Showing papers by "Xidian University published in 2008"
TL;DR: The statistical analysis based on three performance metrics show that the unique selection method is effective, and NNIA is an effective algorithm for solving multiobjective optimization problems.
Abstract: Nondominated Neighbor Immune Algorithm (NNIA) is proposed for multiobjective optimization by using a novel nondominated neighbor-based selection technique, an immune inspired operator, two heuristic search operators, and elitism. The unique selection technique of NNIA only selects minority isolated nondominated individuals in the population. The selected individuals are then cloned proportionally to their crowding-distance values before heuristic search. By using the nondominated neighbor-based selection and proportional cloning, NNIA pays more attention to the less-crowded regions of the current trade-off front. We compare NNIA with NSGA-II, SPEA2, PESA-II, and MISA in solving five DTLZ problems, five ZDT problems, and three low-dimensional problems. The statistical analysis based on three performance metrics including the coverage of two sets, the convergence metric, and the spacing, show that the unique selection method is effective, and NNIA is an effective algorithm for solving multiobjective optimization problems. The empirical study on NNIA's scalability with respect to the number of objectives shows that the new algorithm scales well along the number of objectives.
428 citations
TL;DR: It is shown that ESPRIT exploits the invariance property of both the transmit array and the receive array in a bistatic MIMO radar to estimate the target's direction.
Abstract: It is shown that ESPRIT exploits the invariance property of both the transmit array and the receive array in a bistatic MIMO radar to estimate the target's direction. Some numerical results are presented to verify the effectiveness of this method.
384 citations
TL;DR: The experiments show that the proposed measure is consistent with human visual evaluations and can be applied to evaluate image fusion schemes that are not performed at the same level.
369 citations
TL;DR: A new fusion algorithm for multimodal medical images based on contourlet transform is proposed, which can provide a more satisfactory fusion outcome compared with conventional image fusion algorithms.
353 citations
01 Mar 2008
TL;DR: This paper intends to review and compare a variety of Petri net-based deadlock prevention policies reported in the literature in terms of structural complexity, behavior permissiveness, and computational complexity to facilitate engineers in choosing a suited method for their industrial application cases.
Abstract: Over the last two decades, a great deal of research has been focused on solving deadlock problems in resource allocation systems such as computer communication systems, workflow systems, and flexible manufacturing systems, resulting in a wide variety of approaches. As a well-defined problem in resource allocation systems, deadlock prevention based on a Petri net formalism has received an enormous amount of attention in the literature. This paper intends to review and compare a variety of Petri net-based deadlock prevention policies reported in the literature. Their comparison is done in terms of structural complexity, behavior permissiveness, and computational complexity. This paper should facilitate engineers in choosing a suited method for their industrial application cases.
272 citations
01 Feb 2008
TL;DR: An adaptive backstepping neural-network control approach is extended to a class of large-scale nonlinear output-feedback systems with completely unknown and mismatched interconnections to remove the common assumptions on interconnection such as matching condition, bounded by upper bounding functions.
Abstract: An adaptive backstepping neural-network control approach is extended to a class of large-scale nonlinear output-feedback systems with completely unknown and mismatched interconnections. The novel contribution is to remove the common assumptions on interconnections such as matching condition, bounded by upper bounding functions. Differentiation of the interconnected signals in backstepping design is avoided by replacing the interconnected signals in neural inputs with the reference signals. Furthermore, two kinds of unknown modeling errors are handled by the adaptive technique. All the closed-loop signals are guaranteed to be semiglobally uniformly ultimately bounded, and the tracking errors are proved to converge to a small residual set around the origin. The simulation results illustrate the effectiveness of the control approach proposed in this correspondence.
267 citations
TL;DR: In this article, a cable-suspended parallel robot (CPR) is developed from parallel and serial cable-driven robot, in which cables are utilized to replace links to manipulate objects.
253 citations
TL;DR: In this paper, a scheme for multi-target identification and localization using bistatic MIMO radar systems is proposed, which can be distinguished by Capon method, as well as the targets angles with respect to transmitter and receiver using the received signals.
