L-fuzzy numbers and their properties

In this paper, the notions of L-fuzzy convex sets and L-fuzzy numbers are introduced where L is a completely distributive lattice. The notions of [0, 1]-fuzzy convex sets and [0, 1]-fuzzy numbers are generalized. Furthermore their properties and characterizations are presented in terms of cut sets of L-fuzzy sets.     

Ranking L-R fuzzy number based on deviation degree

This paper proposed a novel approach to ranking fuzzy numbers based on the left and right deviation degree (L-R deviation degree). In the approach, the maximal and minimal reference sets are defined to measure L-R deviation degree of fuzzy number, and then the transfer coefficient is defined to measure the relative variation of L-R deviation degree of fuzzy number. Furthermore, the ranking index value is obtained based on the L-R deviation degree and relative variation of fuzzy numbers. Additionally, to compare the proposed approach with the existing approaches, five numerical examples are used. The comparative results illustrate that the approach proposed in this paper is simpler and better.     

A note on locally bounded L-topological vector spaces

In this note, we give a counterexample showing that Theorem 5 in [C.-H. Yan, J.-X. Fang, Locally bounded L-topological vector spaces, Information Sciences 159 (2004) 273-281] is incorrect and offer a modified version of this theorem.     

On a new class of fuzzy implications: h-Implications and generalizations

A new class of fuzzy implications called the h-implications is introduced. They are implications generated from an additive generator of a representable uninorm in a similar way of Yager’s f- and g-implications which are generated from additive generators of continuous Archimedean t-norms and t-conorms. Basic properties of these implications are studied in detail. Modifications and generalizations of the initial definition are presented and their properties studied and compared between them. One of the modifications, called (h, e)-implications, is another example of a fuzzy implication satisfying the exchange principle but not the law of importation for any t-norm, in fact for any function F : [0, 1]² → [0, 1].     

(?, T)-fuzzy rough approximation operators and the TL-fuzzy rough ideals on a ring

In this paper, we consider a ring as a universal set and study (?, T)-fuzzy rough approximation operators with respect to a TL-fuzzy ideal of a ring. First, some new properties of generalized (?, T)-fuzzy rough approximation operators are obtained. Then, a new fuzzy algebraic structure - TL-fuzzy rough ideal is defined and its properties investigated. And finally, the homomorphism of (?, T)-fuzzy rough approximation operators is studied.     

Low-rank matrix decomposition in L1-norm by dynamic systems

Low-rank matrix approximation is used in many applications of computer vision, and is frequently implemented by singular value decomposition under L₂-norm sense. To resist outliers and handle matrix with missing entries, a few methods have been proposed for low-rank matrix approximation in L₁ norm. However, the methods suffer from computational efficiency or optimization capability. Thus, in this paper we propose a solution using dynamic system to perform low-rank approximation under L₁-norm sense. From the state vector of the system, two low-rank matrices are distilled, and the product of the two low-rank matrices approximates to the given measurement matrix with missing entries, in L₁ norm. With the evolution of the system, the approximation accuracy improves step by step. The system involves a parameter, whose influences on the computational time and the final optimized two low-rank matrices are theoretically studied and experimentally valuated. The efficiency and approximation accuracy of the proposed algorithm are demonstrated by a large number of numerical tests on synthetic data and by two real datasets. Compared with state-of-the-art algorithms, the newly proposed one is competitive.     

Face recognition by sparse discriminant analysis via joint L2,1-norm minimization

Recently, joint feature selection and subspace learning, which can perform feature selection and subspace learning simultaneously, is proposed and has encouraging ability on face recognition. In the literature, a framework of utilizing L_2,1-norm penalty term has also been presented, but some important algorithms cannot be covered, such as Fisher Linear Discriminant Analysis and Sparse Discriminant Analysis. Therefore, in this paper, we add L_2,1-norm penalty term on FLDA and propose a feasible solution by transforming its nonlinear model into linear regression type. In addition, we modify the optimization model of SDA by replacing elastic net with L_2,1-norm penalty term and present its optimization method. Experiments on three standard face databases illustrate FLDA and SDA via L_2,1-norm penalty term can significantly improve their recognition performance, and obtain inspiring results with low computation cost and for low-dimension feature.     

