fuzzy non continuous mappings and fuzzy pre semi separation axioms the aim of the paper is mainly to introduce and study fuzzy pre semi open mapping fuzzy pre semi irresolute mapping fuzzy pre semi separation axioms and fuzzy pre semi connectedness in fuzzy topological spaces

paracompactness in l topological spaces in this paper a certain fuzzy paracompactness is presented by means of the concept of locally finite family of l fuzzy sets the concept of locally finite family can be used to characterize fuzzy countable compactness this fuzzy paracompactness is a natural generalization of lowen fuzzy compactness a fuzzy countably compact l set is fuzzy paracompact if and only if it is fuzzy compact a topological space x j is paracompact if and only if its induced space x j is fuzzy paracompact when ms l the fuzzy enhanced real line r l is fuzzy paracompact the product of a fuzzy compact set and a fuzzy paracompact set is fuzzy paracompact a fuzzy strongly t2 paracompact space is strongly s regular and strongly ws normal moreover a strongly s regular lindelof space is fuzzy paracompact

a note on lo fuzzy nearly compact spaces in this note we define lo fuzzy nc fuzzy sets and introduce the finite intersection property for fuzzy sets in the sense of lowen lo fip for short we give some equivalent characterizations of lo fuzzy nc spaces and lo fuzzy nc fuzzy sets by using lo fip regular open and regular closed fuzzy sets finally we prove that lo fuzzy nearly compactness is preserved under fuzzy almost continuous and almost open mapping

almost compact fuzzy sets in fuzzy topological spaces abstract the study of almost compact fuzzy topological spaces was initiated by concilio and gerla 4 which was followed by further investigations of the same in 11 the present paper aspires for an extension of the same concept to fuzzy sets in a fuzzy topological space we characterize almost compact fuzzy sets in terms of the concept of fuzzy filterbase some properties of such sets are established using the concepts of fuzzy ds closure and fuzzy ds cluster points of fuzzy filterbase

fuzzy nets and their application fuzzy net theory is enriched by the introduction of the fuzzy net of fuzzy sets the limsup liminf and limit of a fuzzy net of fuzzy sets are defined and their various properties are discussed alternative characterizations based on the notion of a fuzzy net are provided for several fuzzy topological concepts including open and closed fuzzy sets fuzzy continuity maps with closed fuzzy graph open fuzzy mapping etc thus the net theoretic approach is shown to be a promising tool in fuzzy topology

on the robustness of transmit beamforming beamforming is a simple transmit strategy that uses only one eigen direction in multiple input multiple output channels this simplicity makes beamforming a competitive strategy in practice but at the same time poses a doubt on the sensitivity of beamforming to the imperfectness of the channel state information at the transmitter csit this paper studies beamforming from the perspective of worst case robustness we show that beamforming can achieve the maximum received signal to noise ratio snr or guarantees a given received snr with the minimum transmit power in the worst channel within an elliptical uncertainty region defined by the weighted spectral norm this result further implies that beamforming has the ability to combat against the imperfectness of csit especially for small channel dimensions or small channel uncertainty

fµ strongly semiopen sets fµ strong semicontinuity and fµ strongly semiretracts throughout the literature if x d is an f ts and y x the induced f topological subspace y d y is defined so that d y n g y n d macho stadler and de prada vicente fuzzy sets and systems 58 1993 365 introduced a new concept of f topological subspaces which coincides with the usual definition in the case that m g y also they introduced the concepts of f m open sets and f m continuity in this paper using the previous concepts we introduce weaker forms of f m open sets and f m continuity the notion of an f retract was introduced by rodabough j math anal appl 79 1981 273 here we introduce the notion of a f m retract and weaker forms of it the basic properties of these notions are given many results are obtained

rs compactness in l fuzzy topological spaces abstract a good definition of rs compactness in l fuzzy topological spaces is suggested for l a fuzzy lattice we define rs compactness on arbitrary l fuzzy sets and study some of its properties

a note on compactness in a fuzzy setting abstract the concept of filter basis in a fuzzy setting is defined and investigated fuzzy filter bases are then used to introduce the notion of compactness in fuzzy setting the expected basic properties of compactness are explored

almost continuous and weakly continuous fuzzy set valued functions on bitopological spaces the aim of this paper is to introduce and study almost continuous and weakly continuous fuzzy pairwise multifunctions where the domain of these functions is a bitopological space with their values as arbitrary fuzzy sets in a fuzzy bitopological space several characterizations and properties of these multifunctions along with their mutual relationships are established

on various weak fuzzy pairwise retracts the notion of a fuzzy retract was introduced by rodabaugh j math anal appl 79 1981 273 and this notion was extended to the fuzzy bitopological setting j fuzzy math 9 1 2001 207 in this paper we define the notions of fuzzy pairwise semiretracts fuzzy pairwise preretracts fuzzy pairwise strongly semiretracts fuzzy pairwise less strongly semiretracts and fuzzy pairwise semi preretracts we establish some properties of these concepts moreover the relations between these new concepts are discussed

