposed for recovering the absorption coefficient in a semi infinite slab a pulsed light source is modeled and only reflected signals are used in the reconstruction the diffusion coefficient and speed of light are assumed constant and known the algorithm is based on the result that the earliest reflected signals obtained from a particular voxel depend either in a linear or in a quadratical fashion on the square of the absorption coefficient in that voxel by solving the discrete model in the forward direction in a region where the absorption coefficient has been calculated already the absorption coefficients in the voxels on the boundary of the region are calculated using interpolation results show that simple absorptive regions can be accurately recovered

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

on loops in the hyperbolic locus of the complex henon map and their monodromies abstract we prove john hubbard s conjecture on the topological complexity of the hyperbolic horseshoe locus of the complex henon map in fact we show that there exist several non trivial loops in the locus which generate infinitely many mutually different monodromies furthermore we prove that the dynamics of the real henon map is completely determined by the monodromy of the complex henon map providing the parameter of the map is contained in the hyperbolic horseshoe locus

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

shortest path problems with partial information models and algorithms for detecting dominance abstract in this work we focus on partial information models for the well known shortest path problem where we consider multiple instances of values for the parameters that determine the cost of each arc this allows coping with the uncertainty about the future the imprecision of data the arbitrariness of some options the evolving values of the decision makers dms and or the multiplicity of dms in group decision making this paper proves some results and presents detailed algorithms to identify the set of non dominated paths a concept from decision theory under partial information we first address problems with a finite set of instances then problems with a general eventually not discrete set of instances and finally we study a particular case of the latter which complies with a condition that may hold in some situations to deal with these partial information problems we propose a new use for existing multicriteria algorithms based on the ranking of shortest paths

implementing stochastic multicriteria acceptability analysis abstract stochastic multicriteria acceptability analysis smaa is a family of methods for aiding multicriteria group decision making in problems with inaccurate uncertain or missing information these methods are based on exploring the weight space in order to describe the preferences that make each alternative the most preferred one or that would give a certain rank for a specific alternative the main results of the analysis are rank acceptability indices central weight vectors and confidence factors for different alternatives the rank acceptability indices describe the variety of different preferences resulting in a certain rank for an alternative the central weight vectors represent the typical preferences favouring each alternative and the confidence factors measure whether the criteria measurements are sufficiently accurate for making an informed decision the computations in smaa require the evaluation of multidimensional integrals that must in practice be computed numerically in this paper we present efficient methods for performing the computations through monte carlo simulation analyze the complexity and assess the accuracy of the presented algorithms we also test the efficiency of these methods empirically based on the tests the implementation is fast enough to analyze typical sized discrete problems interactively within seconds due to almost linear time complexity the method is also suitable for analysing very large decision problems for example discrete approximations of continuous decision problems

preference programming through approximate ratio comparisons abstract in the context of hierarchical weighting this paper operationalizes interval judgments which allow the decision maker to enter ambiguous preference statements by indicating the relative importance of factors as intervals of values on a ratio scale through such judgments the decision maker can capture the subjective uncertainty in his preferences and thus avoid the often cumbersome elicitation of exact ratio estimates after each new statement the interval judgments are synthesized into dominance relations on the alternatives by solving a series of linear programming problems this leads to an interactive process of preference programming which provides more detailed results as the decision maker gradually enters a more specific preference description moreover the overall effort of preference elicitation is smaller than in the analytic hierarchy process because the most preferred alternative can usually be identified before all possible comparisons between pairs of factors have been completed

a multiple criteria decision model with ordinal preference data abstract this paper develops a model for aggregating ordinal preference ranking across multiple criteria criteria weights are developed as part of the optimization process the model utilizes three levels of ordinal priorities 1 preferences among alternatives on the basis of each criterion 2 preferences among the criteria to reflect the importance of those criteria and 3 preferences among the criteria which express the degree to which the respondent can clearly distinguish among the alternatives the model is based upon a data envelopment analysis structure which permits a flexible weighting mechanism for each alternative being ranked

periodic seeded arrays and automorphisms of the shift the automorphism group autfsy of the full 2 shift is conjectured to be generated by the shift and involutions we approach this problem by studying a certain family of automorphisms whose order was unknown but which we show to be finite and for which we find factorizations as products of involutions the result of this investigation is the explicit construction of a subgroup z of aut z2 z is generated by certain involutions g and turns out to have a number of curious properties for example gn and gk commute unless n and k are consecutive integers the order of gn k o o gk is independent of k and z contains elements of all orders the investigation is aided by the development of results about certain new types of arrays of o s and l s called periodic seeded arrays as well as the use of boyle and krieger s work on return numbers and periodic points

on automorphisms of markov chains we prove several theorems about automorphisms of markov chains using the weight per symbol polytope

a method of multiattribute decision making with incomplete information a precise determination of a multiattribute utility function of a decision maker or a group of decision makers requires considerable information that may not be available in many decision situations in this paper the method hopie which allows one to determine a set of utility functions consistent with the incomplete information received from the decision maker is proposed the method is based on holistic judgments of hypothetical alternatives defined by a certain factorial design it requires that the evaluation of the alternatives be given on an interval scale the method can also accommodate other types of additional information such as pairwise comparisons

criteria importance theory for multicriterial decision making problems with a hierarchical structure abstract we develop a new model of multicriterial decision analysis with a hierarchical criteria structure the suggested methodology is based on a rigorously defined specification of qualitative and quantitative importance of criteria of all levels of the hierarchy and enables the comparison of decision alternatives for different types of criteria scale