Adaptive nonlinear excitation control with L2 disturbance attenuation for power systems

This paper presents a design approach to nonlinear feedback excitation control of power systems with unknown disturbance and unknown parameters. It is shown that the stabilizing control law with desired L₂ gain from the disturbance to a penalty signal can be designed by a recursive way without linearization. A state feedback law is presented for the case of the system with known parameters, and then the control law is extended to adaptive controller for the case when the parameters of the electrical dynamics of the power system are unknown. Simulation results demonstrate that the proposed controllers guarantee transient stability of the system regardless of the system parameters and faults.     

H performance of preview control systems

Performance of the preview control is investigated in terms of H^∞-criterion. In the infinite-horizon time setting, the limitation of H^∞ performance in preview control action is characterized with the Hamiltonian matrix. By employing the property of Hamiltonian matrix, the solvability and analytic solution for the preview full-information control problem are clarified based on an auxiliary introduced matrix Riccati equation. The property of resulting control law is illustrated with a numerical example.     

On the H fixed-lag smoothing: how to exploit the information preview

The problem of the continuous-time H^∞ fixed-lag smoothing over the infinite horizon is studied. The first solution to the problem is derived in terms of one algebraic Riccati equation of the same dimension as in the filtering case and the mechanism by which the performance improvements with respect to the H^∞ filtering occur is clarified. It is shown that the H^∞ smoother exploits the information preview in an “H² manner”.     

Second order (F, α, ρ, d)-convexity and duality in multiobjective programming

A class of second order (F, α, ρ, d)-convex functions and their generalizations is introduced. Using the assumptions on the functions involved, weak, strong and strict converse duality theorems are established for a second order Mond-Weir type multiobjective dual.     

Application of rhodamine B thiolactone to fluorescence imaging of Hg in Arabidopsis thaliana

Exposure to mercury causes severe damage to plants, animals and even humans. Concern over mercury toxicity has encouraged the development of efficient, sensitive, and selective methods for the in vivo detection of mercury. Although a variety of studies have been published describing fluorescence imaging of mercury in animal cells and tissues, no in vivo monitoring has been developed for plant systems until now. In this paper, we report the semi-quantitative fluorescence imaging of Hg²⁺ ions in a common model plant Arabidopsis thaliana (A. thaliana), with rhodamine B thiolactone (RBS) as a novel Hg²⁺ probe. The experimental results show that RBS is plant cell wall and cell membrane permeable, and the probe responds selectively to Hg²⁺ ions instead of the other species in plant systems. Real-time monitoring of Hg²⁺ absorption in roots of A. thaliana by RBS shows that saturation of Hg²⁺ uptake could occur in a short period of 3 days at most. The transportation and accumulation of Hg²⁺ ions in roots of A. thaliana have also been studied, revealing that most of Hg²⁺ ions reside in root cap and meristematic zone, and only a small amount of Hg²⁺ ions can reach the maturation zone. This indicates that the interaction of Hg²⁺ ions with any Hg²⁺-philic species including proteins in these regions may be responsible for plant poisoning and even death.     

Algebraic properties of LA-languages

In this study, we introduce the concepts of L-valued regular substitution (LA-substitution), deterministic L-valued regular substitution (DLA-substitution), L-valued fuzzy homomorphism and its inverse images, homomorphism and its inverse images for a lattice-ordered monoid L. We also study the properties of LA-languages and DLA-languages under the above-mentioned algebraic operations. The algebraic characterization of the L-valued regular language is given.     

Neural network estimation of LAI, fAPAR, fCover and LAI×Cab, from top of canopy MERIS reflectance data: Principles and validation

A neural network is developed to operationally estimate biophysical variables over land surfaces from the observations of the ENVISAT-MERIS instrument: the leaf area index (LAI), the fraction of absorbed photosynthetically active radiation (fAPAR), the fraction of vegetation cover (fCover), and the canopy chlorophyll content (LAI×C_ab). The neural network requires as input the geometry of observation and the top of canopy reflectances, corrected from the atmospheric effects, in eleven spectral bands. It is trained on a reflectance database made of radiative transfer model simulations. The principles underlying the generation of the database and the design of the network are first presented. The estimated variables are then compared to other existing products, LAI- and fAPAR-MODIS and MGVI-MERIS, and validated against ground measurements performed in the framework of the VALERI project. Results show remarkable consistency of the temporal dynamics between the several products with however some differences in the range of variation. When compared to actual VALERI ground measurements, the proposed algorithm shows the best performances for LAI (RMSE = 0.47) and fAPAR (RMSE = 0.09).     

