on conditional and intrinsic autoregressions summary gaussian conditional autoregressions have been widely used in spatial statistics and bayesian image analysis where they are intended to describe interactions between random variables at fixed sites in euclidean space the main appeal of these distributions is in the markovian interpretation of their full conditionals intrinsic autoregressions are limiting forms that retain the markov property despite being improper they can have advantages over the standard autoregressions both conceptually and in practice for example they often avoid difficulties in parameter estimation without apparent loss or exhibit appealing invariances as in texture analysis however on small arrays and in nonlattice applications both forms of autoregression can lead to undesirable second order characteristics either in the variables themselves or in contrasts among them this paper discusses standard and intrinsic autoregressions and describes how the problems that arise can be alleviated using dempster s 1972 algorithm or an appropriate modification the approach represents a partial synthesis of standard geostatistical and gaussian markov random field formulations some nonspatial applications are also mentioned

determining the best decision in the presence of imprecise information abstract this paper addresses general aspects of decision making in an imprecise environment here the task of choosing a decision among the available alternatives with imprecisely defined outcomes is analyzed new definitions for the concept of best decision in such an environment are introduced these definitions are based on fuzzy set theoretic representations of decision outcomes

fuzzy shortest paths abstract shortest paths are one of the simplest and most widely used concepts in nonfuzzy networks fuzzy shortest paths also have a variety of applications but are hampered by the possibility that the fuzzy shortest length may not correspond to an actual path in the network in this paper we present new models based on fuzzy shortest paths that circumvent this problem and we also give a general algorithm based on dynamic programming to solve the new models in addition we analyze the fuzzy shortest path algorithms in terms of submodular functions the analysis concepts developed for fuzzy shortest paths are also discussed in terms of general fuzzy mathematical programming

some multivariate tests of independence based on ranks of nearest neighbors abstractseveral parametric and nonparametric tests of independence between two random vectors are available in the literature but many of them perform poorly for high dimensional data and are not applicable when the dimension exceeds the sample size in this article we propose some tests based on ranks of nearest neighbors which can be conveniently used in high dimension low sample size situations several simulated and real data sets are analyzed to show the utility of the proposed tests codes for implementation of the proposed tests are available as supplementary materials

on the application of fuzzy sets theory to the optimal flood control problem arising in water resources systems abstract we first survey the application of fuzzy sets theory to various problems occurring in water resources systems the problem of optimal flood control planning by an appropriate integration of structural and non structural measures with the objective of optimizing the flood damage reduction due to recurrent floods is modeled via fuzzy sets methodologies a two level optimization model appropriate for planning decisions first on a regional or local level and then on a national level is proposed a third phase involving coordination is appended in particular a fuzzy optimization model involving an adroit combination of fuzzy dynamic programming type reasoning and a branch and bound type search procedure is offered as a more utilitarian approach than its crisp equivalent the performance of the algorithm is illustrated with an example

camera calibration from images of spheres this paper introduces a novel approach for solving the problem of camera calibration from spheres by exploiting the relationship between the dual images of spheres and the dual image of the absolute conic iac it is shown that the common pole and polar with regard to the conic images of two spheres are also the pole and polar with regard to the iac this provides two constraints for estimating the iac and hence allows a camera to be calibrated from an image of at least three spheres experimental results show the feasibility of the proposed approach

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

catadioptric camera calibration using geometric invariants central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint in this paper we propose a novel method for the calibration of central catadioptric cameras using geometric invariants lines and spheres in space are all projected into conics in the catadioptric image plane we prove that the projection of a line can provide three invariants whereas the projection of a sphere can only provide two from these invariants constraint equations for the intrinsic parameters of catadioptric camera are derived therefore there are two kinds of variants of this novel method the first one uses projections of lines and the second one uses projections of spheres in general the projections of two lines or three spheres are sufficient to achieve catadioptric camera calibration one important conclusion in this paper is that the method based on projections of spheres is more robust and has higher accuracy than that based on projections of lines the performances of our method are demonstrated by both the results of simulations and experiments with real images

fuzzy sets modeling and optimization for disaster control systems planning abstract various forms of disasters natural and man made abound although to some extent some of these have been exacerbated by modern civilization various technologies have been invoked to control or mitigate their adverse effects modeling and optimization based techniques have also been employed we outline some efforts based on fuzzy sets theory which are utilized in conjunction with classical methods to enhance the reliability and utility of these efforts in particular disasters caused by floods and storm water pollution are used as vehicles for the exemplification of our models

