fade statistics in nakagami lognormal channels new expressions for the average level crossing rate lcr and average time fade duration afd of the signal envelope in microcellular mobile radio channels characterized by nakagami 1960 fading and lognormal shadowing so called nakagami lognormal nln channels are derived new lcr and afd are computed and the effects of the nakagami m factor and shadowing spread spl sigma sub s on these fade statistics are discussed the generality of the nln model is demonstrated by matching some lcr curves with previously reported measurement for the land mobile satellite channel commonly described as the rice lognormal channels

monitored heavy fuzzy measures and their role in decision making under uncertainty we discuss the fuzzy measure and the related idea of choquet aggregation we describe a prototypical application of the fuzzy measure in decision making under uncertainty we introduce an extension of the fuzzy measure called the monitored heavy fuzzy measure we give some examples of these new measures using these measures with the choquet integral we obtain a general class of aggregation operators that include both mean type operators and totaling type operators we consider the application of this measure to the problem of decision making under uncertainty in the case in which the uncertain variable can have multiple solutions

componentwise decomposition of some lattice valued fuzzy integrals lattice valued fuzzy measures are lattice valued set functions which assign the bottom element of the lattice to the empty set the top element of the lattice to the entire universe and satisfy the property of monotonicity if the lattice is complete then a lattice valued fuzzy integral of sugeno type with similar properties such as the sugeno integral in its original form can be introduced in a natural way the main result of the paper is a componentwise decomposition theorem of an l valued fuzzy integral to its l valued fuzzy integrals components where l is a complete lattice with negation and l a b a email protected l a email protected is organized as a complete lattice too this result is useful to obtain the properties of l valued fuzzy integrals from the properties of l valued fuzzy integrals and to calculate in a simple way the values of some integrals from the values of the components the important case l 0 1 when l becomes the lattice of the intuitionistic fuzzy values is distinctly discussed an idea of application to synthetic evaluation of objects is also suggested

nonlinearity of the fuzzy integral we prove that the fuzzy integral has some linearity properties only for small classes of fuzzy measures we also show that an extension of this concept to bounded functions as proposed by kandel 2 5 is not well defined in general

relaxation based bounds for semi infinite programs finite formulations are presented for the calculation of lower and upper bounds on the optimal solution value of semi infinite programs sips involving smooth potentially nonconvex objective function and constraints the lower bounding problem is obtained by a formulation that combines the first and second order kkt necessary conditions of the lower level problem with a discretization of the parameter set the resulting mathematical program with equilibrium constraints mpec is a relaxation of the original sip and furnishes valid lower bounds if the parameter set is subdivided the optimal solution value of the lower bounding problem converges to the optimal solution value of the sip the upper bounding problem is based on convex and linear relaxations of the lower level problem resulting in a restriction of the sip if the parameter set is subdivided the constructed relaxations converge to the original lower level program the existence of sip slater points ensures convergence of the upper bounding problems to the optimal solution value of the sip several alternatives for the upper bounding problem are presented and discussed numerical results are presented for a number of test problems from the literature

measures of fuzzy sets and measures of fuzziness abstract the measures presented in this paper are defined by using weber s concept of decomposable measures m of crisp sets having in particular the archimedean decomposable operations in view section 2 measures m of fuzzy sets are introduced as integrals with respect to m for the archimedean cases weber s integral will be used as alternative to sugeno s and choquet s concepts section 3 what fuzziness means will be described by functions of fuzziness f another name entropy n functions with respect to a negation in addition to the types of functions of fuzziness which are induced by concave functions we discuss also the ones which are induced by fuzzy connectives section 4 now using m for measuring the importance of items and f for the fuzziness of the possible values of a fuzzy set m f serves us as a measure of the fuzziness f of the concepts of de luca and termini capocelli and de luca kaufmann knopfmacher loo gottwald dombi and under the restriction to the archimedean cases also the concepts of trillas and riera and yager turn out to be special cases section 5

on sugeno integral as an aggregation function the sugeno integral for a given fuzzy measure is studied under the viewpoint of aggregation in particular we give some equivalent expressions of it we also give an axiomatic characterization of the class of all the sugeno integrals some particular subclasses such as the weighted maximum and minimum functions are investigated as well