capacity and power allocation for fading mimo channels with channel estimation error in this correspondence we investigate the effect of channel estimation error on the capacity of multiple input multiple output mimo fading channels we study lower and upper bounds of mutual information under channel estimation error and show that the two bounds are tight for gaussian inputs assuming gaussian inputs we also derive tight lower bounds of ergodic and outage capacities and optimal transmitter power allocation strategies that achieve the bounds under perfect feedback for the ergodic capacity the optimal strategy is a modified waterfilling over the spatial antenna and temporal fading domains this strategy is close to optimum under small feedback delays but when the delay is large equal powers should be allocated across spatial dimensions for the outage capacity the optimal scheme is a spatial waterfilling and temporal truncated channel inversion numerical results show that some capacity gain is obtained by spatial power allocation temporal power adaptation on the other hand gives negligible gain in terms of ergodic capacity but greatly enhances outage performance

regularly open sets in fuzzy topological spaces abstract this paper is devoted to the study of the role of fuzzy regularly open sets we prove some properties of fuzzy almost continuous mappings and define fuzzy almost open mappings we prove that under a fuzzy almost continuous and fuzzy almost open map the inverse image of a fuzzy regularly open set is fuzzy regularly open further we define a new type of fuzzy separation axioms fuzzy almost separation axioms it is interesting that there are some deviations in the behaviour of these axioms as compared to those in general topology for example in a fuzzy almost t1 space not every fuzzy singleton is closed also a fuzzy space which is fuzzy almost t 2 1 2 as well as fuzzy almost t0 is fuzzy almost regular while in general topology we have to take an almost t2 space in place of almost t0 space

a competitive minimax approach to robust estimation of random parameters we consider the problem of estimating in the presence of model uncertainties a random vector x that is observed through a linear transformation h and corrupted by additive noise we first assume that both the covariance matrix of x and the transformation h are not completely specified and develop the linear estimator that minimizes the worst case mean squared error mse across all possible covariance matrices and transformations h in the region of uncertainty although the minimax approach has enjoyed widespread use in the design of robust methods we show that its performance is often unsatisfactory to improve the performance over the minimax mse estimator we develop a competitive minimax approach for the case where h is known but the covariance of x is subject to uncertainties and seek the linear estimator that minimizes the worst case regret namely the worst case difference between the mse attainable using a linear estimator ignorant of the signal covariance and the optimal mse attained using a linear estimator that knows the signal covariance the linear minimax regret estimator is shown to be equal to a minimum mse mmse estimator corresponding to a certain choice of signal covariance that depends explicitly on the uncertainty region we demonstrate through examples that the minimax regret approach can improve the performance over both the minimax mse approach and a plug in approach in which the estimator is chosen to be equal to the mmse estimator with an estimated covariance matrix replacing the true unknown covariance we then show that although the optimal minimax regret estimator in the case in which the signal and noise are jointly gaussian is nonlinear we often do not lose much by restricting attention to linear estimators

on some weaker forms of fuzzy continuous and fuzzy open mappings on fuzzy topology spaces abstract the purpose of the present paper is to study some weaker forms of fuzzy continuous and fuzzy open maps between fuzzy topological spaces along with the introduction and investigations of a new class of non fuzzy continuous maps this latter type of mappings is seen to be independent of the other non continuous functions discussed here all these functions are characterized and certain properties concerning them are proved finally a comparative study as to their mutual dependence and interrelations under different conditions is taken up

semi open sets and semi continuity in fuzzy bitopological spaces abstract in this paper the concepts of fuzzy semi open sets and fuzzy semi continuous mappings due to azad 1981 have been generalized to fuzzy bitopological spaces and some of their properties are studied

new applications of l nets in l fuzzy multifunctions in this paper we will give new applications of l net in l fuzzy multifunctions using l net we will further study l fuzzy continuous almost continuous and r continuous multifunctions some interesting characterizations are obtained

on some near fuzzy continuous functions between fuzzy topological spaces abstract the concepts of fuzzy almost strongly continuous fuzzy continuous fuzzy weekly continuous and fuzzy weakly continuous are introduced and studied in the light of the concept of q coincidence in a fuzzy setting together with the concept of q neighbourhoods the notions of fuzzy neighbourhoods and fuzzy neighbourhoods are defined to investigate the characterizations and properties of these functions finally a comparative study regarding the mutual interrelations among these maps along with fuzzy continuous maps is made

relay precoder optimization in mimo relay networks with imperfect csi in this paper we consider robust joint designs of relay precoder and destination receive filters in a nonregenerative multiple input multiple output mimo relay network the network consists of multiple source destination node pairs assisted by a mimo relay node the channel state information csi available at the relay node is assumed to be imperfect we consider robust designs for two models of csi error the first model is a stochastic error se model where the probability distribution of the csi error is gaussian this model is applicable when the imperfect csi is mainly due to errors in channel estimation for this model we propose robust minimum sum mean square error smse mse balancing and relay transmit power minimizing precoder designs the next model for the csi error is a norm bounded error nbe model where the csi error can be specified by an uncertainty set this model is applicable when the csi error is dominated by quantization errors in this case we adopt a worst case design approach for this model we propose a robust precoder design that minimizes total relay transmit power under constraints on mses at the destination nodes we show that the proposed robust design problems can be reformulated as convex optimization problems that can be solved efficiently using interior point methods we demonstrate the robust performance of the proposed design through simulations