forecasting enrollments with fuzzy time series part ii abstract there have been a good many methods to forecast university enrollments in the literature however none of them could be applied when the historical data are linguistic values fuzzy time series is an effective tool to deal with such problems in this paper as an application of fuzzy time series in educational research the forecast of the enrollments of the university of alabama is carried out in so doing a fuzzy time series model is developed using historical data a complete procedure is proposed which includes fuzzifying the historical data developing a fuzzy time series model and calculating and interpreting the outputs to evaluate the forecasting model the robustness of the fuzzy time series model is tested advantages and problems of the forecasting method are also discussed

multiple objective fuzzy dynamic programming problems a survey and some applications many real world problems involve sequential or multistage decision making dynamic programming dp is a powerful optimization technique that is particularly applicable to many complex problems requiring a sequence of interrelated decisions a new methodology multiobjective dynamic programming modp which relies heavily on conventional dynamic programming is developed as a technique for solving problems that involve conflicting objectives that obey dp characteristics in the past two decades a major development of multiobjective dynamic optimization has been made modp one of the most provocative topics within the broader subject a natural extension of dp is its use in conjumction with fuzzy sets this involves the perturbation of its components in a manner that admits of systematic fuzzification fuzzy dynamic programming fdp represents an advance on the theory of dp this paper reviews the major concepts used in modp and fmodp and examins the current progress made in the development of the corresponding theory and methodology

analysis of a class fractional programming problems we propose a solution strategy for fractional programming problems of the form max x x g x u x where the function satisfies certain convexity conditions it is shown that subject to these conditions optimal solutions to this problem can be obtained from the solution of the problem max x x g x u x where is an exogenous parameter the proposed strategy combines fractional programming andc programming techniques a maximal mean standard deviation ratio problem is solved to illustrate the strategy in action

fuzzy optimal search methods abstract this paper gives analytical approaches and algorithms for decision tree search techniques the decision trees are assumed to have a fixed number of stages and predefined possible states at every stage the costs of traversing the tree are characterized as approximate and defined as fuzzy numbers two search methods each drawing from an existing non fuzzy search algorithm are described the first method is a dynamic programming search where the principle of optimality with fuzzy costs is addressed the second method is an a search for which the notion of a lower bound estimate of costs is utilized to increase the efficiency of the search algorithms for each method are included theorems and proofs which complete the analytical development of these techniques are also included finally a numerical example illustrating the procedure is given

conditional decision processes with recursive function we consider stochastic optimization of not necessarily additive but recursive functions over multistage decision processes without assuming any monotonicity we optimize a regular process by a direct dynamic programming approach on the regular decision process we propose two related conditional decision processes an a posteriori conditional decision process and an a priori when the markov transition law degenerates into a deterministic dynamics the two conditional processes reduce to the same deterministic decision process the conditional processes with monotonicity are optimized by the usual backward dynamic programming we show that under additional convexity the regular process dominates the a priori in maximum value function and the a priori does the a posteriori we show that the a posteriori process illustrates kreps and porteus s dynamic choice problem the numerical example also verifies the dominance relation in three optimal value functions

on visualization and aggregation of nearest neighbor classifiers nearest neighbor classification is one of the simplest and most popular methods for statistical pattern recognition a major issue in k nearest neighbor classification is how to find an optimal value of the neighborhood parameter k in practice this value is generally estimated by the method of cross validation however the ideal value of k in a classification problem not only depends on the entire data set but also on the specific observation to be classified instead of using any single value of k this paper studies results for a finite sequence of classifiers indexed by k along with the usual posterior probability estimates a new measure called the bayesian measure of strength is proposed and investigated in this paper as a measure of evidence for different classes the results of these classifiers and their corresponding estimated misclassification probabilities are visually displayed using shaded strips these plots provide an effective visualization of the evidence in favor of different classes when a given data point is to be classified we also propose a simple weighted averaging technique that aggregates the results of different nearest neighbor classifiers to arrive at the final decision based on the analysis of several benchmark data sets the proposed method is found to be better than using a single value of k