Abstract: A scheme for multitarget identification and localization using bistatic MIMO radar systems is proposed. Multitarget can be distinguished by Capon method, as well as the targets angles with respect to transmitter and receiver can be synthesized using the received signals. Thus, the locations of the multiple targets are obtained and spatial synchronization problem in traditional bistatic radars is avoided. The maximum number of targets that can be uniquely identified by proposed method is also analyzed. It is indicated that the product of the numbers of receive and transmit elements minus-one targets can be identified by exploiting the fluctuating of the radar cross section (RCS) of the targets. Cramer-Rao bounds (CRB) are derived to obtain more insights of this scheme. Simulation results demonstrate the performances of the proposed method using Swerling II target model in various scenarios.
248 citations
TL;DR: This paper addresses the deadlock problems in flexible manufacturing systems (FMS) by using a Petri net siphon control method and the theory of regions and shows its computational advantages.
Abstract: This paper addresses the deadlock problems in flexible manufacturing systems (FMS) by using a Petri net siphon control method and the theory of regions. The proposed policy consists of two stages. The first one, called siphons control, is to add, for every siphon that we identify, a monitor to the original net model such that it is optimally invariant controlled. In the second stage, the theory of regions is utilized to derive the net supervisors such that deadlocks can be prevented. The first-stage work significantly lowers the computational cost compared with the approach where the theory of regions is used alone. An FMS example is presented to illustrate the technique. By varying the markings of given net structures, this paper shows its computational advantages.
234 citations
TL;DR: A new algorithm named SC ensemble (SCE) is proposed for the segmentation of synthetic aperture radar (SAR) images and overcomes the shortcomings faced by the SC, such as the selection of scaling parameter, and the instability resulted from the Nystrom approximation method in image segmentation.
Abstract: Spectral clustering (SC) has been used with success in the field of computer vision for data clustering. In this paper, a new algorithm named SC ensemble (SCE) is proposed for the segmentation of synthetic aperture radar (SAR) images. The gray-level cooccurrence matrix-based statistic features and the energy features from the undecimated wavelet decomposition extracted for each pixel being the input, our algorithm performs segmentation by combining multiple SC results as opposed to using outcomes of a single clustering process in the existing literature. The random subspace, random scaling parameter, and Nystrom approximation for component SC are applied to construct the SCE. This technique provides necessary diversity as well as high quality of component learners for an efficient ensemble. It also overcomes the shortcomings faced by the SC, such as the selection of scaling parameter, and the instability resulted from the Nystrom approximation method in image segmentation. Experimental results show that the proposed method is effective for SAR image segmentation and insensitive to the scaling parameter.
230 citations
01 Jan 2008
TL;DR: A deadlock control policy is proposed and proved to be computationally efficient and less conservative than the existing policies in the literature and an industrial case study is used to show the results.
Abstract: In many flexible assembly systems, base components are transported with pallets; parts to be mounted onto the base ones are transported by trays with no pallets. When an assembly operation is performed by using some parts in a tray but not all, the tray with the remaining parts still occupies a buffer space. In this way, an assembly/disassembly material flow is formed. In such a material flow, deadlock can occur both in the base component and part flow. Furthermore, the assembly operations can also result in a deadlock. Thus, it is a great challenge to tackle deadlocks in such processes. This paper models them using resource-oriented Petri nets. Based on the models, a deadlock control policy is proposed and proved to be computationally efficient and less conservative than the existing policies in the literature. An industrial case study is used to show the results.
01 Jan 2008
TL;DR: The importance of siphons is well recognized in the analysis and control of deadlocks in a Petri net, and the proposed elementary siphon concept to the existing deadlock control policies is discussed.
Abstract: The importance of siphons is well recognized in the analysis and control of deadlocks in a Petri net. To minimize the number of siphons that have to be explicitly controlled, siphons in a net are divided in a net into elementary and dependent ones. The concepts of token-rich, token-poor, and equivalent siphons are newly presented. More general conditions under which a dependent siphon can be always marked are established. The existence of dependent siphons in a Petri net is investigated. An algorithm is developed to find the set of elementary siphons in a net system for deadlock control purposes. The application of the proposed elementary siphon concept to the existing deadlock control policies is discussed. A few different-sized manufacturing examples are used to demonstrate the advantages of elementary siphon-based policies. The significant value of the proposed theory via a particular deadlock control policy is shown. Finally, some interesting and open problems are discussed.
01 Mar 2008
TL;DR: A monitor-based deadlock prevention policy is developed that first adds monitors for elementary siphons only to a G-system plant model such that the resultant net system satisfies the maximal controlled-siphon property (maximal cs-property).
