a possibility measure is not a fuzzy measure abstract in this note we show that a possibility measure is not a particular type of fuzzy measure except in trivial cases

semiconormed possibility integrals and multi feature pattern classification abstract the semiconormed possibility integrals are proposed as a multi feature pattern classification model a semiconormed possibility integral is a nonlinear integration of a function and its corresponding non normalized possibility measures over feature space the function of an object s feature vector represents the possibilities with uncertainty that the object belongs to a class the uncertainty is due to the similar characteristics of objects from different classes and the distortion of the original characteristic information caused by feature data acquisition systems the uncertainty is assessed by the non normalized possibility measures a possibility measure of a feature is considered as the credibility of the feature to provide reliable information for pattern classification integration of a function and the possibility measures effectively reduces the uncertainty and improves the pattern classification results a pattern classification algorithm based on the semiconormed possibility integrals was used to classify a set of ellipse data and the well known iris data the classification results were compared with those obtained by using bayes classifier

interactive determination of a utility function represented as a fuzzy integral abstract in this paper we propose an alternative method for interactive assessment of a utility function when this function is represented by a fuzzy integral it is generally agreed that the fuzzy integral provides a good representation of the human subjective structure however this type of integral may not be convenient because the assessment of the underlying fuzzy measure requires a lot of data in this paper we adopt an alternative point of view for determining the values of the fuzzy measure from few data by interactively changing equation constraints our method will contribute to increasing the applicability of the fuzzy measure and of the fuzzy integral in the field of decision support systems

pictorial representations of fuzzy connectives part ii cases of compensatory operators and self dual operators abstract as the continuation of part i in which pictorial representations of t norms t conorms and averaging operators were made with the aid of a computer this paper discusses compensatory operators and proposes generalized compensatory operators which can be obtained from averaging operators self dual operators are discussed which can be defined by using t norms t conorms and averaging operators finally symmetric sums are reviewed which are also self dual operators the pictorial representations of these operators are also made

solutions of asymptotically linear operator equations via morse theory abstract in this paper we use the classical morse theory of critical points to study the existence and multiplicity of solutions of a class of asymptotically linear operator equations as special cases we include multiplicity results for semilinear elliptic bvp s as well as existence and multiplicity of periodic solutions of semilinear wave equation and of hamiltonian systems these results simplify and complement recent work of amann zehnder and castro lazer author

two integrals and some modified versions critical remarks the aim of this paper is to discuss different constructions of integrals sections 3 and 4 based on decomposable measures section 1 according to the classification of the continuous t conorms in essentially two types namely v and archimedean t conorms there exist mainly two types of integrals namely the constructions of sugeno section 3 and of weber section 4 further constructions corresponding to the archimedean case result to be special cases or not well defined section 4 in all cases a crucial property is some restricted distribution law for the pair with an appropriate operation section 2 some applications shall illustrate the use of the two integrals section 5

multiple solutions and eigenvalues for third order right focal boundary value problems abstract we are concerned with the right focal boundary value problem x t f t x t t 1 t t 3 x t 1 x t 2 x t 3 0 and the associated eigenvalue problem x t a t f x t with the same boundary conditions under various assumptions on f a and we establish intervals of the parameter which yield the existence of a positive solution of the eigenvalue problem by placing certain restrictions on the nonlinearity we prove the existence of at least one at least two at least three and infinitely many positive solutions of the boundary value problem by applying some known fixed point theorems as well as some recent generalizations of these fixed point theorems

l additive measures on measure spaces abstract in his thesis sugeno has introduced a class of non additive set functions g which have been called additive measures he has printed out that g can be represented by a density function if it is defined on the power set of a finite set in this article this concept is generalized for arbitrary measure spaces moreover it is shown that any density function on a measure space determines a unique parameter 1 as in the finite case additive measures are belief functions iff 0 and plausibility functions iff 0 the proof of this statement is achieved by a generally applicable reduction of the problem to finite algebras

