branch and price algorithm for fuzzy integer programming problems with block angular structure this paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations this main fuzzy problem is efficiently decomposed and is solved by a branch and price algorithm in the nodes of the branch and price tree the linear relaxation of the problem is solved by applying a column generation method also the relationship between the optimal solutions of this problem under possibility and necessity relations is derived to show the validation of the proposed algorithm some results are proved in addition the application of this algorithm is illustrated on fuzzy multicommodity flow problem for this case a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method some examples are solved and their results are compared with the previous works also the results of the proposed algorithm are reported on some large scale benchmark instances

satisficing solutions and duality in interval and fuzzy linear programming in this paper we introduce a class of fuzzy linear programming problems and define the concepts of feasible and satisficing solutions the necessary tools for dealing with such problems in this way we show that the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems we define the concept of duality and prove the weak and strong duality theorems further we define a class of interval linear programming problems as a special subclass of flp problems and apply the previous results to this special case

geodesical refinement of mimo limited feedback in this paper we investigate a codeword refinement technique called double codeword coding in the context of mimo feedback in the proposed method the second codeword is fed back in addition to the best codeword as their interpolation at the transmitter improves the channel knowledge the derivation of the optimal interpolation parameter is presented together with the derivation of an upper bound to the interpolation parameter based on channel quality feedback available at the transmitter we show that double codeword feedback refinement has slightly lower complexity than alternative techniques and still achieves similar performance furthermore double codeword coding can be generalized to higher transmission ranks using extended multiuser mimo link simulations we verify that the double codeword feedback is able to provide significant gains in 3gpp lte context

multicommodity max flow min cut theorems and their use in designing approximation algorithms in this paper we establish max flow min cut theorems for several important classes of multicommodity flow problems in particular we show that for any n node multicommodity flow problem with uniform demands the max flow for the problem is within an o log n factor of the upper bound implied by the min cut the result which is existentially optimal establishes an important analogue of the famous 1 commodity max flow min cut theorem for problems with multiple commodities the result also has substantial applications to the field of approximation algorithms for example we use the flow result to design the first polynomial time polylog n times optimal approximation algorithms for well known np hard optimization problems such as graph partitioning min cut linear arrangement crossing number vlsi layout and minimum feedback arc set applications of the flow results to path routing problems network reconfiguration communication in distributed networks scientific computing and rapidly mixing markov chains are also described in the paper categories and subject descriptors f 2 2 analysis of algorithms and problem complexity

on mimo beamforming systems using quantized feedback we propose the hadamard matrix as a codebook for multiple input multiple output mimo beamforming systems and show that a quantized equal gain transmission qegt scheme using the hadamard codebook has the same symbol error probability performance as a receiver selection diversity combining scheme operating in independent generalized rayleigh fading channels we show that a mimo beamforming system using quantized feedback over rician fading channels can be analyzed by considering a corresponding receiver selection combining scheme operating in single input multiple output simo systems over correlated generalized rician fading channels also we propose a greedy cophasing scheme for mimo beamforming systems using quantized feedback the greedy cophasing scheme provides 3 2 db power gain over an orthogonal space time block code when the number of transmit antennas is four the number of receive antennas is one and the number of feedback bits is three

adaptive mimo ofdm based on partial channel state information relative to designs assuming no channel knowledge at the transmitter considerably improved communications become possible when adapting the transmitter to the intended propagation channel as perfect knowledge is rarely available transmitter designs based on partial statistical channel state information csi are of paramount importance not only because they are more practical but also because they encompass the perfect and no knowledge paradigms in this paper we first provide a partial csi model for orthogonal frequency division multiplexed ofdm transmissions over multi input multi output mimo frequency selective fading channels we then develop an adaptive mimo ofdm transmitter by applying an adaptive two dimensional 2 d coder beamformer we derived recently on each ofdm subcarrier along with an adaptive power and bit loading scheme across ofdm subcarriers relying on the available partial csi at the transmitter our objective is to maximize the transmission rate while guaranteeing a prescribed error performance under the constraint of fixed transmit power numerical results confirm that the adaptive 2 d space time coder beamformer with two basis beams as the two strongest eigenvectors of the channel s correlation matrix perceived at the transmitter combined with adaptive ofdm power and bit loaded with m ary quadrature amplitude modulated qam constellations improves the transmission rate considerably