Abstract: A fair amount of research has shown the importance of siphons in the analysis and control of deadlocks in a variety of resource allocation systems by using a Petri net formalism. In this paper, siphons in a generalized Petri net are classified into elementary and dependent ones, as done for ordinary nets in our previous work. Conditions are derived under which a dependent siphon is controlled by properly supervising its elementary siphons, which indicates that the controllability of dependent siphons in an ordinary Petri net is a special case of that in a generalized one. The application of the controllability of dependent siphons is shown by considering the deadlock prevention problem for a class of resource allocation systems, namely, G-system that allows multiple resource acquisitions and flexible routings in a flexible manufacturing system with machining, assembly, and disassembly operations. We develop a monitor-based deadlock prevention policy that first adds monitors for elementary siphons only to a G-system plant model such that the resultant net system satisfies the maximal controlled-siphon property (maximal cs-property). Then, by linear programming, initial tokens in the additional monitors are decided such that liveness is enforced to the supervised system. Also, a simplified live marking relationship for a G-system between the initial tokens of the source places and those of the resource places is derived. Finally, the proposed deadlock prevention methods are illustrated by using an example.
15 May 2008
TL;DR: Results of simulation show that, the proposed spectrum aware on-demand routing which doesn't base on control channel can well fit MSCRN and improve the network throughput comparing to the same network scenario without cognitive ability.
Abstract: In multi-hop single transceiver Cognitive Radio networks (MSCRN), routing becomes of great challenge when IEEE 802.11 DCF is used as the MAC protocol. Routing should not base on common control channel because it is not ensured that common control channel can be obtained by each node. In this paper, we propose a spectrum aware on-demand routing which doesn't base on control channel. A channel assignment algorithm aimed at improving link utilization is derived from delay-analysis. The overhead and gain by switching are balanced in this algorithm. For deafness problem caused by switching can result in significant performance degradation, constraints to avoid the appearance of deafness in channel assignment process are given. We stress that our approach can be easily implemented for the using of standard IEEE 802.11DCF. Results of simulation show that, our approach can well fit MSCRN and improve the network throughput comparing to the same network scenario without cognitive ability.
TL;DR: In this paper, a singular value decomposition (SVD) is used to decompose the face image into two complementary parts: a smooth general appearance image and a difference image.
TL;DR: An imaging algorithm based on the complex-valued empirical-mode decomposition is proposed for micromotion targets with rotating parts where the inverse synthetic-aperture-radar image of the main body may be shadowed by the micro-Doppler.
Abstract: For micromotion targets with rotating parts, the inverse synthetic-aperture-radar image of the main body may be shadowed by the micro-Doppler. To solve this problem, this paper proposes an imaging algorithm based on the complex-valued empirical-mode decomposition. First, the radar echoes are decomposed into a series of complex-valued intrinsic-mode functions (IMFs). Then, the IMFs from the rotating parts and those from the main body are separated according to the characteristics of their zero-crossings. Finally, the well-focused imaging of the main body via traditional imaging algorithm and the accurate parameter estimation of the rotating part can be obtained. Both the imaging results for the simulated and measured data are given to verify the validity of the proposed algorithm.
TL;DR: An automatic sketch synthesis algorithm is proposed based on embedded hidden Markov model (E-HMM) and selective ensemble strategy and achieves satisfactory effect of sketch synthesis with a small set of face training samples.
Abstract: Sketch synthesis plays an important role in face sketch-photo recognition system. In this manuscript, an automatic sketch synthesis algorithm is proposed based on embedded hidden Markov model (E-HMM) and selective ensemble strategy. First, the E-HMM is adopted to model the nonlinear relationship between a sketch and its corresponding photo. Then based on several learned models, a series of pseudo-sketches are generated for a given photo. Finally, these pseudo-sketches are fused together with selective ensemble strategy to synthesize a finer face pseudo-sketch. Experimental results illustrate that the proposed algorithm achieves satisfactory effect of sketch synthesis with a small set of face training samples.
TL;DR: The results have demonstrated that there is a brain network associated with the amygdala during a resting condition that encompasses the brain structures that are implicated in both pain sensation and pain modulation, and indicate that acupuncture may change this amygdala-specific brain network into a functional state that underlies pain perception andPain modulation.