an exact penalty function for semi infinite programming this paper introduces a global approach to the semi infinite programming problem that is based upon a generalisation of the l1 exact penalty function the advantages are that the ensuing penalty function is exact and the penalties include all violations the merit function requires integrals for the penalties which provides a consistent model for the algorithm the discretization is a result of the approximate quadrature rather than an a priori aspect of the model

zero crossing rates of mixtures and products of gaussian processes formulas for the expected zero crossing rate of non gaussian mixtures and products of gaussian processes are obtained the approach we take is to first derive the expected zero crossing rate in discrete time and then obtain the rate in continuous time by an appropriate limiting argument the processes considered which are non gaussian but derived from gaussian processes serve to illustrate the variability of the zero crossing rate in terms of the normalized autocorrelation function p t of the process for gaussian processes rice s formula gives the expected zero crossing rate in continuous time as 1 spl pi spl radic spl rho 0 we show processes exist with expected zero crossing rates given by spl kappa spl pi spl radic spl rho 0 with either spl kappa spl gt 1 or spl kappa spl lt 1 consequently such processes can have an arbitrarily large or small zero crossing rate as compared to a gaussian process with the same autocorrelation function

some outer approximation methods for semi infinite optimization problems abstract the paper starts with a simple model and convergence theorem for outer approximation methods this general framework is used to unifyingly derive and modify certain exchange methods cutting methods and discretization methods for semi infinite programming problems by that in particular a cutting plane method for convex semi infinite programs is developed for a practically reasonable specification the method is more generally stated the subproblems in the given algorithm are moderately sized quadratic problems and each step of the algorithm can be performed by means of finitely many operations

the symmetric sugeno integral we propose an extension of the sugeno integral for negative numbers in the spirit of the symmetric extension of choquet integral also called sipos integral our framework is purely ordinal since the sugeno integral has its interest when the underlying structure is ordinal we begin by defining negative numbers on a linearly ordered set and we endow this new structure with a suitable algebra very close to the ring of real numbers in a second step we introduce the mobius transform on this new structure lastly we define the symmetric sugeno integral and show its similarity with the symmetric choquet integral

domain semantics of possibility computations the purpose of this paper is to introduce a kind of computational model called possibility computation to deal with non determinism both its denotational and logical semantics in the framework of domain theory are established and their equivalence is verified in this approach the denotational semantics will be set up by assigning to programs possibility state transformers i e scott continuous functions from the domain of input states to the possibility powerdomain of the codomain of final states this possibility powerdomain of a dcpo will consist of all possibility valuations ordered pointwise of this dcpo the logical semantics will be given by fuzzy predicate transformers introduced by the first author and jung following dijkstra s predicate transformers two semantics equivalence will be verified in terms of the integration of fuzzy predicates with respect to possibility valuations the categorical monad of the possibility powerdomain will be investigated

zero crossing rates of functions of gaussian processes formulas for the expected zero crossing rates of random processes that are monotone transformations of gaussian processes can be obtained by using two different techniques the first technique involves derivation of the expected zero crossing rate for discrete time processes and extends the result of the continuous time case by using an appropriate limiting argument the second is a direct method that makes successive use of r price s 1958 theorem the chain rule for derivatives and s o rice s 1954 formula for the expected zero crossing rate of a gaussian process a constant which depends on the variance of the transformed process and a second moment of its derivative is derived multiplying rice s original expression by this constant yields the zero crossing formula for the transformed process the two methods can be used for the general level crossing problem of random processes that are monotone functions of a gaussian process

measures of fuzziness of fuzzy events abstract we prove some new results on two families of fuzzy integrals defined in a previous paper and by means of them we obtain entropy measures of fuzzy sets not necessarily finite which contain as particular cases the measures of batle and trillas and weber we define another measure of fuzziness which is a function of the previous ones and satisfies with slight restrictions de luca and termini s axioms

fuzzy integral representation abstract in this paper we give representation results for nonlinear functionals in arbitrary spaces as fuzzy integrals the main assumption is that of comonotonic maxitivity i e i f g if ig for comonotonic f g under the more restrictive condition of stochastic dominance we prove a more specific representation as a fuzzy integral with respect to a distorted probability measure we discuss the particular cases of possibility measures and upper fuzzy expectations some partial randon nikodym results are proved for both the choquet and the fuzzy integrals finally an example is shown where the fuzzy integral representation is useful