long term inventory policy making through fuzzy decision making models abstract the inventory policy meant as a replenishment rule has a considerable impact on most firms the paper considers the determination of optimal inventory policy of firms from a global viewpoint of top management the inventory is represented as a fuzzy system with the fuzzy inventory level as the output the fuzzy replenishment as the input and fuzzy demand the control problem is formulated in terms of decision making in a fuzzy environment with fuzzy constraints imposed on replenishments a fuzzy goal for preferable inventory levels to be attained and the fuzzy decision as the intersection of fuzzy constraints and the fuzzy goal at subsequent stages the planning horizon is infinite the problem is to find an optimal time invariant strategy relating the optimal replenishments to the current inventory levels maximizing the membership function of fuzzy decision the existence of such a strategy is proved and an algorithm for its determination is given the optimal time invariant strategy obtained is represented as a fuzzy conditional statement equated with a fuzzy relation which is the firm s optimal fuzzy replenishment rule

on the decomposition problem of fuzzy sets in this paper we consider an important problem that is frequently encountered and yet almost universally ignored both in the application and in the theoretic studies of fuzzy sets we refer to this problem as the decomposition of fuzzy sets in nearly all applications of fuzzy sets theory e g fuzzy decision making fuzzy control fuzzy forecasting etc the output is in general a fuzzy set this is then defuzzified before it is applied although defuzzification may be necessary if a crisp quantity is definitely needed when a fuzzy output is appropriate desired or required in an application then the defuzzification step becomes unnecessary yet in this case one finds that it is some times difficult to correctly interpret a fuzzy quantity or identify the true meaning of this fuzzy output using a family of predefined fuzzy sets thus how to match the fuzzy output and the predefined fuzzy sets is the problem of concern in this paper to address this problem we first present and review some definitions and then proceed with an investigation of the preliminary properties of these concepts complementing them with illustrative examples finally we propose some algorithms for the solution of this problem

selecting preferred solutions in the minimax approach to dynamic programming problems under flexible constraints abstract dynamic programming is a powerful approach to the optimization of sequential or multistage decision processes e g in planning or in system control in this paper we consider both theoretical and algorithmic issues in sequential decision processes under flexible constraints such processes must attain a given goal within some tolerance tolerances or preferences also apply to the values the decision variables may take or on the action chosen at each step such problems boil down to maximin optimization unfortunately this approach suffers from the so called drowning effect lack of discrimination and the optimality principle of dynamic programming is not always verified in this context we introduce a general framework for refined minimax optimization procedures in order to compare and select preferred alternatives this framework encompasses already introduced methods such as leximin and discrimin but it allows their extension to the comparison of vectors of unequal lengths we show that these refined comparisons restore compatibility with the optimality principle and that classical algorithms can be adapted to compute such preferred solutions by exploiting existing results on idempotent semirings

a fuzzy dynamic approach to the multicriterion resource allocation problem abstract in this paper a new approach using fuzzy dynamic programming is proposed for solving the multiple criteria resource allocation problems it has been concluded that solutions obtained by this approach are always efficient hence an optimal compromise solution can be introduced a characteristic feature of the presented approach is that the objective function scalarization can be taken into account by using fuzzy set notations a numerical example is given to clarify the developed approach

a dynamic approach to multiple objective resource allocation problem a new approach using dynamic programming is developed for solving the multiple objective resource allocation problem there are two key issues being addressed in this approach the first one is to develop a methodology of fuzzy evaluation and fuzzy optimization for multiple objective systems the procedure of getting the marginal evaluation for each objective and aggregating them synthetically into a global evaluation is presented in this paper the second one is to design a dynamic optimization algorithm by incorporating the method of fuzzy evaluation and fuzzy optimization with the conventional dynamic programming technique a characteristic feature of the approach presented is that various objectives are synthetically considered by the fuzzy systematic technique instead of the frequently employed weighted average method numeric examples are also given to clarify the developed approach and to demonstrate its effectiveness

fuzzy dynamic programming fuzzy adaptive neuro control and the general medical diagnosis problem abstract the fuzzy medical diagnosis decision models of esogbue and elder employed fuzzy sets theory to directly and more correctly model all the information nets useful in reaching a scientific understanding of a patient s health status this knowledge was utilized in constructing a sensible medical hypothesis decision problem in this paper we show how fuzzy dynamic programming and neural networks can be used to extend the process to other phases by linking the four stages of medical hypothesis physician s observation preliminary diagnosis and final diagnosis in an adroit manner