robust optimization for amplify and forward mimo relaying from a worst case perspective in this paper we consider robust optimization of amplify and forward af multiple input multiple output mimo relay precoders in presence of deterministic imperfect channel state information csi when the csi uncertainty lies in a norm bounded region two widely used performance metrics mutual information mi and mean square error mse are adopted as design objectives according to the philosophy of worst case robustness the robust optimization problems with respect to maximizing the worst case mi and minimizing the worst case mse are formulated as maximin and minimax problems respectively due to the fact that these two problems do not have a concave convex or convex concave structure we cannot rely on the conventional saddle point theory to find the robust solutions nevertheless by exploiting majorization theory we show that the formulated maximin and minimax problems both admit saddle points we further analytically characterize the saddle points and provide closed form solutions to robust relay precoder designs interestingly we find that under both mi and mse metrics the robust relay optimization leads to a channel diagonalizing structure meaning that eigenmode transmission is optimal from the worst case robustness perspective the proposed robust designs can improve the spectral efficiency and reliability of af mimo relaying against csi uncertainties at the similar cost of computational complexity as the existing non robust schemes

a compactness in bifuzzy topological spaces abstract compact fuzzy topological spaces were first introduced by chang 3 compact fuzzy topological spaces were introduced by gantner et al 4 abd el monsef et al 1 introduced the notion of almost compact fuzzy topological spaces mashbour et al 8 introduced the notion of bifuzzy topological spaces and defined the notion of compactness in those spaces in this paper we obtain some new results about compact bifuzzy topological spaces we introduce and study the notion of pairwise almost compact bifuzzy topological spaces

on several types of degree of fuzzy compactness abstract sostak 1985 defined a fuzzy topology on a set x as a fuzzy subset of the family i x of fuzzy subsets of x satisfying some axioms the concept of the degree of compactness of a fuzzy set was first introduced by sostak 1985 in this paper we discuss the degrees of almost compactness near compactness countable compactness light compactness and strong compactness of a fuzzy set also we investigate the behavior of the degrees of compactness under several types of fuzzy continuous functions

fuzzy topology on fuzzy sets fuzzy semicontinuity and fuzzy semiseparation axioms the concept of a fuzzy topology on a fuzzy set was introduced in fuzzy set syst 45 1992 103 the aim of this paper is to introduce fuzzy semicontinuity and fuzzy semiseparation axioms in this new situation and validity of some characterization of these concepts have been examined also we define a fuzzy generalized semiopen set and introduce fuzzy separation axioms by using this concept fuzzy semiconnected and fuzzy semicompact spaces are introduced and some of their properties are discussed

irresolute and lmost open functions between fuzzy topological spaces abstract the aim of this paper is to introduce and characterize the concept of fuzzy irresolute functions which is strictly stronger than the concept of fuzzy semi continuous functions and independent of the concept of fuzzy continuous functions the independence of the two definitions of fuzzy almost open functions as introduced in 5 and 3 and some of their characterizations are also established

almost n compact sets in l fuzzy topological spaces abstract in this paper the concept of almost n compactness in l fuzzy topological spaces is introduced the characterizations of almost n compact sets are systematically discussed it is showed that the fuzzy almost continuous image of an almost n compact set is an almost n compact set it is proved that the almost n compactness is a good extension

robust multicast beamforming for spectrum sharing based cognitive radios we consider a robust downlink beamforming optimization problem for secondary multicast transmission in a multiple input multiple output mimo spectrum sharing cognitive radio cr network the minimization of transmit power is formulated subject to both quality of service qos constraints on the secondary receivers and interference temperature constraints on the primary users under the assumption of imperfect channel state information csi the problem is a nonconvex quadratically constrained quadratic program qcqp and in general it is hard to achieve the global optimality as a compromise we present two randomized approximation algorithms for the problem via convex optimization techniques apart from the general setting of the robust beamforming problem we identify one interesting special case the robust problem of which can be solved efficiently simulation results are presented to demonstrate the performance gains of the proposed algorithms over an existing robust design

the effect of test signal type and bandwidth on the categorical scaling of loudness recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth beyond the critical band affected loudness growth as wideband speech stimuli were judged to be significantly louder than narrow band speech at equivalent overall sound levels in this investigation similar loudness growth patterns were noted across category ratings for all test signal bandwidths in contrast loudness growth data obtained using an intelligible speech signal cox et al the american academy of audiology 1994a revealed loudness growth patterns for speech were fundamentally different than those obtained for tones implications for hearing aid fitting strategies are discussed recently several methods for obtaining clinical measures of loudness growth through the use of categorical scaling cs have been proposed for the selection of hearing aids these methods use differing test signals or suggest frequency specific level corrections in an attempt to reflect the loudness perception of hearing aid processed speech while some decisions regarding the stimuli utilized for loudness perception procedures are based on measured relationships to speech signals the effect on loudness perception of changing signal type and bandwidth as measured by cs remains unclear the relationships between the cs loudness growth of signals of differing type pure tones noise bands filtered temporally inverted passband speech and bandwidth were examined for subjects with both normal and impaired hearing results suggest that when the bandwidth is similar e g pure tone and 1 3 oct signal type does not have significant bearing on loudness perception as expected increasing the bandwidth bey