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

periodic points and automorphisms of the shift on etudie le groupe d automorphisme d un decalage de markov topologique a l aide des points periodiques et des ensembles instables

automorphisms of hyperbolic dynamical systems and on etend la construction de wagoner pour produire un invariant sur le groupe des homeomorphismes d une variete lisse qui commutent avec un diffeomorphisme hyperbolique fixe on montre que cet invariant dynamique peut etre calcule a partir des groupes d homologie de la variete et l action du diffeomorphisme et des homeomorphismes sur les groupes d homologie

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

on formations of finite groups with the generalised wielandt property for residuals abstract a formation f of finite groups has the generalised wielandt property for residuals or f is a gwp formation if the f residual of a group generated by two f subnormal subgroups is the subgroup generated by their f residuals we prove that every gwp formation is saturated this is one of the crucial steps in the hunt for a solution of the classification problem

sequential incorporation of imprecise information in multiple criteria decision processes abstract in this paper we deal with multicriteria decision processes and develop tools that permit to ease the task of analysing such models we provide a methodology to sequentially incorporate imprecise preference information which is given by means of general linear relations in the weighting coefficients the results presented allow us to evaluate the quality of the information supplied and can be used to reduce the number of irrelevant alternatives to be presented to the decision maker dm several examples based on multiple criteria linear programming illustrate the results of the paper

decision analysis with incomplete utility and probability information an approach to the solution of decision analysis problems under uncertainty with imprecise and incomplete information is presented the methodology is designed for cases in which payoffs conditional on the state of nature are known precisely but only limited or imprecise probability and utility information is available regarding a decision maker s beliefs and tastes a decision maker provides conditional payoffs optionally bounds on state probabilities bounds on the certainty equivalent for a simple lottery any known relationships between probabilities of states of nature and a series of strict preferences between pairs of vectors of conditional payoffs we assume an exponential utility function with unknown parameter the method proceeds by sequentially eliciting preferences new bounds on probabilities and or the certainty equivalent and new relationships among probabilities until the problem is solved the methodology is demonstrated through a two state and a three state example which illust

onf subnormal subgroups andf residuals of finite soluble groups all groups that we consider are finite and soluble recall that a formation is a class of groups which is closed under homomorphic images and subdirect products hence if f is a formation and g is a group which is a direct product of the subgroups a and b then g is in f if and only if a and b lie in f more generally doerk and w x hawkes 4 iv 1 18 proved that if g is a group such that g s a b then g s a b where g is the f residual of g that is the smallest normal subgroup of g with quotient in f the main purpose of this paper is the development of this result by means of the concept of f subnormal subgroup suppose that f is a saturated formation a maximal subgroup m of a group g is called f normal in g if grcore m g f a subgroup h of g g is called f subnormal in g if either h s g or there exists a chain h s h f h f f h s g such that h is an f normal maximal 0 1 n i subgroup of h for 0 f i n it is clear that if f s n the saturated iq1 formation of all nilpotent groups the f subnormal subgroups of g are exactly the subnormal subgroups of g let f be a subgroup closed saturated formation containing n it is rather easy to see that if f is closed under the product of normal subgroups then g s a b f for every pair of subnormal subgroups a and b such that g s ab this result does not remain true if a and b are

the restricted weyl group of the cuntz algebra and shift endomorphisms it is shown that modulo the automorphisms which fix the canonical diagonal masa point wise the group of those automorphisms of on which globally preserve both the diagonal and the core uhf subalgebra is isomorphic via restriction with the group of those homeomorphisms of the full one sided n shift space which eventually commute along with their inverses with the shift transformation the image of this group in the outer automorphism group of on can be embedded into the quotient of the automorphism group of the full two sided n shift by its center generated by the shift if n is prime then this embedding is an isomorphism msc 2010 46l40 37b10

automorphisms of the dimension group and gyration numbers o introduction 1 the sign gyration compatibility condition 2 gyration and orbit sign numbers 3 construction of sgcc a m 4 application of sgcc a summary let aut o a denote the group of automorphisms of a subshift of finite type xa o a built from a primitive matrix a we show that the sign gyrationcompatibility condition homomorphism sgcc a m defined on aut 0 a factors through the group aut s a of automorphisms of the dimension group this is used to find a mixing subshift of finite type with a permutation of fixed points that cannot be lifted to an automorphism of the shift we also give an example of a mixing subshift of finite type where the dimension group representation is not surjective this example is used in kr3 to give examples of subshifts of finite type reducible with two mixing components that are shift equivalent but not strong shift equivalent over the nonnegative integers o introduction