combining fuzzy iteration model with dynamic programming to solve multiobjective multistage decision making problems this paper aims to develop a fuzzy dynamic programming approach for multiobjective multistage decision making problems fuzzy dynamic programming usually convert the problems into corresponding single objective problems by an aggregate of hybrid objective values that expresses the performance of the particular stage decision weight assessment is an important problem arising from the evaluation of multiple objectives therefore a fuzzy iteration model is first developed to simultaneously provide the objective weights and the evaluation of alternatives with multiple objectives then a fuzzy dynamic programming is derived by applying the fuzzy iteration model to classic dynamic programming to evaluate the decisions at each stage in the dynamic process of decision makings where the objective weights are initially elicited from the information implicit in alternatives and can be interactively adjusted to reflect the changes of decision situations by using a non structured decision making analysis method if necessary finally the fuzzy dynamic programming is validated through a problem of water resource allocation

likelihood inference in nearest neighbour classification models summary traditionally the neighbourhood size k in the k nearest neighbour algorithm is either fixed at the first nearest neighbour or is selected on the basis of a crossvalidation study in this paper we present an alternative approach that develops the k nearest neighbour algorithm using likelihood based inference our method takes the form of a generalised linear regression on a set of k nearest neighbour autocovariates by defining the k nearestneighbour algorithm in this way we are able to extend the method to accommodate the original predictor variables as possible linear effects as well as allowing for the inclusion of multiple nearest neighbour terms the choice of the final model proceeds via a stepwise regression procedure it is shown that our method incorporates a conventional generalised linear model and a conventional k nearest neighbour algorithm as special cases empirical results suggest that the method out performs the standard k nearest neighbour method in terms of misclassification rate on a wide variety of datasets

towards fuzzy differential calculus part 1 integration of fuzzy mappings abstract this paper deals with fuzzy set valued mappings of the real line and more particularly focuses on mappings from the real line to the set of convex normal fuzzy sets of the real line these mappings can also be viewed as fuzzy relations using zadeh s extension principle the integral of such fuzzy mappings over a crisp interval is defined provided a special analytical representation of the fuzzy mapping the practical computation of such an integral is shown to be easy practically speaking it yields the fuzzy surface of a fuzzily bounded area

a stable model based fuzzy predictive control based on fuzzy dynamic programming a stable model based fuzzy predictive controller based on fuzzy dynamic programming is introduced the objective of the fuzzy predictive controller is to drive the state of the system to a terminal region where a local stabilizing controller is invoked leading to a dual mode strategy the prediction horizon is fixed and specified the stability of the controlled system is studied using the value function as a lyapunov function guaranteed stability is obtained under conditions on the terminal region the local control law and the membership functions of fuzzy goal and constraints therein the solution procedure is based on dynamic programming with branch and bound

geometric interpretations of the relation between the image of the absolute conic and sphere images a spherical object has been introduced into camera calibration for several years through utilizing the properties of an image conic which is the projection of the occluding contour of a sphere in the perspective image however in literature only an algebraic interpretation was presented for the relation between the image of the absolute conic and sphere images in this paper we propose two geometric interpretations of this relation and two novel camera calibration methods using sphere images are derived from these geometric interpretations

choice of the smoothing parameter and efficiency of k nearest neighbor classification abstract a simulation study was performed to investigate the sensitivity of the k nearest neighbor nn k rule of classification to the choice of k the optimal choice of k was found to be a function of the dimension of the sample space the size of the space the covariance structure and the sample proportions the nearest neighbor rules chosen using the k suggested by the simulations had correct classification rates at least as high as those rates for the linear discriminant function and the logistic regression method in particular the rule became more efficient as the difference in the covariance matrices increased and also when the difference in sample proportion was large an adaptive rule which selects k by iteratively maximizing the local mahalanobis distance is shown to be efficient thus abrogating the need to know the underlying population variance covariance structure

a bayesian reassessment of nearest neighbor classification the k nearest neighbor knn procedure is a well known deterministic method used in supervised classification this article proposes a reassessment of this approach as a statistical technique derived from a proper probabilistic model in particular we modify the assessment found in holmes and adams and evaluated by manocha and girolami where the underlying probabilistic model is not completely well defined once provided with a clear probabilistic basis for the knn procedure we derive computational tools for bayesian inference on the parameters of the corresponding model in particular we assess the difficulties inherent to both pseudo likelihood and path sampling approximations of an intractable normalizing constant we implement a correct mcmc sampler based on perfect sampling when perfect sampling is not available we use instead a gibbs sampling approximation illustrations of the performance of the corresponding bayesian classifier are provided for benchmark datasets demonstrating in particula