optimal binary search trees abstract we consider the problem of building optimal binary search trees the binary search tree is a widely used data structure for information storage and retrieval a binary search tree t for a set of keys from a total order is a binary tree in which each node has a key value and all the keys of the left subtree are less than the key at the root and all the keys of the right subtree are greater than the key at the root this property holding recursively for the left and right subtrees of the tree t suppose we are given n keys and the probabilities of accessing each key and those occurring in the gap between two successive keys the optimal binary search tree problem is to construct a binary search tree on these n keys that minimizes the expected access time one variant of this problem is when only the gaps have nonzero access probabilities and is called the optimal alphabetic tree problem another related problem is when there is no order between the keys and there are probabilities associated only with the gaps and the objective is to build a binary tree with minimum expected weighted path length from the root this is called the huffman tree problem in this survey we assess known results on the structural properties of the optimal trees algorithms and lower bounds to construct and to verify optimal trees and heuristics to construct nearly optimal trees and other related results

constructing huffman trees in parallel we present a parallel algorithm for the huffman coding problem we reduce the huffman coding problem to the concave least weight subsequence problem and give a parallel algorithm that solves the latter problem in o sqrt n log n time with n processors on a concurrent read exclusive write parameter random access machine crew pram this leads to the first sublinear time o n 2 total work parallel algorithm for huffman coding this reduction of the huffman coding problem to the clws problem also yields an alternative o n log n time or linear time for a sorted input sequence algorithm for huffman coding

existence of solutions for an asymptotically linear dirichlet problem via lazer solimini results abstract in this paper we prove that an asymptotically linear dirichlet problem has at least three nontrivial solutions when the range of the derivative of the nonlinearity includes at least the first k eigenvalues of minus laplacian without any restriction about nondegeneracy of solutions a pair is of one sign positive and negative respectively we construct a third solution using arguments of the type lazer solimini see a c lazer s solimini nontrivial solutions of operator equations and morse indices of critical points of min max type nonlinear anal 12 8 1988 761 775 this gives a partial answer to a conjecture stated in j cossio s herron nontrivial solutions for a semilinear dirichlet problem with nonlinearity crossing multiple eigenvalues j dyn differential equations 16 3 2004 795 803 moreover in the particular case of nondegenerate critical points we prove that there are at least four nontrivial solutions the one sign solutions are of morse index equal to 1 the third solution has morse index k and there is a fourth solution for this case we use the leray schauder degree and lazer solimini results

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

the warm up algorithm a lagrangian construction of length restricted huffman codes given an alphabet a 1 an with the corresponding list of weights w1 wn and a number l geq lceil log n rceil we introduce the warm up algorithm a lagrangian algorithm for constructing suboptimal length restricted prefix codes two implementations of the algorithm are proposed the first one has time complexity o n log n n log fmax where mbox overline w is the highest presented weight the second one runs in o nl log n l time the number of additional bits per symbol generated by warm up when comparing to huffman encoding is not greater than 1 psi l lceil log n lceil log n rceil l rceil 2 even though the algorithm is approximated it presents an optimal behavior for practical settings an important feature of the proposed algorithm is its implementation simplicity the algorithm is basically a selected sequence of huffman tree constructions for modified weights the approach gives some new insights on the problem

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 the construction of fuzzy measures a relation defined on a s algebra called relative likelihood is introduced it is shown how to construct fuzzy measures which are compatible with a relative likelihood