the automorphism group of a shift of finite type let xt at be a shift of finite type and g aut vt denote the group of homeomorphisms of xt commuting with t we investigate the algebraic properties of the countable group g and the dynamics of its action on xt and associated spaces using marker constructions we show g contains many groups such as the free group on two generators however g is residually finite so does not contain divisible groups or the infinite symmetric group the doubly exponential growth rate of the number of automorphisms depending on n coordinates leads to a new and nontrivial topological invariant of crt whose exact value is not known we prove that modulo a few points of low period g acts transitively on the set of points with least at period n using padic analysis we generalize to most finite type shifts a result of boyle and krieger that the gyration function of a full shift has infinite order the action of g on the dimension group of at is investigated we show there are no proper infinite compact g invariant sets we give a complete characterization of the g orbit closure of a continuous probability measure and deduce that the only continuous g invariant measure is that of maximal entropy examples questions and problems complement our analysis and we conclude with a brief survey of some remaining open problems

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

multiple criteria robust interactive decision analysis mcrid for optimizing public policies abstract important public policy decisions are often very complex involving many factors large uncertainties and multiple conflicting objectives decision analysis which is a formal framework for dealing with such issues has been applied to a variety of public sector problems over the last two decades a limitation of using decision analysis is the often onerous assessment burden it places on the decision maker dm we have developed a novel interactive procedure and decision support system dss for performing decision analysis on the personal computer called robust interactive decision analysis rid which avoids the difficult problems of precisely assessing a dm s utility and state probability functions associated with traditional decision treee analysis the rid method permits a dm to voluntarily and interactively express strong viz sure binary preferences for actions partial decision functions and full decision functions and only imprecise probability and utility function assessments the inputs are used with various dominance operators via a mathematical programming framework to prune the state probability utility and decision space until there is convergence on a relatively small subset of efficient strategies or an optimal choice strategy conceptually the operation of the rid method can be regarded as a state pruning system and its computer implementation as a dss in this paper we extended the rid concept and dss to deal with multiple criteria decisions obviating the need to precisely and completely assess attribute weights tradeoffs consequences and or value utility functions the approach which we call multiple criteria robust interactive decision analysis mcrid is developed illustrated and shown to be effective in eliminating many inefficient alternatives however since the aggregate utility of each alternative is interval valued it then becomes difficult to intuitively choose an optimal alternative from among the remaining efficient ones since the intervals are not defined by any specific probability distributions we have tentatively shown that aggregate utility intervals ultimately converge toward a normal density function and can be so approximated with relatively few attributes hence stochastic dominance is employed to further filter out alternatives an interactive goal programming gp technique is then developed to assist the dm in choosing an optimal alternative

endomorphisms of expansive systems on compact metric spaces and the pseudo orbit tracing property we investigate the interrelationships between the dynamical properties of commuting continuous maps of a compact metric space let x be a compact metric space first we show the following if t x x is an expansive onto continuous map with the pseudo orbit tracing property potp and if there is a topologically mixing continuous map sp x x with r p 99t then t is topologically mixing if t x x and o x x are commuting expansive onto continuous maps with potp and if r is topologically transitive with period p then for some k dividing p x ui o bi where the b 0 x is a topologically transitive expansive homeomorphism having potp and o x x is a positively expansive onto continuous map with pw 9s then p has potp and is constant to one further we define essentially lr endomorphisms for systems of expansive onto continuous maps of compact metric spaces and prove that if r x x x is an expansive homeomorphism with canonical coordinates and s is an essentially lr automorphism of x r then po has canonical coordinates we add some discussions on basic properties of the essentially lr endomorphisms

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

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

a criterion for the existence of normal π complements in finite groups abstract the purpose of this article is to prove using the classification of the finite simple groups the following conjecture let be a set of odd primes then a finite group is homogeneous if and only if it is closed using this several open problems can be settled including an affirmative answer to the following problem of baer let g be a finite group and g suppose that g is both homogeneous and homogeneous is g a direct product of a group and a group finally we note that the proof of the conjecture yields proof to some theorems proved earlier without using the classification of the finite simple groups

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

weighted sum model with partial preference information application to multi objective optimization multi objective optimization problems often lead to large nondominated sets as the size of the problem or the number of objectives increases generating the whole nondominated set requires significant computation time while most of the corresponding solutions are irrelevant to the decision maker dm optimizing an aggregation function reduces the computation time and produces one or a very limited number of more focused solutions this requires however the elicitation of precise preference parameters which is often difficult and partly arbitrary and might discard solutions of interest an intermediate approach consists in using partial preference information with an aggregation function in this work we present a preference relation based on the weighted sum aggregation where weights are not precisely defined we give some properties of this preference relation and define the set of preferred points as the set of nondominated points with respect to this relation we provide an efficient and generic way of generating this preferred set using any standard multi objective optimization algorithm this approach shows competitive performances both on computation time and quality of the generated preferred set

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