the application of the enhanced hoshen kopelman algorithm for processing unbounded images the enhanced hoshen kopelman ehk algorithm for the analysis of connected components in images that are unbounded in one of their dimensions is introduced the algorithm characterizes in a single pass the shapes of all the connected components in a multiple class image by computing the spatial moments the area the boundary and the bounding boxes of the connected components the algorithm is applied to a real time surface defect simulation and to a landsat image analysis the algorithm s performance is compared to the performances of related algorithms

bayesian experimental design for multiple hypothesis testing abstract the problem of designing an optimal experiment for the purpose of performing one or more hypothesis tests is considered the bayesian decision theoretic approach is used to arrive at several new optimality criteria for this purpose for a single hypothesis test the resulting optimal designs are the well known optimal designs that minimize the posterior variance of the parameter being tested for multiple tests an experimental design must perform well under several competing criteria different approaches to achieving this goal are explored including constrained optimization and an additive weighted loss the resulting optimality criteria are sensitive not only to the posterior variances of the parameters under test but also to their prior means

membership function as an evaluation abstract after giving an overview of the different kinds of mathematical forms of the membership functions we extract the different demands and determine the rational class of the membership functions from the generalisation of our result we can determine it giving four parameters the internal a b the sharpness and the decision level we show the correspondence of this membership function to the zimmermann zysno model and using their empirical data we also test our mathematical model we also show the connections between the operators of the evaluation and membership functions which gives the generalisation of this concept in a more general form as a special case we can get a linear form

bayesian designs for maximizing information and outcome abstract this article deals with a novel utility function to design experiments in a bayesian framework this utility function is a linear combination of the gain in shannon information and of the total outcome of the experiment defined as the sum of observed values in the dependent variable of a linear model thus the expected posterior utility to be maximized is a combination of the bayes d optimality criterion and the posterior expectation of the total output earlier studies have shown that bayesian parallels of the classical d a and e optimal designs can be obtained by considering utility or loss functions concerned with efficient estimation of the parameters of interest a different requirement that might be desirable in applied problems is to combine the accuracy of parameter estimation with the maximization of experimental output the utility function considered here does this we look at the implications of using this utility in deriving designs in the context of hierarchical linear models

a model for the measurement of membership and the consequences of its empirical implementation representation and uniqueness theorems are presented for the fundamental measurement of the membership of a fuzzy set when the domain of discourse is order dense the conclusion that membership is on an interval scale is justified by the inapplicability of extensive measurement to fuzziness and the lack of a natural origin for membership some descriptive statistics are also presented from an empirical study currently in progress to construct membership functions they suggest that subjects differ in their perception of fuzziness and that the models in the literature for certain linguistic operators such as not very and antonym are not sufficiently general to account for the range of individual perceptions of vague attributes a more general mathematical model is proposed the question of the meaningfulness of statements about membership functions is also discussed in the light of the assertion that membership can be fundamentally measured at best on an interval scale some of the difficulties which arise in fuzzy set theory due to this property are illustrated and a solution is suggested involving the use of a function which is derived from membership but is on an absolute scale

bayesian prediction of deterministic functions with applications to the design and analysis of computer experiments abstract this article is concerned with prediction of a function y t over a multidimensional domain t given the function values at a set of sites t 1 t 2 t n in t and with the design that is with the selection of those sites the motivating application is the design and analysis of computer experiments where t determines the input to a computer model of a physical or behavioral system and y t is a response that is part of the output or is calculated from it following a bayesian formulation prior uncertainty about the function y is expressed by means of a random function y which is taken here to be a gaussian stochastic process the mean of the posterior process can be used as the prediction function t and the variance can be used as a measure of uncertainty this kind of approach has been used previously in bayesian interpolation and is strongly related to the kriging methods used in geostatistics here emphasis is placed on product linear and product cubic correlation func