on beamforming with finite rate feedback in multiple antenna systems we study a multiple antenna system where the transmitter is equipped with quantized information about instantaneous channel realizations assuming that the transmitter uses the quantized information for beamforming we derive a universal lower bound on the outage probability for any finite set of beamformers the universal lower bound provides a concise characterization of the gain with each additional bit of feedback information regarding the channel using the bound it is shown that finite information systems approach the perfect information case as t 1 2 sup b t 1 where b is the number of feedback bits and t is the number of transmit antennas the geometrical bounding technique used in the proof of the lower bound also leads to a design criterion for good beamformers whose outage performance approaches the lower bound the design criterion minimizes the maximum inner product between any two beamforming vectors in the beamformer codebook and is equivalent to the problem of designing unitary space time codes under certain conditions finally we show that good beamformers are good packings of two dimensional subspaces in a 2t dimensional real grassmannian manifold with chordal distance as the metric

a dual approach to solve the fuzzy linear programming problem abstract a concept of fuzzy objective based on the fuzzification principle is presented in accordance with this concept the fuzzy linear mathematical programming problem is easily solved a relationship of duality among fuzzy constraints and fuzzy objectives is given the dual problem of a fuzzy linear programming problem is also defined

duality in fuzzy linear programming with possibility and necessity relations a class of fuzzy linear programming flp problems with fuzzy coefficients based on fuzzy relations is introduced the concepts of feasible and a b maximal and minimal solutions are defined the class of crisp classical lp problems can be embedded into the class of flp ones moreover for flp problems a new concept of duality is introduced and the weak and strong duality theorems are derived the introduced concepts and results are illustrated and discussed on a simple numerical example

virtual branch analysis of symbol error probability for hybrid selection maximal ratio combining in rayleigh fading we derive analytical expressions for the symbol error probability sep for a hybrid selection maximal ratio combining h s mrc diversity system in multipath fading wireless environments with h s mrc l out of n diversity branches are selected and combined using maximal ratio combining mrc we consider coherent detection of m ary phase shift keying mpsk and quadrature amplitude modulation mqam using h s mrc for the case of independent rayleigh fading with equal signal to noise ratio averaged over the fading the proposed problem is made analytically tractable by transforming the ordered physical diversity branches which are correlated into independent and identically distributed i i d virtual branches which results in a simple derivation of the sep for arbitrary l and n we further obtain a canonical structure for the sep of h s mrc as a weighted sum of the elementary seps which are the seps using mrc with i i d diversity branches in rayleigh fading or equivalently the seps of the nondiversity single branch system in nakagami fading whose closed form expressions are well known we present numerical examples illustrating that h s mrc even with l spl lt n can achieve a performance close to that of n branch mrc

ranking function based solutions of fully fuzzified minimal cost flow problem the aim of minimal cost flow problem mcfp is to find the least transportation cost of a single commodity through a capacitated network this paper presents a model to deal with one particular group of such problems in which the supply and demand of nodes and the capacity and cost of edges are represented as fuzzy numbers for easier reference hereafter we refer to this group of problems as fully fuzzified mcfp to represent our model hukuhara s difference and approximated multiplication are used thereafter we sort fuzzy numbers by an order using a ranking function and show that it is a total order i e a reflexive anti symmetric transitive and complete binary relation utilizing the proposed ranking function we transform the fully fuzzified mcfp into three crisp problems solvable in polynomial time from this standpoint combinatorial algorithms are provided to solve the above mentioned problem and find the fuzzy optimal flow furthermore the proposed order is related to the importance weights of the center the left spread and the right spread of each fuzzy number thus this method is capable of handling the decision maker s risk taking by comparing some previous ranking function based works with our method the efficiency of the latter is revealed finally an application of our proposed method to petroleum industry is presented

optimal transmitter eigen beamforming and space time block coding based on channel mean feedback optimal transmitter designs obeying the water filling principle are well documented they are widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information is impossible to be known perfectly at the transmitter in practical wireless systems we design in this paper an optimal multiantenna transmitter based on the knowledge of mean values of the underlying channels our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the correlation matrix of the estimated channel at the transmitter and with proper power loading across beams the optimality pertains to minimizing an upper bound on the symbol error rate which leads to better performance than maximizing the expected signal to noise ratio snr at the receiver coupled with orthogonal space time block codes two directional eigen beamforming emerges as a more attractive choice than conventional one directional beamforming with uniformly improved performance without rate reduction and without essential increase in complexity with multiple receive antennas and reasonably good feedback quality the two directional eigen beamformer is also capable of achieving the best possible performance in a large range of transmit power to noise ratios without a rate penalty

