canonical fuzzy numbers of dimension two abstract recently several authors have dealt with interactive fuzzy numbers this paper proposes a new approach to interactions between fuzzy numbers by using canonical fuzzy numbers of dimension two

a note on the embedding problem for multidimensional fuzzy number spaces this paper generalize the results in wu and zhang fuzzy sets and systems in press the embedding is extended from one dimensional to n dimensional case

on measurability of fuzzy number valued functions this paper gives a new definition of the measurability of fuzzy number valued functions and shows the relationship among this measurability and those derived from the corresponding set valued functions

embedding problem of fuzzy number space part ii abstract using a concrete structure into which we embed the fuzzy number space e1 several necessary and sufficient conditions of fuzzy set valued functions are given by means of abstract function theory

a class of m channel linear phase biorthogonal filter banks and their applications to subband coding this correspondence presents a new factorization for linear phase biorthogonal perfect reconstruction pr fir filter hanks using this factorization we propose a new family of lapped transform called the generalized lapped transform glt since the analysis and synthesis filters of the glt are not restricted to be time reverses of each other they can offer more freedom to avoid blocking artifacts and improve coding gain in subband coding applications the glt is found to have higher coding gain and smoother synthesis basis functions than the lapped orthogonal transform lot simulation results also demonstrated that the glt has significantly less blocking artifacts higher peak signal to noise ratio psnr and better visual quality than the lot in image coding simplified glt with different complexity performance tradeoff is also studied

characterization of compact subsets of fuzzy sets a characterization of compact subsets is presented for the metric space of normal fuzzy convex fuzzy sets on the base space rn the metric for which is the supremum over the hausdorff distances between corresponding level sets it is shown that a closed subset is compact if and only if it is uniformly support bounded and the corresponding set of support functions is equileftcontinuous in the membership grade variable

a new look at digital orthogonal transmultiplexers for cdma communications orthogonal transmultiplexers have been successfully utilized for multiuser communications they are of the fdma type in their most common version the transmultiplexers using frequency selective pr qmfs as their user codes were reported in the literature this approach conflicts with the requirements of a cdma communications system we introduce novel spread spectrum pr qmf codes wherein the orthogonality is distributed over both time and frequency domains it is shown that the proposed multivalued spread spectrum pr qmf codes with minimized auto and cross correlation properties outperform the conventional binary gold codes in cdma communication scenarios considered in the article

optimal sequences and sum capacity of synchronous cdma systems the sum capacity of a multiuser synchronous cdma system is completely characterized in the general case of asymmetric user power constraints this solves the open problem posed by rupf and massey see ibid vol 40 p 1261 6 1994 which had solved the equal power constraint case we identify the signature sequences with real components that achieve sum capacity and indicate a simple recursive algorithm to construct them

existence and nonexistence of almost perfect autocorrelation sequences shows that almost perfect autocorrelation sequences are the same as certain cyclic divisible difference sets the authors apply known theorems on divisible difference sets to simplify and strengthen results by j wolfmann 1992 in particular they answer two questions which were posed by wolfman

on the representation of n dimensional fuzzy numbers and their informational content in the former part of this paper we gave representation theorems for n dimensional fuzzy numbers for the special case of n 1 it is just the same as theorem 1 1 in goetschel and voxman fuzzy sets and systems 18 1986 31 which expresses a fuzzy number with two functions in the latter part of this paper we will extend the three parameters value ambiguity and fuzziness defined for the one dimensional fuzzy numbers in delgado et al fuzzy sets and systems 93 1998 125 94 1998 205 to the n dimensional case

ds cdma signature sequences based on pr qmf banks in this paper we propose two classes of multivalued signature sequences for direct sequence code division multiple access ds cdma systems the proposed classes are obtained from the coefficients of the subbands of perfect reconstruction quadrature mirror filterbanks pr qmf the first and second classes are derived from the tree and lattice structure pr qmf banks respectively and they both have perfect correlation properties for synchronous ds cdma systems the second class in addition has generally better correlation properties than other well known sequences in asynchronous ds cdma systems some numerical results for the performance of the asynchronous ds cdma systems with several sequences including the second class of sequences are obtained

metric spaces of fuzzy sets two classes of metrics are introduced for spaces of fuzzy sets their equivalence is discussed and basic properties established a characterisation of compact and locally compact subsets is given in terms of boundedness and p mean equileft continuity and the spaces shown to be locally compact complete and separable metric spaces

integrals of fuzzy number valued functions abstract using the representation theorem of fuzzy numbers we give an alternative approach for the integrals of fuzzy number valued functions and for the radon nikodym theorem of the fuzzy number valued measures

a fuzziness measure for fuzzy numbers applications abstract extending the ideas of delgado et al 1995 to include the notion of fuzziness we obtain canonical representations of fuzzy numbers in particular we show that any fuzzy number can be represented by either a trapezoidal or a quasitrapezoidal number having the same basic attributes as the original fuzzy number

dynamics and approximations of a velocity tracking problem for the navier stokes flows with piecewise distributed controls we study the dynamics of a piecewise in time distributed optimal control problem for the navier stokes equations which models velocity tracking over time we also study the dynamics of semidiscrete and fully discrete approximations of this velocity tracking problem we prove that the rates of velocity tracking are exponential some computational results are presented which reinforces the theoretical results derived

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

bounds on partial correlations of sequences two approaches to bounding the partial auto and crosscorrelations of binary sequences are considered the first approach uses the discrete fourier transform and bounds for character sums to obtain bounds on partial autocorrelations of m sequences and on the partial auto and crosscorrelations for the small kasami sets and dual bch families of sequences the second approach applies to binary sequences obtained by interleaving m sequences a bound on the peak partial correlation of such sequences is derived in terms of the peak partial autocorrelation of the underlying m sequences the bound is applied to gmw no 1987 and other families of sequences for particular parameters a comparison of the two approaches shows that the elementary method gives generally weaker results but is more widely applicable on the other hand both methods show that well known sequence families can have favorable partial correlation characteristics making them useful in certain spread spectrum applications

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

on a canonical representation of fuzzy numbers abstract fuzzy numbers and more generally linguistic values are approximate assessments given by experts and accepted by decision makers when obtaining more accurate values is impossible or unnecessary to simplify the task of representing and handling fuzzy numbers several authors have introduced real indices in order to capture the information contained in a fuzzy number in this paper we propose two parameters value and ambiguity for this purpose we use these parameters to obtain canonical representations and to deal with fuzzy numbers in decision making problems several examples illustrate these ideas