homogeneity properties of seminormed fuzzy integrals this paper is concerned with the maxitivity and homogeneity of integrals in a very general setting for the semi co normed fuzzy integrals we study the maxitivity minitivity and homogeneity homogeneity properties some necessary conditions for the fuzzy integrals to have such homogeneity properties are obtained

the smallest semicopula based universal integrals i properties and characterizations abstract in this article we provide a detailed study of basic properties of the smallest universal integral i s with s being the underlying semicopula and review some of the recent developments in this direction the class of integrals under study is also known under the name seminormed integrals and includes the well known sugeno and shilkret integrals as special cases we present some representations and equivalent formulations for i s further we discuss basic properties such as translatability linearity homogeneity and maxitivity in particular we provide the characterizations of the two prominent integrals of sugeno and shilkret we also raise and discuss some open questions

convergence theorems for monotone measures in classical measure theory there are a number of convergence theorems such as the egorov the riesz and the lusin theorem among others we consider monotone measures i e monotone set functions vanishing in the empty set and defined on a measurable space and discuss how and to which extent classical convergence theorems can be carried over to this more general case

a globally convergent sqp method for semi infinite nonlinear optimization abstract a new approach for semi infinite programming problems is presented which belongs to the class of successive quadratic programming sqp methods with trust region technique the proposed algorithm employs the exact l penalty function as a criterion function and incorporates an appropriate scheme for estimating active constraints it is proved that the algorithm is globally convergent under some assumptions numerical experiments show that the algorithm is very promising in practice

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

on level crossing excursions of gaussian low pass random processes level crossing problems have been the subject of much study for centuries practical applications can be found in many fields of engineering e g predicting flood levels random mechanical stress analysis electrical excursions that overload equipment and disruptive effects in signal processing in this paper we focus on stationary gaussian low pass random processes and in particular of the discrete time first order markov type we derive new results for discrete time processes and links to known results for continuous time processes to arrive at a general understanding of the excursion statistics expressions are derived for the crossing rate shape of large excursions peak distribution and sojourn probability simulation results are compared with the various theoretical formulations along the way we obtain a new continuous time sojourn density approximation that extends the useful range of rice s formula to longer intervals

on chebyshev type inequalities for generalized sugeno integrals abstract we give the necessary and sufficient conditions guaranteeing the validity of chebyshev type inequalities for generalized sugeno integrals in the case of functions belonging to a much wider class than the comonotone functions for several choices of operators we characterize the classes of functions for which the chebyshev type inequality for the classical sugeno integral is satisfied

an algorithm for identification of fuzzy measure in the paper the connection between fuzzy measures and lebesgue measure is discussed special attention is focused on fuzzy measures which satisfy the so called l rule a relation between such measures and probability measures is given basing on this relation a simple and fast algorithm for identification of a sugeno fuzzy measure is presented

on egoroff s theorems on finite monotone non additive measure space in this note we give four versions of egoroff s theorem in non additive measure theory by using condition e the pseudo condition e of set function and the duality relations between the conditions these conditions offered are not only sufficient but also necessary for the four kinds of egoroff s theorems

generalized convergence theorems for monotone measures abstract in this paper we propose three types of absolute continuity for monotone measures and present some of their basic properties by means of these three types of absolute continuity we establish generalized egoroff s theorem generalized riesz s theorem and generalized lebesgue s theorem in the framework involving the ordered pair of monotone measures the egoroff theorem the riesz theorem and the lebesgue theorem in the traditional sense concerning a unique monotone measure are extended to the general case these three generalized convergence theorems include as special cases several previous versions of egoroff like theorem riesz like theorem and lebesgue like theorem for monotone measures respectively

on the multivariate nakagami m distribution with exponential correlation capitalizing on the proof of a theorem presented by l e blumenson and k s miller see ann math statist vol 34 p 903 10 1963 we propose a useful closed formula for the exponentially correlated n variate nakagami m probability density function moreover an infinite series approach for the corresponding cumulative distribution function is presented bounds on the error resulting from the truncation of the infinite series are also derived finally in order to check the accuracy of the proposed formulation numerical results are presented