bayesian estimation in forest surveys when samples or prior information are fuzzy abstract fuzzy phenomena are frequently encountered in forestry due to the complexity of the systems under investigation in this paper existing inference methods are presented to accommodate situations in which random events take place in fuzzy circumstances fuzzy concepts are incorporated into these commonly accepted approaches to account for uncertainties used by factors other than randomness which traditional statistical approaches deal primarily with based on two extensions of likelihood functions for fuzzy samples bayesian estimates are generalized for use when sample information and prior distribution of parameters are fuzzy the estimators are developed for some typical membership functions for fuzzy samples and fuzzy priors applications are illustrated using examples for forestry

fuzzy logic of lukasiewicz logic a clarification pavelka 10 had shown in 1979 that the only natural way of formalizing fuzzy logic for truth value in the unit interval 0 1 is by using lukasiewicz s implication operator a b min 1 1 a b or some isomorphic form of it a considerable number of other papers around the same time had attempted to formulate alternative definitions for a b by giving intuitive justifications for them there continues to be some confusion however even today about the right notion of fuzzy logic much of this has its origin in the use of improper and or and the not operations and a misunderstanding of some of the key differences between proofs or inferencing in fuzzy logic and those in lukasiewicz s logic we point out the need for defining the strong conjunction operator in connection with fuzzy modus ponens rule and why we do not need the fuzzy syllogism rule we also point out the shortcomings of many of the alternative definitions of a b which indicate further support for pavelka s result we hope that these discussions help to clarify the misconceptions about fuzzy logic

experimental designs for model discrimination abstract we present designs that perform well for several objectives simultaneously three different approaches are discussed to augment a given design in an optimal way to evaluate a mixture of the various criteria and to optimize one objective subject to achieving a prescribed efficiency level for the others our sample designs are for the situation of discriminating between a second and third degree polynomial fit under the d criterion and geometric mixtures of d criteria

constructing membership functions using statistical data abstract determination of the membership functions is vital in practical applications of the fuzzy set theory this paper presents a guideline to construct the membership functions for fuzzy sets whose elements have a defining feature with a known probability density function pdf in the universe of discourse the method finds the smallest fuzzy set which assigns high average membership values to those objects with the defining features distributed according to the given pdf it is show that for any pdf the method is capable of generating membership functions in accordance with the possibility probability consistency principle membership functions derived from some of the well known pdfs and an application in solving noise contaminated linear system of equations are presented

percolation and cluster structure parameters the radius of gyration the squared radius of gyration of percolation clusters are determined in terms of the clusters second spatial moments using the enhanced hoshen kopelman algorithm for square and triangular lattices containing sites correlation length exponents and related exponents as well as their corresponding amplitudes are calculated in terms of the squared radius of gyration above and below the percolation threshold a coefficient for cluster compactness that is based on the squared radius of gyration of a cluster is introduced that coefficient is compared with a similar coefficient of compactness that is based on the cluster cyclomatic number

the logic of tied implications part 1 properties applications and representation a conjunction t ties an implication operator a if the identity a a a b z a t a b z holds a a abdel hamid n n morsi associatively tied implications fuzzy sets and systems 136 2003 291 311 we study the class of tied adjointness algebras which are five connective algebras on two partially ordered sets in which the implications are tied by triangular norms this class contains besides residuated implications several other implications employed in fuzzy logic nevertheless we show that the algebraic inequalities of residuated algebras remain true for our tied implications but in forms that distribute roles over the five connectives of the algebra we apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules we prove its equivalence to a scheme with one compound rule when both schemata are interpreted by the compositional rule of inference and all connectives are taken from one tied adjointness algebra then we quote another application of this rich theory a notion of many valued rough sets which exhibit the basic mathematical behaviour of the rough sets of pawlak a comparator h is said to be prelinear if it satisfies h y z h z y 1 for all y z hajek we introduce prelinear tied adjointness algebras in which two comparators are prelinear we provide a representation of those algebras as subdirect products of tied adjointness chains on the lines of hajek s representation of bl algebras but our representations are more economical because we employ minimal prime filters on residuated lattices only rather than all prime filters