stability of vector optimization problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints the aim of this paper is to investigate the stability of multiobjective nonlinear programming problems with fuzzy weights in the objective functions and fuzzy matrix parameters in the constraints and represent in addition the related dual problems for which the set of feasible parameters and the solvability set are studied these fuzzy weights and fuzzy matrix parameters are characterized by fuzzy numbers the existing results concerning the basic notions parametric space in convex programs are redefined and analyzed qualitatively under the concept of a pareto optimality an illustrative example is given to clarify the obtained results

bector chandra type duality in fuzzy linear programming with exponential membership functions in this paper we study a pair of fuzzy primal dual linear programming problems and calculate duality results using an aspiration level approach we use an exponential membership function which is in contrast to the earlier works that relied on a linear membership function as the fuzzy environment causes a duality gap we investigate how choosing the exponential membership function impacts this gap this issue is particularly important for fuzzy linear programming where in general the primal and dual objective values may not be bounded

differential feedback in codebook based multiuser mimo systems in slowly varying channels in downlink multiuser multiple input multiple output mimo systems system performance highly depends on the reliability of downlink channel state information csi at the base station bs in frequency division duplexing the most practical solution is to have downlink csi from the users fed back to the bs most work on this feedback design has assumed independent block fading channels however this paper proposes a new differential feedback scheme using the observation that the channel realizations are usually temporally correlated the sum rate loss assuming differential feedback is analyzed for a system with the number of users k equal to the number of transmit antennas m when k m a user selection algorithm based on an approximated signal to interference plus noise ratio sinr estimation is proposed in simulation results the proposed differential feedback scheme increases the sum rate compared to previous differential feedback schemes moreover the proposed user selection algorithm outperforms semi orthogonal user selection in the moderate signal to noise ratio snr region despite requiring less feedback information in low mobility channels utilizing the channels time correlation during quantization is shown to play a bigger role in determining sum rate performance than multiuser diversity for most snr regimes when a practical number of users is considered

a global search method for discrete stochastic optimization this paper is concerned with the problem of optimizing the performance of a stochastic system over a finite set of alternatives in situations where the performance of the system cannot be evaluated analytically but must be estimated or measured for instance through simulation we present two variants of a new method for solving such discrete stochastic optimization problems this new method uses global search to look for the optimal solution it generates a sequence taking values in the set of feasible alternatives where each new element of the sequence is generated by comparing the current element with another candidate alternative and letting the next element of the sequence be the one of the current and candidate alternatives that appears to yield better performance for both versions of the proposed method the element of the set of feasible alternatives that the generated sequence visits most often is shown to converge almost surely to a globally optimal solution of the underlying optimization pr

limited feedback for temporally correlated mimo channels with other cell interference limited feedback improves link reliability with a small amount of feedback from the receiver to the transmitter in cellular systems the performance of limited feedback will be degraded in the presence of other cell interference when the base stations have limited or no coordination this paper establishes the degradation in sum rate of users in a cellular system due to uncoordinated other cell interference and feedback delay a goodput metric is defined as the rate when the bits are successfully received at the mobile station and used to derive an upper bound on the performance of limited feedback systems with delay this paper shows that the goodput gained from having delayed limited feedback decreases doubly exponentially as the delay increases the analysis is extended to precoded spatial multiplexing systems where it is shown that the same upper bound can be used to evaluate the decay in the achievable sum rate to reduce the effects of interference zero forcing interference nulling is applied at the receiver where it is shown that the effect of the interference on the achievable sum rate can be suppressed by nulling out the interferer numerical results show that the decay rate of the goodput decreases when the codebook quantization size increases and when the doppler shift in the channel decreases

some remarks on vanishing theorems for holomorphic vector bundles this theorem generalizes kodaira s vanishing theorem 13 and has found a number of geometric applications 2 19 griffiths proof uses method ii above doing curvature calculations for line bundles then the object of this note is to reduce theorem g directly to the kodaira vanishing theorem answering a question of viehweg during the complex analysis meeting in oberwolfach 1982 thus avoiding any curvature calculation this proof has the further advantage that one obtains better results let us state as a sample