fuzzy preopen sets and fuzzy preseparation axioms abstract in this paper the concept of preopen sets due to a s mashhour m e abd el monsef and s n el debb 7 has been generalised to the fuzzy setting further fuzzy separation axioms have been introduced and investigated with the help of fuzzy preopen sets

robust transceiver optimization in downlink multiuser mimo systems we study robust transceiver optimization in a downlink multiuser wireless system where the transmitter and the receivers are equipped with antenna arrays the robustness is defined with respect to imperfect knowledge of the channel at the transmitter the errors in the channel state information are assumed to be bounded and certain quality of service targets in terms of mean square errors mses are guaranteed for all channels from the uncertainty regions iterative algorithms are proposed for the transceiver design the iterations perform alternating optimization of the transmitter and the receivers and have equivalent semidefinite programming representations with efficient numerical solutions the framework supports robust counterparts of several mse optimization problems including transmit power minimization with per user or per stream mse constraints sum mse minimization min max fairness etc although the convergence to the global optimum cannot be claimed due to the intricacy of the problems numerical examples show good practical performance of the presented methods we also provide various possibilities for extensions in order to accommodate a broader set of scenarios regarding the precoder structure the uncertainty modeling and a multicellular setup

a robust maximin approach for mimo communications with imperfect channel state information based on convex optimization this paper considers a wireless communication system with multiple transmit and receive antennas i e a multiple input multiple output mimo channel the objective is to design the transmitter according to an imperfect channel estimate where the errors are explicitly taken into account to obtain a robust design under the maximin or worst case philosophy the robust transmission scheme is composed of an orthogonal space time block code ostbc whose outputs are transmitted through the eigenmodes of the channel estimate with an appropriate power allocation among them at the receiver the signal is detected assuming a perfect channel knowledge the optimization problem corresponding to the design of the power allocation among the estimated eigenmodes whose goal is the maximization of the signal to noise ratio snr is transformed to a simple convex problem that can be easily solved different sources of errors are considered in the channel estimate such as the gaussian noise from the estimation process and the errors from the quantization of the channel estimate among others for the case of gaussian noise the robust power allocation admits a closed form expression finally the benefits of the proposed design are evaluated and compared with the pure ostbc and nonrobust approaches

on nearly compact and 0 rigid fuzzy sets in fuzzy topological spaces abstract this paper intends to initiate the study of nearly compact and rigid fuzzy sets in a fuzzy topological space these two classes of fuzzy sets are seen to be properly contained in the class of fuzzy compact sets and properly contain the class of fuzzy almost compact sets several characterizations and certain other properties of these two types of fuzzy sets are established by using the concepts of fuzzy closures and closures of fuzzy sets and fuzzy filterbases

robust mimo cognitive radio via game theory cognitive radio cr systems improve the spectral efficiency by allowing the coexistence in harmony of primary users pus the legacy users with secondary users sus this coexistence is built on the premises that no su can generate interference higher than some prescribed limits against pus the system design based on perfect channel state information csi can easily end up violating the interference limits in a realistic situation where csi may be imperfect in this paper we propose a robust design of cr systems composed of multiple pus and multiple noncooperative sus in either single input single output siso frequency selective channels or more general multiple input multiple output mimo channels we formulate the design of the su network as a noncooperative game where the sus compete with each other over the resources made available by the pus by maximizing their own information rates subject to the transmit power and robust interference constraints following the philosophy of the worst case robustness we take explicitly into account the imperfectness of su to pu csi by adopting proper interference constraints that are robust with respect to the worst channel errors relying on the variational inequality theory we study the existence and uniqueness properties of the nash equilibria of the resulting robust games and devise totally asynchronous and distributed algorithms along with their convergency properties we also propose efficient numerical methods based on decomposition techniques to compute the robust transmit strategy for each su

fuzzy weak semicontinuity abstract in this paper we introduce the fuzzy weakly semicontinuous mapping which is the weaker form of both fuzzy semicontinuous and fuzzy almost continuous mappings in fuzzy topological spaces however fuzzy weakly semicontinuous mapping and fuzzy weakly continuous mapping are independent notions then we discuss some characteristic properties of fuzzy semicontinuous fuzzy semiopen fuzzy semiclosed and fuzzy pre semi open mappings