fuzzy boundary element method for the analysis of imprecisely defined systems many engineering systems contain uncertainties that cannot be described by either deterministic or probabilistic approaches the uncertainties present may be associated with parameters that are vague imprecise or linguistic for example the geometry material properties external actions loads and boundary conditions may be imprecise in a practical system a fuzzy boundary element method for the analysis of imprecisely defined systems is developed starting from the basic concepts of fuzzy sets and fuzzy arithmetic the various steps of the boundary element method are redefined using fuzzy concepts the resulting fuzzy equations are solved using a fuzzified version of gaussian elimination procedure coupled with truncation the truncation method limits the growth of interval ranges of response parameters to obtain realistic and accurate solutions the procedure is illustrated by considering the analysis of a potential flow problem the methodology is applicable to uncertain systems that are described in linguistic terms as well as those that are described by incomplete information the approach represents a unique methodology that enables the analysis and design of many engineering systems more realistically

cluster size distribution at criticality monte carlo studies of the cluster size distribution for the site percolation problem on the triangular lattice are extended to lattices with up to 4 1011 sites agreement with the predictions of scaling theory at pc is excellent over a range of cluster sizes spanning five orders of magnitude

contribution to application of energy measure of fuzzy sets abstract the works of de luca termini continued by for example knopfmacher loo and gottwald are the most important on the topic of determination of measures of fuzzy sets the matter is to evaluate how fuzzy a fuzzy set is there are two general concepts of measures of fuzzy set i e entropy and energy measures we show that the special kind of energy measure is better suited than the entropy kind of measure in many practical situations applications of the use of energy measure discussed in detail include decision making fuzzy process control and prediction in fuzzy systems

optimal data augmentation strategies for additive models abstract consider an experiment where the factors are measured on a continuous scale and suppose that the experimenter is permitted to augment the existing observations with one or more new data points bondar s universal optimality criterion u optimality suggests that the problem is best studied in the eigenvector coordinate system we proceed by showing how to construct new points that first equate and then jointly increase the smaller eigenvalues of the crossproduct of the independent variables we discuss the limitations of design augmentation strategies based solely on the crossproduct matrix our goals are to equate and minimize the variances of the estimated regression coefficients keep the new points constrained in a prespecified experimental region use as much of the information in the original points as possible and keep the number of required new points as small as possible we offer several data augmentation strategies to meet these requirements as u optimality subsumes each of the d a

the generalized truth degree of quantitative logic in the logic system l n n valued nm logic system the concept of the truth degree of a formula is the crucial tool and the building block in quantitative logic from which the concept of logic metric in quantitative logic is derived logic metric takes an important role in quantitative logic related to which are other concepts in quantitative logic such as divergence consistency etc in the present paper having combined the theory of generalized tautologies with the theory of truth degrees in quantitative logic we have proposed the theory of s c truth degrees of formulas related to theory c in the logic system l n n valued nm logic system and discussed some of its properties with the help of the properties of s c truth degrees t c a email protected c a b email protected c b we have obtained the c logic metric on the set f s of formulas in the propositional logic system l n n valued nm logic system by the work of this paper we can generalize the theory of quantitative logic in all round way and establish an approximate reasoning s framework related to theory c in the logic system l n n valued nm logic system

fuzzy sets as a basis for a theory of possibility the theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable more specifically if f is a fuzzy subset of a universe of discourse u u which is characterized by its membership function f then a proposition of the form x is f where x is a variable taking values in u induces a possibility distribution tx which equates the possibility of x taking the value u to f u the compatibility of u with f in this way x becomes a fuzzy variable which is associated with the possibility distribution tx in much the same way as a random variable is associated with a probability distribution in general a variable may be associated both with a possibility distribution and a probability distribution with the weak connection between the two expressed as the possibility probability consistency principle a thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is in the main possibilistic rather than probabilistic in nature thus by employing the concept of a possibility distribution a proposition p in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p several types of conditional translation rules are discussed and in particular a translation rule for propositions of the form x is f is possible where is a number in the interval 0 1 is formulated and illustrated by examples

some guidelines for constructing exact d optimal designs on convex design spaces some problems unique to the construction of n point d optimal designs on convex design spaces are considered multiple point augmentation and exchange algorithms are shown to be more costly and less efficient than the analogous single point procedures moreover some recommendations for improving single point methods are given finally empirical evidence is found that supports the galil and kiefer option for constructing initial designs and powell s optimization method for design augmentation