control of a deterministic system es a fuzzy environment over infinite planning horizon the multistage control of a time invariant finite state deterministic system in a fuzzy environment over infinite planning horizon is considered the fuzzy environment is meant as fuzzy constraints imposed on controls and fuzzy goals to be attained the fuzzy constraints are assumed to be state dependent the fuzzy decision is assumed to he the intersection of fuzzy constraints and fuzzy goals the problem is to find an optimal strategy i e a sequence of policies relating the control to the state maximizing the membership function of fuzzy decision for the problem a functional equation is formulated an algorithm of policy iteration type is given the existence of a lime invariant optimal strategy and the convergence of the algorithm are proved a numerical example is shown

fuzzy approach to multilevel knapsack problems this study proposes a fuzzy approach for solving the multiobjective and multilevel knapsack problems kps the problem was first formulated as a multilevel programming problem with multiple decision makers dms then the degree of satisfaction of each dm was established and represented by their individual membership functions the recursive formulation of dynamic programming was used to solve the decisions of the interrelated stages the overall satisfaction of the decision was obtained through this stage wise operation on the hierarchical structure capacity allocation was developed and a step by step solution procedure was illustrated a detailed comparison between multiobjective and multilevel kps was also carried out finally the possible use of turnpike theorem in kps was scrutinized in the fuzzy domain

job search and employment abstract a multistage search method based on fuzzy preference is used to analyze the processes of job search an employment decision based on fuzzy preference results in an exact choice the incorporation of fuzzy interval preference into employment decision however may lead to multiple choices which provides a theoretical justification for the existence of fuzzy supply of labor thus fuzziness in addition to randomness offers an explanation to wage dispersion

fuzzy dynamic programming approach to hybrid multiobjective multistage decision making problems the purpose of this paper is to develop a new fuzzy dynamic programming approach for solving hybrid multiobjective multistage decision making problems we first present a methodology of fuzzy evaluation and fuzzy optimization for hybrid multiobjective systems in which the qualitative and quantitative objectives are synthetically considered the qualitative objectives are evaluated by decision makers with linguistic variables and the quantitative objectives are converted into proper dimensionless indices after getting the marginal evaluations for each objective a new aggregation method based on the principle of fuzzy pattern recognition is developed to get a global evaluation for all objectives with the global evaluation obtained a fuzzy optimization process is performed then we present a dynamic optimization algorithm by incorporating the fuzzy optimization process with the conventional dynamic programming technique to solve hybrid multiobjective multistage decision making problems a characteristic feature of the approach proposed is that various objectives are synthetically considered by the fuzzy systematic technique instead of the frequently employed weighted average method finally an illustrative example is also given to clarify the developed approach and to demonstrate its effectiveness

geometric properties of central catadioptric line images and their application in calibration in central catadioptric systems lines in a scene are projected to conic curves in the image this work studies the geometry of the central catadioptric projection of lines and its use in calibration it is shown that the conic curves where the lines are mapped possess several projective invariant properties from these properties it follows that any central catadioptric system can be fully calibrated from an image of three or more lines the image of the absolute conic the relative pose between the camera and the mirror and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected this result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors moreover it is proven that systems with a hyperbolic elliptical mirror can be calibrated from the image of two lines if both the shape and the pose of the mirror are known then two line images are enough to determine the image of the absolute conic encoding the camera s intrinsic parameters the sensitivity to errors is evaluated and the approach is used to calibrate a real camera

fuzzy dynamic programming main developments and applications abstract we survey major developments and applications of fuzzy dynamic programming which is here advocated as a promising attempt at making dynamic programming models more realistic by a relaxation of often artificial assumptions of precision as to the constraints goals states and their transitions termination time etc issues related to numerical efficiency are considered applications in r d planning health care and medicine socioeconomic regional development energy systems water and environmental systems chemical engineering etc are surveyed

an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards abstract this paper deals with an optimal stopping problem in dynamic fuzzy systems with fuzzy rewards and shows that the optimal discounted fuzzy reward is characterized by a unique solution of a fuzzy relational equation we define a fuzzy expectation with a density given by fuzzy goals and we estimate discounted fuzzy rewards by the fuzzy expectation this paper characterizes the optimal fuzzy expected value and gives an optimal stopping time