some remarks on lo rs fuzzy compactness abstract in this paper we define lo rs fuzzy compact fuzzy sets we study some properties of lo rs fuzzy compact spaces and lo rs fuzzy compact fuzzy sets we give some characterizations of these notions by fuzzy regularly open sets and fuzzy regularly closed sets we prove that lo rs fuzzy compactness is preserved under a fuzzy almost continuous and fuzzy almost open mapping

robust energy efficiency maximization in cognitive radio networks the worst case optimization approach energy efficiency ee is very crucial for future wireless communication systems especially for cognitive radio networks crns the ee performance relies on channel state information csi of channels besides the interference from secondary users sus to primary users pus also closely depends on csi in underlay crns however available works on ee usually assume that csi is perfect which is often inaccurate in practical systems thus in this paper we investigate the robust ee maximization problem in underlay crns with multiple sus and pus assuming csi error to be bounded we consider that all channels lie in some bounded uncertainty regions from the perspective of worst case optimization we formulate it as the max min problem with infinite constraint which is nontrivial even without this constraint this is because that the outer maximization problem is non convex and the inner minimization problem is a concave minimization problem known as np hard in general we propose a scheme to handle this problem via the fractional programming and global optimization techniques particularly we efficiently solve this problem in two special cases simulation results validate that our proposed scheme can improve the worst case ee of sus distinctly and strictly guarantee the quality of service qos of pus under all parameters uncertainties

fuzzy topology and fuzzy multifunctions the fundamental concept of a fuzzy set was first introduced by zadeh in his classical paper 141 since then work has been done by many authors in several directions which has resulted in the formation of a new mathematical field called fuzzy mathematics the theory of fuzzy topological spaces is a branch of such mathematics chang in 2 was the first to introduce the notion of fuzzy topology several others continued the work in this area for example see 12 131 we remark that general point set topology can be regarded as a special case of fuzzy topology where all membership functions are just characteristic functions in this paper we introduce several fuzzy topological concepts and examine their properties our basic tool in that process is the notion of the fuzzy neighborhood of a point introduced by warren in ill we also introduce the notion of fuzzy multifunctions which we strongly believe will be useful in the study of fuzzy games and general fuzzy optimization problems we study the continuity and measurability properties of these multifunctions also we introduce linear fuzzy multifunctions and study their properties in the light of the recent work of katsaras 5 katsaras and liu s and lowen 9 on fuzzy vector spaces

a note on regular semiopen l sets and s closed spaces in this paper we introduce the concept of regular semiopen l set and investigate some of its properties and obtain a characterization of regular semiopen l sets also we characterize that every cover of an l topological space x by semiopen l sets has a finite subcover whose semiclosures cover x

q convergence of ideals in fuzzy lattices and its applications abstract in this paper we study q convergence and q convergence of ideals in fuzzy lattices by the concept of q remote neighborhood then we introduce the strong s irresoluteness s irresoluteness and s strong semicontinuity on fuzzy lattices we also study some properties of the notions above and strong semicontinuity 2 3 and s irresoluteness 3 4 with the aid of the q convergence q convergence of ideals

fuzzy subcontinuity inverse fuzzy subcontinuity and a new category of fuzzy topological spaces the notions of subcontinuity and inverse subcontinuity are extended to the fuzzy setting adopting fuzzy net theoretic approach various properties of fuzzy subcontinuous and inversely fuzzy subcontinuous mappings are studied a category of fuzzy topological spaces is constructed canonical example is constructed by using fuzzy translation of fuzzy numbers introduced by rodabaugh to show that fuzzy subcontinuity does not imply kfuzzy continuity in the process n compactness is characterized and fuzzy unit interval is shown to be n compact also a direct proof is provided showing that fuzzy addition of fuzzy numbers is fuzzy continuous

statistically robust design of linear mimo transceivers the treatment of channel state information csi is critical in the design of mimo systems accurate csi at the transmitter is often not possible or may require high feedback rates herein we consider the robust design of linear mimo transceivers with perfect csi either at the transmitter or at both sides of the link the framework considers the design problem where the imperfect csi consists of the channel mean and covariance matrix or equivalently the channel estimate and the estimation error covariance matrix the robust transceiver design is based on a general cost function of the average mses as well as a design with individual mse based constraints in particular a lower bound of the average mse matrix is explored for the design when only the csi at the transmitter is imperfect under different csi conditions the proposed robust transceivers exhibit a similar structure to the transceiver designs for perfect csi but with a different equivalent channel and or noise covariance matrix

on fuzzy pairwise semi precontinuity abstract in this paper we generalize the concepts of fuzzy semi preopen semi preclosed sets and fuzzy semi precontinuous mappings due to park and lee fuzzy sets and systems 67 1994 359 364 into fuzzy bitopological setting and discuss some of its basic properties

optimized one way relaying strategy with outdated csi quantization for spatial multiplexing this correspondence considers a mimo relay downlink system using precoding and limited feedback since the conventional precoding matrices are directly obtained by treating the quantized channel state information csi feedback as real csi we propose an optimized relay precoding strategy by taking both effects of channel quantization error and feedback delay into account conditioned on the outdated csi quantization available at the relay station the relay precoding is optimized via minimizing an expected mean square error mse criterion over csi mismatches by using karush kuhn tucker kkt conditions a closed form solution to the relay design is achieved with comparable computational complexity relative to the conventional approach numerical results verify the effectiveness of the proposed scheme