a projected lagrangian algorithm for semi infinite programming a globally convergent algorithm is presented for the solution of a wide class of semi infinite programming problems the method is based on the solution of a sequence of equality constrained quadratic programming problems and usually has a second order convergence rate numerical results illustrating the method are given

an interior point sequential quadratic programming type method for log determinant semi infinite programs abstract in this paper we consider a nonlinear semi infinite program that minimizes a function including a log determinant logdet function over positive definite matrix constraints and infinitely many convex inequality constraints we call this problem siplog where sip stands for semi infinite program and log comes from log det function the main purpose of the paper is to develop an algorithm for efficiently computing a karush kuhn tucker kkt point for the siplog more specifically we propose an interior point sequential quadratic programming type method that solves inexactly a sequence of semi infinite quadratic programs approximating the siplog furthermore to generate a search direction in the dual matrix space associated with the semi definite constraint we solve scaled newton equations that yield the family of monteiro zhang directions we prove that the proposed method weakly converges to a kkt point under some mild assumptions finally we conduct some numerical experiments to demonstrate the efficiency of the proposed method

level crossing rate in terms of the characteristic function a new approach for calculating the fading rate in diversity systems the level crossing rate lcr of a random process conveys useful information about the underlying process and is of interest in diverse engineering fields in wireless communications it is related to the system characteristics such as handoff outage probability fading rate average duration of fades velocity or maximum doppler shift of the mobile and the effect of diversity on fading the lcr formula was originally derived by rice in terms of the joint probability density function pdf of the underlying process and its time derivative in this letter we express the lcr in terms of the joint characteristic function cf this new formula is useful for many cases where the joint cf is simpler to derive than the associated joint pdf as an application and for a direct sequence code division multiple access system the fading rate at the output of a rake receiver with either maximal ratio combiner or postdetection equal gain combiner operating over a frequency selective fading channel with different path statistics is easily calculated using the new cf based lcr formula

on the use of e most active constraints in an exact penalty function method for nonlinear optimization this note presents an algorithm for nonlinear programming problems which utilizes the e most active constraint strategy in an exact penalty function method with trust region the algorithm is particularly suitable for problems containing a large number of constraints the global convergence of the proposed algorithm is proved the results of limited computational experiments for discretized semi infinite programming problems are also reported to demonstrate the effectiveness of the present approach

fuzzy measures and integrals we present fuzzy measures and fuzzy integrals as special poset homeomorphisms besides general fuzzy integrals regular fuzzy integrals are introduced and some of their properties are discussed state of art of fuzzy measure and fuzzy integral theory are briefly summarized and some further streaming is sketched

some notes on homogeneity property of semiconormed fuzzy integrals in this note we show that some results of homogeneity of semiconormed fuzzy integrals which are given by kim homogeneity properties of seminormed fuzzy integrals fuzzy sets and systems 157 2006 411 426 are not valid

additions of interactive fuzzy numbers this paper provides an account of an approach to modeling unknown data by means of fuzzy set theory and addresses the problem of deriving the uncertainty on a sum of variables whose values lie within fuzzy intervals the first part is an extensive presentation of the theoretical background of the approach the extension principle is stated in terms of possibility of an event the concept of variable interaction is investigated at length section ii gives new results regarding the effective practical computation of additions of fuzzy numbers its originality lies in the introduction of interaction which enables to control the growth of uncertainty in calculations moreover the problem of computing mathematical expectations with fuzzy probabilities is solved the results derived in this paper can easily be used in decision problems where values of parameters or decision variables are not yet precisely fixed or assessed typical applications could be multicriteria optimization and decision making under uncertainty where fuzzy expected utilities can be obtained out of uncompletely assessed probabilities more generally fuzzy arithmetic can be an important tool for sophisticated computationally tractable sensitivity analysis in systems modeling computer aided design and operations research

on the level crossing duration distributions of nakagami processes the problem related to the fade and non fade duration distributions fdd and nfdd of randomly distributed signals has been studied for more than forty years however for non gaussian processes closed form general solutions for these distributions are still unknown in this paper we use an orthogonal series expansion to analyze the fdd and nfdd also known as downcrossing and upcrossing duration distributions respectively for the rather general case of nakagami distributed random processes our results show that for asymptotic and non asymptotic threshold levels the crossing duration distributions can be approximated in a simple closed form way using the gamma distribution we back up this approximation with some goodness of fit metrics and show how the parameters of such distribution can be computed a priori analytically