paths of least resistance in possibilistic production systems abstract we introduce the idea of possibilistic production systems we provide a general algorithm for finding a path from an initial node to a goal node we show that the use of a heuristic function can help in the efficient implementation of the search process we see that a significant role in determining potential optimal paths is played by concentrating on the most difficult activity to accomplish

catadioptric projective geometry catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera central catadioptric sensors are the class of these devices having a single effective viewpoint in this paper we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications we show that a central catadioptric projection is equivalent to a two step mapping via the sphere the second step is equivalent to a stereographic projection in the case of parabolic mirrors conventional lens based perspective cameras are also central catadioptric devices with a virtual planar mirror and are thus covered by the unifying model we prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images conics it turns out that planar and parabolic mirrors build a dual catadioptric projection pair as a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system

paracatadioptric camera calibration catadioptric sensors refer to the combination of lens based devices and reflective surfaces these systems are useful because they may have a field of view which is greater than hemispherical providing the ability to simultaneously view in any direction configurations which have a unique effective viewpoint are of primary interest among these is the case where the reflective surface is a parabolic mirror and the camera is such that it induces an orthographic projection and which we call paracatadioptric we present an algorithm for the calibration of such a device using only the images of lines in space in fact we show that we may obtain all of the intrinsic parameters from the images of only three lines and that this is possible without any metric information we propose a closed form solution for focal length image center and aspect ratio for skewless cameras and a polynomial root solution in the presence of skew we also give a method for determining the orientation of a plane containing two sets of parallel lines from one uncalibrated view such an orientation recovery enables a rectification which is impossible to achieve in the case of a single uncalibrated view taken by a conventional camera we study the performance of the algorithm in simulated setups and compare results on real images with an approach based on the image of the mirror s bounding circle

an optimistic decision making in fuzzy environment bellman and zadeh have originated three systems of multistage decision processes in a fuzzy environment deterministic stochastic and fuzzy systems in this article we consider an optimization problem with an optimistic criterion on a fuzzy system by making use of minimization maximization expectation in a fuzzy environment we derive a recursive equation for the fuzzy decision process through invariant imbedding approach by illustrating a three state two decision and two stage model we give an optimal solution through dynamic programming the optimal solution is also verified by the method of multistage fuzzy decision tree table

interactive fuzzy goal programming approach for bilevel programming problem abstract this paper presents an interactive fuzzy goal programming fgp approach for bilevel programming problems with the characteristics of dynamic programming dp in the proposed approach the tolerance membership functions in fuzzy sets for measuring the degree of satisfactions of the objectives of both the decision makers and degree of achievement of the decision vector controlled by the leader is defined first then the dynamic fuzzy goal programming model for achievement of highest degree unity to the extent possible to each of the defined membership functions for the fuzzy goal is developed to solve the decisions of the interrelated stages a satisfactory solution is derived efficiently by updating the satisfactory degrees of the decision makers with the consideration of overall satisfactory balance between both the levels illustrative numerical examples are provided to demonstrate the feasibility of the proposed method

identical projective geometric properties of central catadioptric line images and sphere images with applications to calibration central catadioptric cameras are imaging devices that use mirrors to enhance the field of view while preserving a single effective viewpoint lines and spheres in space are all projected into conics in the central catadioptric image planes and such conics are called line images and sphere images respectively we discovered that there exists an imaginary conic in the central catadioptric image planes defined as the modified image of the absolute conic miac and by utilizing the miac the novel identical projective geometric properties of line images and sphere images may be exploited each line image or each sphere image is double contact with the miac which is an analogy of the discovery in pinhole camera that the image of the absolute conic iac is double contact with sphere images note that the iac also exists in the central catadioptric image plane but it does not have the double contact properties with line images or sphere images this is the main reason to propose the miac from these geometric properties with the miac two linear calibration methods for central catadioptric cameras using sphere images as well as using line images are proposed in the same framework note that there are many linear approaches to central catadioptric camera calibration using line images it seems that to use the properties that line images are tangent to the miac only leads to an alternative geometric construction for calibration however for sphere images there are only some nonlinear calibration methods in literature therefore to propose linear methods for sphere images may be the main contribution of this paper our new algorithms have been tested in extensive experiments with respect to noise sensitivity