worst case mse precoder design for imperfectly known mimo communications channels this paper considers a worst case precoder design problem for multiple input multiple output mimo wireless communication systems with imperfect channel knowledge at the transmitter when the mimo channel is a full row rank matrix which arises generically when the number n sub t of transmit antennas is greater or equal to the number n sub r of receive antennas and when channel state information is known perfectly at the transmitter the channel can be equalized exactly by employing a precoder equal to the channel pseudo inverse however in actual systems it is necessary to take into account the channel estimation error we consider here a worst case precoder design problem where the goal is to find the precoder minimizing the equalization mean square error for the least favorable channel located in a ball centered about the estimated channel lagrangian optimization is used to convert this min max problem into a min min convex minimization problem over a convex domain which can be solved in closed form the robust precoder and associated least favorable channel have an intuitive interpretation since the least favorable channel zeroes out the weakest subchannels and the robust precoder implements a pseudo inverse only for the remaining subchannels

almost compactness in fuzzy topological spaces abstract we introduce and study almost compactness for fuzzy topological spaces we show that the almost continuous image of an almost compact fuzzy topological space is almost compact moreover we show that generally almost compactness for fuzzy topological spaces is not product invariant but if x and y are almost fuzzy topological spaces and x is product related to y then their fuzzy topological product is almost compact

cross modality matching and the loudness growth function for click stimuli loudness intensity functions for click stimuli were obtained from 30 adult listeners having normal n 10 flat n 10 or sloping n 10 high frequency cochlear hearing loss configurations the procedure of cross modality matching cmm between loudness and perceived line length r p hellman and c h meiselman j speech hear res 31 605 615 1988 j acoust soc am 88 2596 2606 1990 j acoust soc am 93 966 975 1993 was used to validate their loudness growth functions mean group loudness exponents were similar to those reported in recent investigations that utilized pure tone stimuli further supporting the validity and reliability of the cmm task as an estimate of the loudness growth function the results also suggest that the mean loudness function for clicks is similar to the function obtained with tonal stimuli at least for listeners with moderately impaired hearing or better moreover cmm produced less variability than the more conventional psychophysical methods of magnitude estimation and production for the groups with cochlear hearing loss toward direct application of the cmm technique in lieu of absolute exponential slope values the individually determined loudness growth function over a range of intensities should be compared to the normal mean functions for calculations of deviations

categorical loudness scaling and equal loudness contours in listeners with normal hearing and hearing loss this study describes procedures for constructing equal loudness contours elcs in units of phons from categorical loudness scaling cls data and characterizes the impact of hearing loss on these estimates of loudness additionally this study developed a metric level dependent loudness loss which uses cls data to specify the deviation from normal loudness perception at various loudness levels and as function of frequency for an individual listener with hearing loss cls measurements were made in 87 participants with hearing loss and 61 participants with normal hearing an assessment of the reliability of cls measurements was conducted on a subset of the data cls measurements were reliable there was a systematic increase in the slope of the low level segment of the cls functions with increase in the degree of hearing loss elcs derived from cls measurements were similar to standardized elcs international organization for standardization iso 226 2003 the presence of hearing loss decreased the vertical spacing of the elcs reflecting loudness recruitment and reduced cochlear compression representing cls data in phons may lead to wider acceptance of cls measurements like the audiogram that specifies hearing loss at threshold level dependent loudness loss describes deficit for suprathreshold sounds such information may have implications for the fitting of hearing aids

fuzzy s continuous functions and semilocally connected fuzzy topological spaces abstract the concept of s continuous functions kohli 1978 is translated in fuzzy setting into two concepts fuzzy s continuous functions and fuzzy os continuous functions the concepts of semiconnected functions kohli 1978 and semilocally connected spaces kohli 1978 do the same interactions between those concepts in fuzzy setting and fuzzy continuity chang 1968 are discussed also characterizations of semilocally connected and semilocally o connected fuzzy topological spaces in terms of fuzzy s continuous functions and fuzzy os continuous functions respectively are obtained

functions and as closedness in fuzzy topological spaces abstract in this paper we discuss s closedness in fuzzy topological spaces and we give some characterizations of s closedness also we investigate the image and the inverse image of s closed spaces under some types of functions and we improve and generalize some results on s closed spaces in fuzzy setting