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

unfair coins and necessity measures towards a possibilistic interpretation of histograms this short note defines a bijective mapping which turns a probability measure into a possibility measure this transformation has intuitive grounds especially the converse mapping corresponds to the usual assignment of identical probability values to elementary events of a given set when no information is available

on nontrivial solutions of an asymptotically linear dirichlet problem let be a bounded domain in rn n 2 with smooth boundary let r r be a continuous function such that 0 0 and lim exist we discuss the existence of nontrivial solutions of the dirichlet problem u u in u 0 on our hypotheses seem to allow significantly greater freedom for the numbers lim than is usually found in the literature in that the interval with end points is here permitted to contain an eigenvalue of subject to zero dirichlet data furthermore we do not require any differentiability of and we weaken other technical conditions on that are generally assumed in other papers dealing with this problem

fuzzy integrals and conditional fuzzy measures we introduce a fuzzy integral for fuzzy events with respect to l additive fuzzy measures this integral is the canonical generalization of the lehesgue integral a radon nikodym like theorem is used to give the definition of the conditional fuzziness

measures of fuzzy sets in this paper a fuzzy set is considered as a point of a segment in riesz space using the daniell representation theorem of positive linear functionals on riesz space it is demonstrated that n a the s finite measure of fuzzy set a equals ua u n du some fundamental properties of measures and signed measures of fuzzy sets are discussed the law of large numbers in fuzzy occasions and a few useful properties of the conditional probability of fuzzy events are obtained

nontrivial critical points for asymptotically quadratic function abstract in this paper we study the existence of nontrivial critical points as applications we study the existence of nontrivial solutions of the dirichelet problem for nonlinear elliptic pde and periodic boundary value problem for nonlinear ope

a note on λ additive fuzzy measures abstract a relation between additive fuzzy measures and measures is given this relation is used to prove some properties of additive fuzzy measures

sugeno s fuzzy measure and fuzzy clustering abstract this paper discusses in detail some properties of sugeno s g measure a clustering algorithm making use of these properties is presented and its performance when run on the well known set of the iris data is briefly described the inherent advantages of the approach proposed are pointed out in the concluding part of the paper

a heuristic simulated annealing algorithm of learning possibility measures for multisource decision making abstract in multisource decision making non normalized possibility measures are used to gauge the credibilities of each subset of information sources in order to reduce the uncertainty introduced by the sources and minimize decision error the credibility of individual information source i e the possibility density is objectively learned from subjectively chosen training data a learning algorithm of the possibility measures is constructed based on the ideas of simulated annealing and feasible direction the algorithm is designed for large training data set two multifeature image segmentation experiments and a comparison of learning speed are presented

seminormed possibility integrals for application oriented modelling abstract semiconormed possibility integrals are proposed as a family of models for decision making which have some special properties due to the non normalized possibility measures the semiconormed possibility integrals are developed from the semiconormed fuzzy integrals and the non normalized possibility measures the non normalized possibility measures induced from the fuzzy sets have the property that the measure of the universe canbe less than equal to one when the universe consists of a set of information sources the possibility measure of a subset of information sources is considered as the credivility of the subset sources the non normalization is due to the fact that an information source in application introduces certainty during data acquisition therefore an information source in reality usually is not fully credible to improve the precision of modelling the credibility values of each information source are learned form training data in term of learning computation a non normalized possibility measure is much simpler to construct than a fuzzy measure finally two applications of the semiconormed possibility integrals are presented

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

existence and multiplicity results for a semilinear elliptic problem abstract in this paper we establish sufficient conditions for an asymptotically linear elliptic boundary value problem to have at least five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues we make extensive use of variational methods and characterizations of the local degree of critical points furthermore uniqueness and qualitative properties of the solutions are investigated

nontrivial solutions of operator equations and morse indices of critical points of min max type on montre que si les hypotheses du theoreme de point selle sont satisfaites si dim y 2 et si f 1 c contient seulement des points critiques non degeneres alors f 1 c contient au moins un point critique u 0 tel que 2 indice de morse u 0 dim y

on multiple solutions of a nonlinear dirichlet problem we prove that a semilinear elliptic boundary value problem has five solutions when the range of the derivative of the nonlinearity includes at least the first two eigenvalues we also prove that if the region is a ball the semilinear elliptic problem has two solutions that change sign and are nonradial