Abstract: Recently, increasing evidence has indicated that the primary acupuncture effects are mediated by the central nervous system. However, specific brain networks underpinning these effects remain unclear. In the present study using fMRI, we employed a within-condition interregional covariance analysis method to investigate functional connectivity of brain networks involved in acupuncture. The fMRI experiment was performed before, during and after acupuncture manipulations on healthy volunteers at an acupuncture point, which was previously implicated in a neural pathway for pain modulation. We first identified significant fMRI signal changes during acupuncture stimulation in the left amygdala, which was subsequently selected as a functional reference for connectivity analyses. Our results have demonstrated that there is a brain network associated with the amygdala during a resting condition. This network encompasses the brain structures that are implicated in both pain sensation and pain modulation. We also found that such a pain-related network could be modulated by both verum acupuncture and sham acupuncture. Furthermore, compared with a sham acupuncture, the verum acupuncture induced a higher level of correlations among the amygdala-associated network. Our findings indicate that acupuncture may change this amygdala-specific brain network into a functional state that underlies pain perception and pain modulation.
TL;DR: An iterated algorithm for model selection is proposed in this paper, which can automatically give the optimal aspect-frames boundaries and determine the optimal number of factors in each aspect-frame and the proposed adaptive partition approach can further improve the recognition performance with higher recognition efficiency.
Abstract: Statistical modeling for radar high-resolution range profile (HRRP) is a challenging task in radar HRRP statistical recognition. Theoretical analysis and experimental results show that elements in an HRRP sample are statistically correlated and non-Gaussian distributed. First, this paper introduces three joint-Gaussian models, i.e., subspace approximation model, probability principal components analysis (PPCA) model and factor analysis (FA) model, into radar HRRP statistical recognition. Due to the experimental results, we can have the conclusion that the jointly non-Gaussian distributed HRRP samples approximately follow the joint-Gaussian distribution described by FA model. Therefore, we can apply FA model to radar HRRP statistical recognition rather than a joint-Gaussian mixture model, e.g., PPCA mixture model or FA mixture model, which is a more accurate choice for modeling non-Gaussian distributed correlations in multidimensional data but with high learning complexity and large computation burden, and the difficulty in the statistical modeling for HRRP samples is largely reduced. Second, this paper concerns model selection of FA model in radar HRRP statistical recognition, in which there are two issues, i.e., the partition of target-aspect frames and the determination of the number of factors in each frame. Based on the Akaike information criterion (AIC) and the Bayes' information criterion (BIC), an iterated algorithm for model selection is proposed in this paper, which can automatically give the optimal aspect-frame boundaries and determine the optimal number of factors in each aspect-frame. The recognition experiments based on measured data show that the proposed adaptive partition approach can further improve the recognition performance with higher recognition efficiency.
TL;DR: This paper investigates the satisfiability of Propositional Projection Temporal Logic with infinite models, and Normal Form and Labeled Normal Form Graph for PPTL formulas are defined and finiteness of LNFGs is proved.
Abstract: This paper investigates the satisfiability of Propositional Projection Temporal Logic (PPTL) with infinite models. A decision procedure for PPTL formulas is given. To this end, Normal Form (NF) and Labeled Normal Form Graph (LNFG) for PPTL formulas are defined, and algorithms for transforming a formula to its normal form and constructing the LNFG for the given formula are presented. Further, the finiteness of LNFGs is proved in details. Moreover, the decision procedure is extended to check the satisfiability of the formulas of Propositional Interval Temporal Logic. In addition, examples are also given to illustrate how the decision procedure works.
TL;DR: In this article, a stack gate HfO2/Al2O3 structure grown by atomic layer deposition was used for high-electron mobility transistors with 1- mum gate lengths.
Abstract: We have developed a novel AlGaN/GaN metal-oxide-semiconductor high-electron mobility transistor using a stack gate HfO2/Al2O3 structure grown by atomic layer deposition. The stack gate consists of a thin HfO2 (30-A) gate dielectric and a thin Al2O3 (20- A) interfacial passivation layer (IPL). For the 50-A stack gate, no measurable C-V hysteresis and a smaller threshold voltage shift were observed, indicating that a high-quality interface can be achieved using a Al2O3 IPL on an AlGaN substrate. Good surface passivation effects of the Al2O3 IPL have also been confirmed by pulsed gate measurements. Devices with 1- mum gate lengths exhibit a cutoff frequency (fT) of 12 GHz and a maximum frequency of oscillation (f MAX) of 34 GHz, as well as a maximum drain current of 800 mA/mm and a peak transconductance of 150 mS/mm, whereas the gate leakage current is at least six orders of magnitude lower than that of the reference high-electron mobility transistors at a positive gate bias.