worst case robust mimo transmission with imperfect channel knowledge in this paper we consider robust transmit strategies against the imperfectness of the channel state information at the transmitter csit for multi input multi output mimo communication systems following a worst case deterministic model the actual channel is assumed to be inside an ellipsoid centered at a nominal channel the objective is to maximize the worst case received signal to noise ratio snr or to minimize the worst case chernoff bound of the error probability thus leading to a maximin problem moreover we also consider the qos problem as a complement of the maximin design which minimizes the transmit power consumption and meanwhile keeps the received snr above a given threshold for any channel realization in the ellipsoid it is shown that for a general class of power constraints both the maximin and qos problems can be equivalently transformed into convex problems or even further into semidefinite programs sdps thus efficiently solvable by the numerical methods the most interesting result is that the optimal transmit directions i e the eigenvectors of the transmit covariance are just the right singular vectors of the nominal channel under some mild conditions this result leads to a channel diagonalizing structure as in the cases of perfect csit and statistical csit with mean or covariance feedback and reduces the complicated matrix valued problem to a scalar power allocation problem then we provide the closed form solution to the resulting power allocation problem

mimo minimum total mse transceiver design with imperfect csi at both ends this paper presents new results on joint linear transceiver design under the minimum total mean square error mse criterion with channel mean as well as both transmit and receive correlation information at both ends of a multiple input multiple output mimo link the joint design is formulated into an optimization problem the optimum closed form precoder and decoder are derived compared to the case with perfect channel state information csi linear filters are added at both ends to balance the suppression of channel noise and the noise from imperfect channel estimation the impact of channel estimation error as well as channel correlation on system performance is assessed based on analytical and simulation results

t closure and d closure operators on fuzzy bitopological spaces abstract the concepts of closure and closure operators are introduced and studied in the light of quasi coincidence due to pu and liu 1980 1980 in a fuzzy bitopological setting as applications of these concepts we give characterizations of fuzzy pairwise regularity and some of its weaker forms in terms of closures and closures the concept of fuzzy pairwise continuity has been introduced and characterized by using quasi coincidence between fuzzy sets and its relation with fuzzy pairwise almost continuity has been established in a fuzzy bitopological setting

on almost continuous and weakly continuous fuzzy multifunctions abstract the paper deals with the study of almost continuous and weakly continuous multifunctions in fuzzy setting several characterizations and certain properties of these fuzzy multifunctions along with their mutal relationships are established attempts are also made to correlate them with fuzzy lower and upper semi continuous multifunctions

joint precoding optimization for multiuser multi antenna relaying downlinks using quadratic programming this paper studies the optimization problem for joint precoding design in a multi antenna downlink channel using relaying we formulate the joint source and relay precoding design by aiming at sum capacity maximization since this problem is in general nonconvex we first convert this problem into standard convex quadratic programs and then propose an iterative joint precoding optimization algorithm by utilizing efficient quadratic programming approaches we observe that the iterative method always yields optimal precoding matrices which diagonalize the compound channel of the backward source to relay and the forward relay to destination links at high snr regimes motivated by this observation we further develop an efficient structured precoding design simulation results are presented to verify the effectiveness of our proposed precoding schemes

on lower separation axioms abstract in 3 mashhour et al introduced the concept of fuzzy disjointness two fuzzy sets a b in x are said to be fuzzy disjoint if a co b where co b is the complement of b using this concept they introduced fti separation axioms as a generalization for the basic separation axioms ti i 1 4 in 5 singal and rajvanshi used the concepts of regular open fuzzy sets 1 and fuzzy disjointness to introduce some fuzzy almost separation axioms which are stronger than those of mashhour unfortunately some results in 5 are incorrect in this paper we use the concept of the quasi coincident relation 4 to restate lower fuzzy separation axioms and give a corrected version for some definitions and results in 5

robust mmse precoding in mimo channels with pre fixed receivers in this paper we design robust precoders under the minimum mean square error mmse criterion for different types of channel state information csi in multiple input multiple output mimo channels we consider low complexity pre fixed receivers that may adapt to the channel but are oblivious to the existence of a precoder at the transmitter in particular three types of csi are taken into account i perfect csi ii statistical csi in the form of mean feedback and iii deterministic imperfect csi assuming that the actual channel is within the neighborhood of a nominal channel which leads to the worst case robust design that is the focus of this paper interestingly it is found that under some mild conditions the optimal transmit directions i e the left singular vectors of the precoder are equal to the right singular vectors of the channel the channel mean and the nominal channel for perfect csi statistical csi and the worst case design respectively consequently the matrix valued problems can be simplified to scalar power allocation problems that either admit closed form solutions or can be efficiently solved by the proposed algorithm

some stronger forms of fuzzy continuous mapping on fuzzy topological spaces abstract the paper is devoted to the introduction and study of the concepts of certain classes of functions between fuzzy topological spaces each of these functions presents a stronger form of the fuzzy continuous functions these maps have been characterized and investigated mainly in the light of the notions of q neighbourhoods quasi coincidence fuzzy closure and ds neighbourhoods they have also been compared as to their mutual dependence as also with regard to their interactions with certain other fuzzy non continuous functions

the characterizations of semi continuous and irresolute order homomorphisms on fuzzes abstract the concepts of semi continuous and irresolute order homomorphisms on fuzzes were introduced in j jianghan petroleum institute 2 1988 96 97 in this paper we first present the theory with respect to s convergence s convergence of molecular nets and ideals on fuzzes secondly we introduce the notions of strong semicontinuity strong irresoluteness and s irresoluteness on fuzzes then we systematically study the characterizations of these notions with the aid of the s convergence s convergence of molecular nets and ideals and give the relations of them