issues on adjointness in multiple valued logics we contribute to the theory of implications and conjunctions related by adjointness in multiple valued logics we suggest their use in zadeh s compositional rule of inference to interpret generalized modus ponens inference schemata we provide new complete characterizations of implications that distinguish left arguments implications that satisfy the exchange principle divisible conjunctions commutative conjunctions associative conjunctions and triangular norms we also introduce and characterize pseudo strict and pseudo continuous implications and conjunctions and we explore the close relationship between these two notions

an algebraic approach to linguistic hedges in zadeh s fuzzy logic the paper addresses the mathematical modelling of domains of linguistic variables i e term sets of linguistic variables in order to obtain a suitable algebraic structure for the set of truth values of zadeh s fuzzy logic we shall give a unified algebraic approach to the natural structure of domains of linguistic variables which was proposed by ho and wechler fuzzy sets and systems 35 1990 281 and then by ho and nam proc ncst vietnam 9 1 1997 15 logic algebra and computer science vol 46 banach center publications pwn warsaw 1999 p 63 in this approach every linguistic domain can be considered as an algebraic structure called hedge algebra because properties of its unary operations reflect semantic characteristics of linguistic hedges many fundamental properties of refined hedge algebras rh algebras are examined especially it is shown that every rh algebra of a linguistic variable with a chain of the primary terms is a distributive lattice rh algebras with exactly two distinct primary terms one being an antonym of the other will also be investigated and they will be called symmetrical rh algebras it is shown that a class of finite symmetrical rh algebras has a rich enough algebraic structure

induction of fuzzy decision trees abstract most decision tree induction methods used for extracting knowledge in classification problems do not deal with cognitive uncertainties such as vagueness and ambiguity associated with human thinking and perception in this paper cognitive uncertainties involved in classification problems are explicitly represented measured and incorporated into the knowledge induction process a fuzzy decision tree induction method which is based on the reduction of classification ambiguity with fuzzy evidence is developed fuzzy decision trees represent classification knowledge more naturally to the way of human thinking and are more robust in tolerating imprecise conflict and missing information

miscellanea a note on bayesian design for the normal linear model with unknown error variance summary the bayesian theory of optimal experimental design for the normal linear model has been developed under the assumption of known variance the insensitivity of specific design criteria to prior assumptions on the variance distribution has been demonstrated in special cases but a general result showing the way in which bayesian optimal designs are affected by prior information on the variance is lacking this note proves that bayesian designs are insensitive to information about

percolation and cluster structure parameters the enhanced hoshen kopelman algorithm an enhanced hoshen kopelman ehk algorithm for calculating cluster structure parameters is presented for the site percolation problem the ehk algorithm enables efficient calculation of cluster spatial moments perimeters and bounding boxes for very large monte carlo simulated lattices the algorithm is used to compute the squared radius of gyration and internal perimeters of clusters in 3000 ifmmode times else texttimes fi 3000 square simulated lattices the squared radius of gyration was used to calculate the value of the correlation length exponent

fuzzy control from the logical point of view abstract this paper is a discussion of the logical aspect in fuzzy control which is an application of the theory of approximate reasoning first we analyze approximate reasoning and show that it is a concise logical theory based on many valued logic integrated with some parts of linguistics then we demonstrate that fuzzy control based on equality relations can transparently be formulated as a result of the logical theory finally we demonstrate that fuzzy control can be seen as a repeated derivation in a continuously modified logical theory and propose a hypothesis on the role of linguistics in the controllability problem

optimal bayesian designs for models with partially specified heteroscedastic structure we consider the problem of finding a nonsequential optimal design for estimating parameters in a generalized exponential growth model this problem is solved by first considering polynomial regression models with error variances that depend on the covariate value and unknown parameters a bayesian approach is adopted and optimal bayesian designs supported on a minimal number of support points for estimating the coefficients in the polynomial model are found analytically for some criteria the optimal bayesian designs depend only on the expectation of the prior but generally their dependence includes the derivative of the logarithm of the laplace transform of a measure induced by the prior the optimal design for the generalized exponential growth model is then determined from these optimal bayesian designs