01 Oct 2008
TL;DR: Theoretical analysis proves that QICA converges to the global optimum and the proposed quantum recombination realizes the information communication between subpopulation groups to improve the search efficiency.
Abstract: Based on the concepts and principles of quantum computing, a novel immune clonal algorithm, called a quantum-inspired immune clonal algorithm (QICA), is proposed to deal with the problem of global optimization. In QICA, the antibody is proliferated and divided into a set of subpopulation groups. The antibodies in a subpopulation group are represented by multistate gene quantum bits. In the antibody's updating, the general quantum rotation gate strategy and the dynamic adjusting angle mechanism are applied to accelerate convergence. The quantum NOT gate is used to realize quantum mutation to avoid premature convergences. The proposed quantum recombination realizes the information communication between subpopulation groups to improve the search efficiency. Theoretical analysis proves that QICA converges to the global optimum. In the first part of the experiments, 10 unconstrained and 13 constrained benchmark functions are used to test the performance of QICA. The results show that QICA performs much better than the other improved genetic algorithms in terms of the quality of solution and computational cost. In the second part of the experiments, QICA is applied to a practical problem (i.e., multiuser detection in direct-sequence code-division multiple-access systems) with a satisfying result.
TL;DR: In this paper, a generalized gradient of the output with respect to the input of the hysteresis and the derivative of the input that represents the frequency change of input are introduced into the input space.
Abstract: A method for the identification of the rate-dependent hysteresis in piezoceramic actuators is proposed. In this approach, both a so-called generalized gradient of the output with respect to the input of the hysteresis and the derivative of the input that represents the frequency change of the input are introduced into the input space. Then an expanded input space is established. Thus, the multi-valued mapping of the rate-dependent hysteresis can be transformed into a one-to-one mapping based on the expanded of the input space. In this case, the neural network method can be applied to the modeling of the rate-dependent hysteresis. Finally, the experimental results are presented to illustrate the performance of the proposed approach.
TL;DR: In this article, a compact printed ultra-wideband (UWB) monopole antenna with dual band-notched characteristics is presented, where one complementary split-ring resonator (CSRR) is etched inside the patch of the antenna to achieve dual notch frequency bands.
Abstract: A compact printed ultra-wideband (UWB) monopole antenna with dual band-notched characteristics is presented. One complementary split-ring resonator (CSRR) is etched inside the patch of the monopole antenna to achieve dual notch frequency bands. A practical example for a UWB antenna (working from 2.90 to 12 GHz) is demonstrated, with one notch frequency band at 3.40-3.48 GHz and the other at 5.40-5.98 GHz. In addition, the effect of the dimensions of the CSRR on the dual notch frequency bands is also analysed.
01 May 2008
TL;DR: A polynomial-time algorithm for finding the set of elementary siphons is proposed, which avoids complete siphon enumeration and it is shown that a dependent siphon can always be controlled by properly supervising its Elementary siphons.
Abstract: As a structural object, siphons are well recognized in the analysis and control of deadlocks in resource allocation systems modeled with Petri nets. Many deadlock prevention policies characterize the deadlock behavior of the systems in terms of siphons and utilize this characterization to avoid deadlocks. This paper develops a novel methodology to find interesting siphons for deadlock control purposes in a class of Petri nets, i.e., a system of simple sequential processes with resources . Resource circuits in an are first detected, from which, in general, a small portion of emptiable minimal siphons can be derived. The remaining emptiable ones can be found by their composition. A polynomial-time algorithm for finding the set of elementary siphons is proposed, which avoids complete siphon enumeration. It is shown that a dependent siphon can always be controlled by properly supervising its elementary siphons. A computationally efficient deadlock control policy is accordingly developed. Experimental study shows the efficiency of the proposed siphon computation approach.
TL;DR: In this article, the design and analysis of an ultra-wideband (UWB) aperture antenna with dual band-notched characteristics are presented, which consists of a circular exciting stub on the front side and a U-shaped aperture on the back ground plane.