on the compound capacity of a class of mimo channels subject to normed uncertainty the compound capacity of uncertain multiple input multiple output channels is considered when the channel is modeled by a class described by a known nominal channel and a constrained norm unknown uncertainty within this framework two types of classes are investigated with additive and multiplicative uncertainties subject to a spectral norm constraint using the singular value decomposition and related singular value inequalities as the main tools the compound capacity is a maxmin mutual information representing the capacity of the class in which the minimization is done over the class of channels while the maximization is done over the transmit covariance closed form solutions for the compound capacity of the classes are obtained and several properties related to transmit and receive eigenvectors are presented it is shown that under certain conditions the compound capacity of the class is equal to the worst case channel capacity thus establishing a saddle point property explicit closed form solutions are given for the worst case channel uncertainty and the capacity achieving transmit covariance matrix the best transmission strategy achieving the compound capacity is a multiple beamforming on the nominal known channel eigenmodes with the beam power distribution via the water filling at a degraded snr as the uncertainty increases fewer eigenmodes are used until only the strongest one remains active so that transmit beamforming is an optimal robust transmission strategy in this large uncertainty regime for which explicit conditions are given using these results upper and lower bounds of the compound capacity are constructed for other bounded uncertainties and some generic properties are pointed out the results are extended to compound multiple access and broadcast channels in all considered cases the price to pay for channel uncertainty is an snr loss or equivalently the nominal channel degradation commensurate with the uncertainty set radius measured by the spectral norm and the optimal signaling strategy is the transmission on the degraded nominal channel

on fuzzy compactness in this paper we characterize well known fuzzy compactness see 3 4 9 and 10 using the notion of fuzzy upper limit see 5 also we give and study new fuzzy compactness in fuzzy topological spaces

directed family of fuzzy sets and fuzzy perfect maps the present paper deals with the perfect functions in fuzzy setting fuzzy filter bases of fuzzy sets are also studied vis a vis such functions finally certain fuzzy topological properties are taken up for their study with regard to fuzzy perfect functions

fuzzy strongly semiopen sets and fuzzy strong semicontinuity abstract in this paper we first introduce and study the fuzzy strongly semiopen and fuzzy strongly semiclosed sets in fuzzy space then we introduce the strong semi interior and strong semiclosure of a fuzzy set and kuratowski s 14 sets theorem of general topology is generalized finally we introduce the fuzzy strongly semicontinuous fuzzy strongly semiopen and fuzzy strongly semiclosed mappings on fuzzy topological spaces and also establish some of their characteristic properties and discuss relations between fuzzy continuous fuzzy semicontinuous and fuzzy strongly semicontinuous mappings

on fuzzy t convergences abstract in this paper we introduce and study the notions of fuzzy convergence and weakly convergence on a fuzzy topological space these notions can be considered as generalizations of the convergence defined in georgiou and papadopoulos 1998 also the forementioned convergence does not coincide with the one defined in chen and chenn 1997 the importance of these convergences relies on the fact that they behave equally well as the convergence defined in georgiou and papadopoulos 1998

regularly open sets and a good extension on fuzzy topological spaces singal and rajvanshi 1992 have introduced the concepts of fuzzy almost separation axioms and they investigated some results on these concepts and the concepts of fuzzy almost continuity and fuzzy almost open mappings in this paper we have succeeded in showing goodness of extension of fuzzy almost separation axioms and we show by producing counterexamples that some results which appeared in the work of singal and rajvanshi are incorrect also we discuss under which conditions some of these results are true and we give an improvement of some results in singal and rajvanshi 1992

θ connectedness and δ connectedness in fuzzy bitopological spaces in this paper we introduce the concepts of connectedness and connectedness with the help of quasi coincidence due to pu and liu 6 for fuzzy sets in fuzzy bitopological setting as a weaker version of connectedness in particular we investigate their properties in almost regular semi regular and regular spaces their invariants and preservations under mappings

optimization of mimo relays for multipoint to multipoint communications nonrobust and robust designs in this paper we propose algorithms to jointly optimize the multiple multiantenna relays which assist multipoint to multipoint communications in wireless networks assuming that the knowledge of the second order statistics of the channels such as covariance matrices are available the multiple input multiple output mimo relays are designed using two different methods 1 minimize the sum of the powers of the relays while fulfilling the signal to interference plus noise ratio sinr requirements for all destinations and 2 maximize the minimum of the sinrs of all destinations satisfying the transmit power constraint of each mimo relay furthermore considering the fact that the covariance matrices of the channels between the mimo relays and destinations are subject to uncertainty due to feedback and quantization errors the robust versions of the aforementioned methods based on worst case concept are proposed it is shown that the proposed nonrobust as well as robust designs are nonconvex optimization problems but they can be solved accurately and efficiently using the standard semidefinite relaxation and randomization techniques computer simulations verify the improved performance of the robust designs over nonrobust methods