a generalization of fuzzy multistage decision making and control via linguistic quantifiers abstract multistage incision making control under fuzziness is considered at each control stage a fuzzy constraint is imposed on the control applied and a fuzzy goal is imposed on the state attained an optimal sequence of controls is sought which maximizes the membership function of the fuzzy decision which is assumed to be the intersection of fuzzy constraints and fuzzy goals thin is basically equivalent to the determination of an optimal sequence of controls which best satisfies the fuzzy constraints and fuzzy goals at nil the control stages the generalization proposed in the paper replaces the strict all the something milder for example most thus we seek an optimal sequence of controls which best satisfies the fuzzy constraints and fuzzy goals at for example most of the control stages a calculus of linguistically quantified statements based upon fuzzy sets and possibility theory is used first the algebraic method is employed the resulting control problem is solved by dy

stochastic optimization of forward recursive functions this note solves a finite horizon stochastic optimization problem with forward recursive criterion through dynamic programming the forward recursive criterion is wide it includes additive discounted multiplicative discounted risk sensitive minimum and terminal criteria the basic idea is to apply invariant imbedding method for the stochastic optimization the method incorporates recursive accumulation process into dynamics by expanding the original state space

a generalization of discounted multistage decision making andcontrol through fuzzy linguistic quantifiers an attempt to introduce commonsense knowledge abstract this paper is an extension of work published by kacprzyk in 1983 in which by using a fuzzy logic based calculus of linguistically quantified propositions some generalizations of multistage decision making and control have been proposed namely a new class of models has been developed that make it possible roughly speaking to find an optimal sequence of controls best satisfying fuzzy constraints and goals at say most or any other suitable linguistic quantifier for example almost all at least a few of the control stages in this paper we further extend the above mentioned approach by introducing discounting a variable importance of particular control stages in principle the earlier the more important we propose a new model that can find an optimal sequence of controls best satisfying the fuzzy constraints and goals at say most of the earlier control stages we employ a fuzzy logic based calculus of linguistically quantified propositions and develop a branch and bound algo

sequential decision making in fuzzy environment in this paper we reexamine bellman and zadeh s seminal paper on multistage decision making in a fuzzy environment we propose a correction to their functional equation associated with a stochastic system and formulate a model for deterministic processes governed by fuzzy dynamics

following a moving target monte carlo inference for dynamic bayesian models markov chain monte carlo mcmc sampling is a numerically intensive simulation technique which has greatly improved the practicality of bayesian inference and prediction however mcmc sampling is too slow to be of practical use in problems involving a large number of posterior target distributions as in dynamic modelling and predictive model selection alternative simulation techniques for tracking moving target distributions known as particle filters which combine importance sampling importance resampling and mcmc sampling tend to suffer from a progressive degeneration as the target sequence evolves we propose a new technique based on these same simulation methodologies which does not suffer from this progressive degeneration

dynamic programming for fuzzy systems with fuzzy environment abstract a dynamic programming functional equation for a multi stage decision problem with fuzzy dynamics and environment is formulated and solved by a process of fuzzy interpolation this is an extension of the bellman zadeh model

a goal programming procedure for solving problems with multiple fuzzy goals using dynamic programming abstract this paper describes how the preemptive priority based goal programming gp can be used to solve a class of fuzzy programming fp problems with the characteristics of dynamic programming dp in the proposed approach the membership functions of the objective goals of a problem with fuzzy aspiration levels are defined first then under the framework of preemptive priority based gp a multi stage dp model of the problem for achievement of the highest degree unity of each of the membership functions is developed in the decision process the goal satisficing philosophy of gp is used recursively to arrive at the most satisfactory solution two numerical examples are provided to illustrate the approach

classification based on hybridization of parametric and nonparametric classifiers parametric methods of classification assume specific parametric models for competing population densities e g gaussian population densities can lead to linear and quadratic discriminant analysis and they work well when these model assumptions are valid violation in one or more of these parametric model assumptions often leads to a poor classifier on the other hand nonparametric classifiers e g nearest neighbor and kernel based classifiers are more flexible and free from parametric model assumptions but the statistical instability of these classifiers may lead to poor performance when we have small numbers of training sample observations nonparametric methods however do not use any parametric structure of population densities therefore even when one has some additional information about population densities that important information is not used to modify the nonparametric classification rule this paper makes an attempt to overcome these limitations of parametric and nonparametric approaches and combines their strengths to develop some hybrid classification methods we use some simulated examples and benchmark data sets to examine the performance of these hybrid discriminant analysis tools asymptotic results on their misclassification rates have been derived under appropriate regularity conditions