optimal solutions in optimization problem with objective function depending on fuzzy parameters in this paper we first introduce a broad class of fuzzy optimization problems with an objective function depending on fuzzy parameters fo problems and introduce the concept a maximal solutions of fo problems with respect to some fuzzy relation we derive a simple and natural sufficient condition for a feasible solution to be an a maximal solutions of fo problem later on we define possibly and necessarily a maximal solutions of fo problems and prove that any possibly or necessarily a maximal solution of fo problem is an a maximal solution with respect to the possibilistic fuzzy relation or necessity fuzzy relation respectively the introduced concepts and results are illustrated and discussed on two numerical examples

on starshaped fuzzy sets in this paper we firstly define some new types of fuzzy starshapedness discuss the relationships among the different types of fuzzy starshapedness and then present some basic properties of them finally we develop several important results on the shadows of starshaped fuzzy sets

vanishing theorems for ample vector bundles the main result of this article is a general vanishing theorem for the cohomology of tensorial representations of an ample vector bundle on a smooth complex projective variety in particular we extend classical theorems of griffiths and le potier to the whole dolbeault cohomology prove a variant of an uncorrect conjecture of sommese and answer a question of demailly as an application we prove conjectures of debarre and kim for branched coverings of grassmannians and extend a well known barth lefschetz type theorem for branched covers of projective spaces due to lazarsfeld we also obtain new restriction theorems for certain degeneracy loci

mimo systems with limited rate differential feedback in slowly varying channels in this paper an adaptive limited feedback linear precoding technique for temporally correlated multiple input multiple output mimo channels is proposed where the receiver has perfect channel knowledge but the transmitter only receives a quantized channel direction to perform adaptation to the time correlation structure we employ a differential feedback where the amount of the perturbation added to the previous precoder is determined by the statistics of the directional variation based on random matrix quantization analysis we develop a spherical cap codebook approach where the cap is centered at the previous precoder and the radius of the cap is determined proportional to the identified directional variation if the channel is highly correlated in time it is shown that the proposed differential feedback scheme achieves significant throughput improvement in the large codebook size regime the rest of the paper is devoted to developing a systematic spherical cap codebook generation method the developed approach employs a feedback scheme that uses a differential rotation of the previously used precoder our codebook adaptation is based on generating a perturbation in euclidean space and projecting the perturbation onto the unitary space simulation results show that the proposed adaptation scheme accurately tracks the channel using only a small rate of feedback

channel adaptive quantization for limited feedback mimo beamforming systems multiple input multiple output mimo wireless systems can achieve significant diversity and array gain by using transmit beamforming and receive combining techniques in the absence of full channel knowledge at the transmitter the transmit beamforming vector can be quantized at the receiver and sent to the transmitter using a low rate feedback channel in the literature quantization algorithms for the beamforming vector are designed and optimized for a particular channel distribution commonly the uncorrelated rayleigh distribution when the channel is not uncorrelated rayleigh however these quantization strategies result in a degradation of the receive signal to noise ratio snr in this paper switched codebook quantization is proposed where the codebook is dynamically chosen based on the channel distribution the codebook adaptation enables the quantization to exploit the spatial and temporal correlation inherent in the channel the convergence properties of the codebook selection algorithm are studied assuming a block stationary model for the channel in the case of a nonstationary channel it is shown using simulations that the selected codebook tracks the distribution of the channel resulting in improvements in snr simulation results show that in the case of correlated channels the snr performance of the link can be significantly improved by adaptation compared with nonadaptive quantization strategies designed for uncorrelated rayleigh fading channels

application of fuzzy minimum cost flow problems to network design under uncertainty this paper deals with fuzzy quantities and relations in multi objective minimum cost flow problem when t norms and t conorms are available the goal programming is applied to minimize the deviation among the multiple costs of fuzzy flows and the given targets when the fuzzy supplies and demands are satisfied to obtain the most optimistic and the most pessimistic satisficing solutions of this problem two polynomial time algorithms are introduced applying some network transformations to demonstrate the performance of this approach in actual substances network design under fuzziness is considered and an efficient scheme is proposed including genetic algorithm together with fuzzy minimum cost flow problem this scheme is applied on a pilot network for more description

vanishing theorems for tensor powers of an ample vector bundles lete be a holomorphic vector bundle of rankr on a compact complex manifoldx of dimensionn it is shown that the cohomology groupshp q x e k dete l vanish ife is ample andp q n 1 l n p r 1 the proof rests on the well known fact that every tensor powere k splits into irreducible representations of gl e by bott s theory each component is canonically isomorphic to the direct image onx of a homogeneous line bundle over a flag manifold ofe the proof is then reduced to the kodaira akizuki nakano vanishing theorem for line bundles by means of the leray spectral sequence using backward induction onp we also obtain a generalization of le potier s isomorphism theorem and a counterexample to a vanishing conjecture of sommese