on set valued fuzzy measures so far there have been many discussions on sugeno s fuzzy measures and fuzzy integrals but most of them are concentrated on single valued functions motivated by aumann s set valued integral j math anal appl 12 1965 1 we have introduced the fuzzy integral of set valued functions fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341 ph d dissertation harbin institute of technology 1998 it is a well behaved extension of fuzzy integrals of single valued functions it is well known that arstein s set valued measure trans am math soc 165 1972 103 is an important branch in set valued analysis set valued analysis birkhauser berlin 1990 or theory of correspondences theory of correspondences wiley new york 1984 compared to it the present paper will try to establish the basic idea of set valued fuzzy measures which are monotone set valued set functions it is also a natural generalization of single valued fuzzy measures as well as an extension of set valued measures in the case of one dimension these works include the concept of set valued fuzzy measures set valued fuzzy measures defined by set valued fuzzy integrals and set valued pseudo additive measures it can be viewed as a continuation of previous work fuzzy sets syst 56 1993 237 fuzzy sets syst 76 1995 365 fuzzy sets syst 78 1996 341

a comparative study of several semi infinite nonlinear programming algorithms abstract a computational comparison of several recent semi infinite nonlinear programming algorithms is presented because of the importance of this area there have recently been proposed a number of algorithms having a global convergence property the algorithms used in this study include a feasible direction method and some variants of successive quadratic programming methods robustness and relative efficiency of the algorithms are examined on the basis of the results for some standard test examples chosen from earlier literature

problems of classification in a fuzzy environment this paper presents a classification model in a fuzzy environment by using possibility distributions and fuzzy measures optimal in bayes sense membership functions are induced these functions are similar to decision rules used in classical discriminant analysis the relations between fuzzy measures and possibility measures are also discussed to formulate a classification model where sugeno s fuzzy measures and integrals are used

two families of fuzzy integrals abstract in this paper we present two definitions of fuzzy integrals arising from the t seminorm and the t semiconorm concepts we show that sugeno s fuzzy integral is a particular case of them and we study their principal properties finally we suggest some applications of these results

triangular norm based iterative compensatory operators abstract aggregation operators based on a fixed t norm and on suitable transformations of processed data are introduced a special attention is paid to the class of iterative compensatory operators containing also the classical arithmetic geometric and harmonic means several properties of introduced operators are studied e g the symmetry the associativity the idempotency the anihilation etc several examples are given including continuous idempotent bisymmetric iterative compensatory operators with zero anihilator

characterization of invariant aggregation operators abstract following the ideas of bartlomiejczyk and drewniak minimal invariant subsets of 0 1 n are investigated an equivalence relation on these subsets is introduced consequently invariant aggregation operators are characterized by means of choquet integral based representation there are exactly 68 binary invariant aggregation operators 4 among them are also continuous further there are 6 self dual invariant binary aggregation operators a recurrent method of constructing invariant aggregation operators for n 2 is proposed restriction of invariant aggregation operators to finite scales is also discussed

stability analysis of stochastic programs with second order dominance constraints in this paper we present a stability analysis of a stochastic optimization problem with stochastic second order dominance constraints we consider a perturbation of the underlying probability measure in the space of regular measures equipped with pseudometric discrepancy distance romisch in stochastic programming elsevier amsterdam pp 483 554 2003 by exploiting a result on error bounds in semi infinite programming due to gugat math program ser b 88 255 275 2000 we show under the slater constraint qualification that the optimal value function is lipschitz continuous and the optimal solution set mapping is upper semicontinuous with respect to the perturbation of the probability measure in particular we consider the case when the probability measure is approximated by an empirical probability measure and show an exponential rate of convergence of the sequence of optimal solutions obtained from solving the approximation problem the analysis is extended to the stationary points

on fuzzy number valued fuzzy measures defined by fuzzy number valued fuzzy integrals ii abstract in this paper we discuss some properties of a fuzzy number valued fuzzy set function defined by a fuzzy number valued fuzzy integral on the fuzzy set and give sufficient conditions that it is a fuzzy number valued fuzzy measure