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

an approach to stopping problems of a dynamic fuzzy system we formulate a stopping problem for dynamic fuzzy systems concerning with fuzzy decision environment it could be regarded as a natural fuzzification of non fuzzy stopping problem with a deterministic dynamic system the validity of the approach by cuts of fuzzy sets will be discussed in constructing one step look ahead policy of an optimal fuzzy stopping time a numerical example is given to illustrate the theoretical results and to show a merit to use fuzzy stopping times in dynamic fuzzy systems

a probabilistic nearest neighbour method for statistical pattern recognition summary nearest neighbour algorithms are among the most popular methods used in statistical pattern recognition the models are conceptually simple and empirical studies have shown that their performance is highly competitive against other techniques however the lack of a formal framework for choosing the size of the neighbourhood k is problematic furthermore the method can only make discrete predictions by reporting the relative frequency of the classes in the neighbourhood of the prediction point we present a probabilistic framework for the k nearest neighbour method that largely overcomes these difficulties uncertainty is accommodated via a prior distribution on k as well as in the strength of the interaction between neighbours these prior distributions propagate uncertainty through to proper probabilistic predictions that have continuous support on 0 1 the method makes no assumptions about the distribution of the predictor variables the method is also fully automatic with no user set parameters and empirically it proves to be highly accurate on many bench mark data sets

a penalized likelihood based pattern classification algorithm penalized likelihood is a general approach whereby an objective function is defined consisting of the log likelihood of the data minus some term penalizing non smooth solutions subsequently this objective function is maximized yielding a solution that achieves some sort of trade off between the faithfulness and the smoothness of the fit most work on that topic focused on the regression problem and there has been little work on the classification problem in this paper we propose a new classification method using the concept of penalized likelihood for the two class case by proposing a novel penalty term based on the k nearest neighbors simple analytical derivations have led to an algorithm that is proved to converge to the global optimum moreover this algorithm is very simple to implement and converges typically in two or three iterations we also introduced two variants of the method by distance weighting the k nearest neighbor contributions and by tackling the unbalanced class patterns situation we performed extensive experiments to compare the proposed method to several well known classification methods these simulations reveal that the proposed method achieves one of the top ranks in classification performance and with a fairly small computation time

fuzzy stopping in continuous time dynamic fuzzy systems in a continuous time dynamic fuzzy system a stopping problem regarding fuzzy rewards is discussed using fuzzy stopping times the fuzzy rewards are evaluated by an expectation generated from a linear ranking function the optimality equations for the optimal fuzzy rewards are given by variational inequalities and an optimal fuzzy stopping time is constructed under assumptions of monotonicity and regularity for stopping rules a numerical example is given to discuss that fuzzy stopping times are better than non fuzzy ones in comparison between the fuzzy stopping models and the non fuzzy ones

a class of dual fuzzy dynamic programs in this paper we propose a large class of fuzzy dynamic programs by use of the notion of dual binary relation we define a dual fuzzy dynamic program in the class we establish two duality theorems between primal and dual fuzzy dynamic programs one is for the two parametric recursive equations the other is for the nonparametric we specify maximum minimum process and minimum minimum process in fuzzy environment and multiplicative multiplicative process in quasi stochastic environment it is shown that the duality theorems hold between primal and dual programs

markov type fuzzy decision processes with a discounted reward on a closed interval abstract we formulate a new multi stage decision process with markov type fuzzy transition which is termed markov type fuzzy decision process in the general framework of the decision process both of state and action are assumed to be fuzzy itself the transition of states is defined using the fuzzy relation with markov property and the discounted total reward is described as a fuzzy number on a closed bounded interval to discuss the optimization problem a partial order of convex fuzzy numbers is introduced in this paper the discounted total reward associated with an admissible stationary policy is characterized by a unique fixed point of the contractive mapping moreover the optimality equation for the fuzzy decision model is derived under some continuity conditions also an illustrated example is given to explain the theoretical results and the computation in the paper

associative dynamic programs abstract in this paper we consider finite stage stochastic dynamic programs with associative reward systems an invariant imbedding technique yields a dynamic program with a terminal reward system on an augmented state space according to the associativity we clarify the validity of three possible recursive equations one parametrized equation and two non parametrized ones each of the additive multiplicative and multiplicative additive dynamic programs admits the three recursive equations further the corresponding composite relations among three optimum value functions hold however minimum maximum and fractional dynamic programs admit only the parametrized recursive equation they do not admit the two non parametrized equations further the corresponding relations among the three optimum value functions do not hold