cohomology of twisted holomorphic forms on grassmann manifolds and quadric hypersurfaces on etudie la cohomologie de q k q l k pour des espaces symetriques hermitiens de types a iii b i et d i

grassmannian beamforming for multiple input multiple output wireless systems transmit beamforming and receive combining are simple methods for exploiting the significant diversity that is available in multiple input multiple output mimo wireless systems unfortunately optimal performance requires either complete channel knowledge or knowledge of the optimal beamforming vector both are hard to realize in this article a quantized maximum signal to noise ratio snr beamforming technique is proposed where the receiver only sends the label of the best beamforming vector in a predetermined codebook to the transmitter by using the distribution of the optimal beamforming vector in independent and identically distributed rayleigh fading matrix channels the codebook design problem is solved and related to the problem of grassmannian line packing the proposed design criterion is flexible enough to allow for side constraints on the codebook vectors bounds on the codebook size are derived to guarantee full diversity order results on the density of grassmannian line packings are derived and used to develop bounds on the codebook size given a capacity or snr loss monte carlo simulations are presented that compare the probability of error for different quantization strategies

the solution and duality of imprecise network problems duality properties have been investigated by many researchers in the recent literature they are introduced in this paper for a fully fuzzified version of the minimal cost flow problem which is a basic model in network flow theory this model illustrates the least cost of the shipment of a commodity through a capacitated network in terms of the imprecisely known available supplies at certain nodes which should be transmitted to fulfil uncertain demands at other nodes first we review on the most valuable results on fuzzy duality concepts to facilitate the discussion of this paper by applying hukuhara s difference approximated and exact multiplication and wu s scalar production we exhibit the flow in network models then we use combinatorial algorithms on a reduced problem which is derived from fully fuzzified mcfp to acquire fuzzy optimal flows to give duality theorems we utilize a total order on fuzzy numbers due to the level of risk and realize optimality conditions for providing some efficient combinatorial algorithms finally we compare our results with the previous worthwhile works to demonstrate the efficiency and power of our scheme and the reasonability of our solutions in actual decision making problems

a simple gradient sign algorithm for transmit antenna weight adaptation with feedback in this paper a simple algorithm for adaptation of the complex baseband weights of a transmit antenna array using feedback from the receiver is proposed and analyzed the system utilizes stochastic gradient adaptation to maximize the power delivered to the receiver for a constrained transmission power which provides both fading diversity and beam steering gain dual perturbed transmission weight vectors are time multiplexed onto the pilot signal and the receiver generates feedback selecting the perturbed weight vector which delivers greater power this feedback is used to provide weight adaptation at the transmitter and this adaptation is shown to be an update by a coarse estimate of the gradient of the delivered power the performance of the algorithm is analyzed in terms of convergence and tracking of an ar1 fading channel with simulations confirming the analysis bit error rate ber simulations in a dynamic fading channel show that the algorithm outperforms previously proposed vector selection feedback and in slower fading the algorithm substantially outperforms diversity space time coding

performance analysis of quantized beamforming mimo systems multiple input multiple output mimo wireless systems can achieve significant diversity and array gain by using single stream transmit beamforming and receive combining a mimo beamforming system with feedback using a codebook based quantization of the beamforming vector allows practical implementation of such a strategy in a single user scenario the performance of this system in uncorrelated rayleigh flat fading channels is studied from the point of view of signal to noise ratio snr and outage probability in this paper lower bounds are derived on the expected snr loss and the outage probability of systems that have a single receive antenna or two transmit antennas for arbitrary transmit and receive antennas approximations for the snr loss and outage are derived in particular the snr loss in a quantized mimo beamforming system is characterized as a function of the number of quantization bits and the number of transmit and receive antennas the analytical expressions are proved to be tight with asymptotically large feedback rate simulations show that the bounds and approximations are tight even at low feedback rates thereby providing a benchmark for feedback system design

soft robust solutions to possibilistic optimization problems abstract this paper discusses a class of uncertain optimization problems in which unknown parameters are modeled by fuzzy intervals the membership functions of the fuzzy intervals are interpreted as possibility distributions for the values of the uncertain parameters it is shown how the known concepts of robustness and light robustness for the traditional interval uncertainty representation of the parameters can be generalized to choose solutions that optimize against plausible parameter realizations under the assumed model of uncertainty in the possibilistic setting furthermore these solutions can be computed efficiently for a wide class of problems in particular for linear programming problems with fuzzy parameters in constraints and objective function thus the problems under consideration are not much computationally harder than their deterministic counterparts in this paper a theoretical framework is presented and results of some computational tests are shown