Another look at finite horizon H control problems for systems with input delays

We discuss a finite horizon H^∞ control problem for time-varying systems with input delays. Clarifying a relationship between two H^∞ control problems in input delay case and in measurement delay case, we derive a solution in input delay case based on the known result for the H^∞ control problem in measurement delay case, and show that the solution has the same predictor-observer structure as the solution in measurement delay case has. Using this structural information on the solution, we also present an elementary proof of the solution to the finite horizon H^∞ control problem for systems with input delays, which is based only on completion of squares.     

Remote sensing chlorophyll a of optically complex waters (rias Baixas, NW Spain): Application of a regionally specific chlorophyll a algorithm for MERIS full resolution data during an upwelling cycle

This study takes advantage of a regionally specific algorithm and the characteristics of Medium Resolution Imaging Spectrometer (MERIS) in order to deliver more accurate, detailed chlorophyll a (chla) maps of optically complex coastal waters during an upwelling cycle. MERIS full resolution chla concentrations and in situ data were obtained on the Galician (NW Spain) shelf and in three adjacent rias (embayments), sites of extensive mussel culture that experience frequent harmful algal events. Regionally focused algorithms (Regional neural network for rias Baixas or NNRB) for the retrieval of chla in the Galician rias optically complex waters were tested in comparison to sea-truth data. The one that showed the best performance was applied to a series of six MERIS (FR) images during a summer upwelling cycle to test its performance. The best performance parameters were given for the NN trained with high-quality data using the most abundant cluster found in the rias after the application of fuzzy c-mean clustering techniques (FCM). July 2008 was characterized by three periods of different meteorological and oceanographic states. The main changes in chla concentration and distribution were clearly captured in the images. After a period of strong upwelling favorable winds a high biomass algal event was recorded in the study area. However, MERIS missed the high chlorophyll upwelled water that was detected below surface in the ria de Vigo by the chla profiles, proving the necessity of in situ observations. Relatively high biomass “patches” were mapped in detail inside the rias. There was a significant variation in the timing and the extent of the maximum chla areas. The maps confirmed that the complex spatial structure of the phytoplankton distribution in the rias Baixas is affected by the surface currents and winds on the adjacent continental shelf. This study showed that a regionally specific algorithm for an ocean color sensor with the characteristics of MERIS in combination with in situ data can be of great help in chla monitoring, detection and study of high biomass algal events in an area affected by coastal upwelling such as the rias Baixas.     

Neural network estimation of chlorophyll a from MERIS full resolution data for the coastal waters of Galician rias (NW Spain)

In typical Case 2 waters, accurate remote sensing retrieval of chlorophyll a (chla) is still a challenging task. In this study, focusing on the Galician rias (ΝW Spain), algorithms based on neural network (NN) techniques were developed for the retrieval of chla concentration in optically complex waters, using Medium Resolution Imaging Spectrometer (MERIS) data. There is considerable interest in the accurate estimation of chla for the Galician rias, because of the economic and social importance of the extensive culture of mussels, and the high frequency of harmful algal events. Fifteen MERIS full resolution (FR) cloud-free images paired with in situ chla data (for 2002-2004 and 2006-2008) were used for the development and validation of the NN. The scope of NN was established from the clusters obtained using fuzzy c-mean (FCM) clustering techniques applied to the satellite-derived data. Three different NNs were developed: one including the whole data set, and two others using only points belonging to one of the clusters. The input data for these latter two NNs was chosen depending on the quality level, defined on the basis of quality flags given to each data set. The fitting results were fairly good and proved the capability of the tool to predict chla concentrations in the study area. The best prediction was given for the NN trained with high-quality data using the most abundant cluster data set. The performance parameters in the validation set of this NN were R² = 0.86, mean percentage error (MPE) = − 0.14, root mean square error (RMSE) = 0.75 mg m^− 3, and relative RMSE = 66%. The NN developed in this study detected accurately the peaks of chla, in both training and validation sets. The performance of the Case-2-Regional (C2R) algorithm, routinely used for MERIS data, was also tested and compared with our best performing NN and the sea-truthing data. Results showed that this NN outperformed the C2R, giving much higher R² and lower RMSE values.This study showed that the combination of in situ data and NN technology improved the retrieval of chla in Case 2 waters, and could be used to obtain more accurate chla maps. A local-based algorithm for the chla retrieval from an ocean colour sensor with the characteristics of MERIS would be a great support in the quantitative monitoring and study of harmful algal events in the coastal waters of the Rias Baixas. The limitations and possible improvements of the developed chla algorithms are also discussed.