solvability of fuzzy relational equations and manipulation of fuzzy data abstract the problem of characterization of fuzzy relational equations with respect to their solvability property is studied some aspects of manipulation of fuzzy data with the aid of fuzzy relational equations are considered two stages of manipulation process are indicated combining pieces of evidence and inferring their mutual correspondence both of them are formulated and solved by the use of fuzzy relational equations the role of a solvability index is extensively studied numerical considerations give an illustration of the approach we propose and deal with some real data used for fuzzy controllers

equality relations as a basis for fuzzy control abstract the aim of this paper is to introduce a fuzzy control model with well founded semantics in order to explain the concepts applied in fuzzy control assuming that the domains of the input and output variables for the process are endowed with equality relations that reflect the indistinguishability of values lying closely together the use of triangular and trapezoidal membership functions can be justified and max inference where is a t norm turns out to be a consequence of our model distinguishing between a functional and a relational view of the control rules it is possible to explain when defuzzification strategies like mom or coa are appropriate or lead to undesired results

the equivalence of constrained and weighted designs in multiple objective design problems abstract several competing objectives may be relevant in the design of an experiment the competing objectives may not be easy to characterize in a single optimality criterion one approach to these design problems has been to weight each criterion and find the design that optimizes the weighted average of the criteria an alternative approach has been to optimize one criterion subject to constraints on the other criteria an equivalence theorem is presented for the bayesian constrained design problem equivalence theorems are essential in verifying optimality of proposed designs especially when as in most nonlinear design problems numerical optimization is required this theorem is used to show that the results of cook and wong on the equivalence of the weighted and constrained problems apply much more generally the results are applied to bayesian nonlinear design problems with several objectives

bayes optimal designs for two and three level factorial experiments abstract two and three level factorial designs are often used for exploratory experiments with many independent variables the purpose of such experiments is to estimate the effects of all active independent variables and their interactions for reasons of economy or other constraints only a fraction of the full number of experimental settings of the independent variables may be run precluding the separate data based estimation of all the effects in this situation of relatively sparse data and many unknown parameters the benefits of reliable prior information used in the estimation and experimental design can be especially significant in this article exact bayes optimal designs of two and three level fractional factorial experiments and of blocked two and three level factorial experiments are derived the optimality criteria used in this process are versions of the bayes criterion introduced by duncan and degroot it is shown that the classical fractional factorial designs for the 2k experime

the relation between inference and interpolation in the framework of fuzzy systems abstract this papers aims at clarifying the meaning of different interpretations of the max min or more generally the max t norm rule in fuzzy systems it turns out that basically two distinct approaches play an important role in fuzzy logic and its applications fuzzy interpolation on the basis of an imprecisely known function and logical inference in the presence of fuzzy information

the possibilistic moments of fuzzy numbers and their applications this paper introduces the nearest weighted interval and point approximations of a fuzzy number and then suggests weighted possibilistic moments about these points of fuzzy numbers the possibilistic moments play an important role in fuzzy sets and systems specifically in physics mathematics and statistics we provide the definition of the moments of fuzzy numbers as well as the definition of moments in probability theory some of their applications are mentioned

combined algorithm to compute d optimal designs algorithmic techniques for computing optimal designs continue being a need in the optimal experimental design field the increasing interest in finding the optimal experimental conditions makes that new methods are demanded for more complex frameworks showing more realistic situations numerical techniques are often the unique viable option for computing these designs since to tackle analytically the problem results impracticable in most of cases wynn fedorov algorithm multiplicative algorithm and their modifications are the more frequently used methods in the literature for computing d optimal designs however they are not always suitable and efficient to compute optimal designs since their procedures are very limited by the computational requirements a new algorithm to obtain d optimal designs is proposed in this paper it is based on combining suitable strategies followed by the traditional algorithms a proof of the convergence is provided and several numerical examples are presented to illustrate its improved results