optimal transmitter eigen beamforming and space time block coding based on channel correlations optimal transmitter designs obeying the water filling principle are well documented and widely applied when the propagation channel is deterministically known and regularly updated at the transmitter because channel state information csi may be costly or impossible to acquire in rapidly varying wireless environments we develop in this paper statistical water filling approaches for stationary random fading channels these approaches require only knowledge of the channel correlations that do not necessitate frequent updates and can be easily acquired applied to a multiple transmit antenna paradigm our optimal transmitter design turns out to be an eigen beamformer with multiple beams pointing to orthogonal directions along the eigenvectors of the channel s correlation matrix and with proper power loading across the beams the optimality pertains to minimizing a tight bound on the symbol error rate the resulting loaded eigen beamforming outperforms not only the equal power allocation across all antennas but also the conventional beamformer that transmits the available power along the strongest direction coupled with orthogonal space time block codes two dimensional 2 d eigen beamforming emerges as a more attractive choice than conventional one dimensional 1 d beamforming with uniformly better performance without rate reduction and without complexity increase

ranking fuzzy numbers in the setting of possibility theory the arithmetic manipulation of fuzzy numbers or fuzzy intervals is now well understood equally important for application purposes is the problem of ranking fuzzy numbers or fuzzy intervals which is addressed in this paper a complete set of comparison indices is proposed in the framework of zadeh s possibility theory it is shown that generally four indices enable one to completely describe the respective locations of two fuzzy numbers moreover this approach is related to previous ones and its possible extension to the ranking of n fuzzy numbers is discussed at length finally it is shown that all the information necessary and sufficient to characterize the respective locations of two fuzzy numbers can be recovered from the knowledge of their mutual compatibilities

possible and necessary optimality tests in possibilistic linear programming problems in this paper two kinds of optimality concepts are introduced into fuzzy linear programming problems in order to discuss the rationality of an obtained solution one is possible optimality evaluating the possibility degree to which the solution is optimal the other the dual concept is necessary optimality evaluating the necessity degree to which the solution is optimal when possibility distributions are defined by closed intervals degrees of possible and necessary optimalities become binary necessary and sufficient conditions for possible and necessary optimalities are induced in this case extending the results methods of calculating the degrees of possible and necessary optimalities are proposed some numerical examples are given to demonstrate the proposed methods

fuzzy capital rationing model in this paper we study the fuzzification of weingartner s pure capital rationing model and its analysis we develop a primal dual pair based on t norm t conorm relation for the constraints and objective function for a fully fuzzified pure capital rationing problem except project selection variables we define the a interval under which the weak duality is proved we perform sensitivity analysis for a change in a budget level or in a cash flow level of a non basic as well as a basic variable we analyze the problem based on duality and complementary slackness results we illustrate the proposed model by computational analysis and interpret the results

solutions for fuzzy matrix games in this paper we deal with two person zero sum games with fuzzy payoffs and fuzzy goals we have presented two models for studying two person zero sum matrix games with fuzzy payoffs and fuzzy goals we assume that each player has a fuzzy goal for each of the payoffs we obtained that the fuzzy relation approach and the max min solution are equivalent

on the minimum differential feedback for time correlated mimo rayleigh block fading channels in this paper we investigate the differential channel state information csi feedback problem for a general multiple input multiple output mimo system over time correlated rayleigh block fading channels specifically we derive the closed form minimum differential feedback rate in the presence of channel estimation errors and quantization distortion with the feedback channel capacity constraint we further study the ergodic capacity in a periodic feedback system in terms of the minimum differential feedback rate and the feedback interval through theoretical analysis we find that there exists an optimal differential feedback interval to achieve the maximum ergodic capacity analytical results are verified by simulations in a practical periodic differential feedback system employing water filling precoder and lloyd s quantization algorithm

some properties of extended fuzzy preference relations using modalities abstract a fuzzy preference relation is extended to six kinds of relations between fuzzy sets the properties of the six extended relations are investigated especially a sufficient condition for reducing the extended relations to four kinds is discussed when fuzzy sets are bounded and normal and some examples are given to illustrate it further a sufficient condition for the extended negative relations to coincide with the extended inverse relations is described