Abstract: The design and analysis of an ultra-wideband (UWB) aperture antenna with dual band-notched characteristics are presented. The antenna consists of a circular exciting stub on the front side and a U-shaped aperture on the back ground plane. By inserting a slot and a parasitic strip to the antenna, dual notched frequency bands are achieved. A conceptual circuit model, which is based on the measured impedance of the proposed antenna, is also shown to investigate the dual band-notched characteristics. The measured impedance bandwidth defined by VSWR<2 of 9.0 GHz (2.2-11.2 GHz), with the dual bands of 3.25-4.25 and 5.0-6.05 GHz notched, is obtained.
TL;DR: It is proved that the super connectivity of Xn is 2n−2 for n≥3 and the conditional diagnosability is 4n−7 for n ≥5 and the hypercubes, twisted cubes, crossed cubes, and Möbius cubes all belong to the class of BC networks.
Abstract: An n-dimensional bijective connection network (in brief, BC network), denoted by X n , is an n-regular graph with 2 n nodes and n2 n?1 edges Hypercubes, crossed cubes, twisted cubes, and Mobius cubes all belong to the class of BC networks (Fan and He in Chin J Comput 26(1):84---90, [2003]) We prove that the super connectivity of X n is 2n?2 for n?3 and the conditional diagnosability of X n is 4n?7 for n?5 As a corollary of this result, we obtain the super connectivity and conditional diagnosability of the hypercubes, twisted cubes, crossed cubes, and Mobius cubes
TL;DR: A new robust adaptive synchronization approach for the global synchronization of complex dynamical networks is proposed based on the LaSalle–Yoshizawa theorem and by introducing an update law, a sufficient condition of theglobal synchronization is obtained.
Abstract: A new robust adaptive synchronization approach for the global synchronization of complex dynamical networks is proposed. Both the characteristics of the uncoupled nodes of the network and the coupling matrix are unknown, but only a time-varying coupling strength is used in this paper. Based on the LaSalle–Yoshizawa theorem and by introducing an update law, a sufficient condition of the global synchronization is obtained. The update law is only dependent on the states of the complex dynamical network, which do not need any other information such as the characteristic of the uncoupled nodes of the network and the second largest eigenvalue of the coupling matrix. Compared with the existing results, our synchronization strategy is still useful when the existing synchronization methods become invalid. Moreover, it is very convenient to use. An example of the complex network is finally used to verify the proposed theoretical result.
TL;DR: A system for sampling UWB echo signal at a rate much lower than Nyquist rate and performing signal detection is proposed in this paper, and an approach of constructing basis functions according to matching rules is proposed to achieve sparse signal representation.
Abstract: A major challenge in ultra-wide-band (UWB) signal processing is the requirement for very high sampling rate. The recently emerging compressed sensing (CS) theory makes processing UWB signal at a low sampling rate possible if the signal has a sparse representation in a certain space. Based on the CS theory, a system for sampling UWB echo signal at a rate much lower than Nyquist rate and performing signal detection is proposed in this paper. First, an approach of constructing basis functions according to matching rules is proposed to achieve sparse signal representation because the sparse representation of signal is the most important precondition for the use of CS theory. Second, based on the matching basis functions and using analog-to-information converter, a UWB signal detection system is designed in the framework of the CS theory. With this system, a UWB signal, such as a linear frequency-modulated signal in radar system, can be sampled at about 10% of Nyquist rate, but still can be reconstructed and detected with overwhelming probability. The simulation results show that the proposed method is effective for sampling and detecting UWB signal directly even without a very high-frequency analog-to-digital converter.
TL;DR: In this paper, strong consistence and weak consistence of decision formal context are defined respectively, the judgment theorems of consistent sets are examined, and approaches to reduction are given.
Abstract: The theory of concept lattices is an efficient tool for knowledge representation and knowledge discovery, and is applied to many fields successfully One focus of knowledge discovery is knowledge reduction Based on the reduction theory of classical formal context, this paper proposes the definition of decision formal context and its reduction theory, which extends the reduction theory of concept lattices In this paper, strong consistence and weak consistence of decision formal context are defined respectively For strongly consistent decision formal context, the judgment theorems of consistent sets are examined, and approaches to reduction are given For weakly consistent decision formal context, implication mapping is defined, and its reduction is studied Finally, the relation between reducts of weakly consistent decision formal context and reducts of implication mapping is discussed