With the rise of smart home applications, WiFi-based posture estimation has become a research focus. Existing methods often emphasize end-to-end feature extraction while neglecting high-resolution intermediate spatial features. We observe that horizontal and vertical antennas capture electromagnetic wave distributions in different directions, while multiple subcarrier frequencies inherently enhance multipath resolution. By analyzing signal correlations among subcarriers, we achieve equivalence to virtual antennas, enabling the generation of high-resolution spatial correlation maps. Using a cascaded network with UNet, we extract human spatial transformation features and a steering vector to obtain a spatial spectrum, mapping keypoints with high precision. Tests in through-wall environments achieve an average mPCK of 0.90 at 20 pixels and 0.98 at 50 pixels, significantly improving detection accuracy.

Most existing image deblurring methods construct statistical prior to describe the difference between blur and clear image. They discard the position information and ignore pixel feature changing in deblurring, which results in inferior restoration performance for images unsatisfying corresponding assumptions. Intuitively, fuzziness of pixel belonging to different image regions will reduce along with image deblurring. This phenomenon could intrinsically describe the pixel characteristic. To this end, we analyze fuzziness of pixels and objects in a blurry image, and utilize the similarity between two fuzzy objects on image pixels to depict the blur degree of an image, which is inspired by overlap functions and overlap indices. To minimize the similarity between fuzzy objects, we introduce the non-parameters model to construct an integer programming problem. Energy minimization could significantly reduce the similarity between two fuzzy objects. Experimental results show that the proposed method can achieve better performance than the state-of-the-art blind deblurring methods on benchmark datasets and natural images.

The relation between a linguistic value and its meaning is one-to-many rather than one-to-one. How to precisiate meaning of a linguistic value and even fuzzy linguistic propositions or rules remain open problems in computing with words (CW). In the paper, according to a linguistic value describes a class of objects with unsharp or fuzzy boundary, label of the linguistic value in its universe of discourse is proposed to formalize a possible position of objects described by the linguistic value via a group of subjects' commonsense cognition. Then credibility of a membership function related to a linguistic value is presented by measuring “objects in its support are close to label of the linguistic value”, which can be used to determine whether the membership function can be regarded as representation of meaning of the linguistic value. By combining credibility of a membership function related to a linguistic value with overlap indices between two membership functions, an alternative method is provided to precisiate meaning of a linguistic value and deduce fuzzy truth values of meaning rules of fuzzy If-Then linguistic rules, all of these can be exploited to improve test-score semantics ofCW. Finally a case in designing fuzzy linguistic estimator is employed to show useful and effective improvement ofCW.

In this paper, the issue of tracking control for connected servosystems with coupling input and false data injection (FDI) attacks is studied. A fuzzy linguistic knowledge reasoning-based secure control scheme is proposed. Firstly, the dynamic model of connected nonlinear servosystems suffer from coupling input and FDI attacks is modeled. Then, a fuzzy linguistic estimator based on experimental observation and human knowledge is proposed to approximate the nonlinear function. Furthermore, an observer depended on the fuzzy linguistic estimator is designed to observe the system state. Thirdly, to achieve the tracking control of connected nonlinear servosystems, a fuzzy linguistic knowledge reasoning-based secure control algorithm is presented. Finally, simulation and experiment results demonstrate the effectiveness of the algorithm.

Abstract One of characteristics of large-scale linguistic decision making problems is that decision information with respect to decision making attributes is derived from multi-sources information. In addition, the number of decision makers, alternatives or criteria of decision making problems in the context of big data are increasingly large. Correlation analysis between decision making attributes has become an important issue of large-scale linguistic decision making problems. In the paper, we concentrate on correlation analysis between decision making attributes to deal with large-scale decision making problems with linguistic intuitionistic fuzzy values. Firstly, we proposed a new similarity measure between two linguistic intuitionistic fuzzy sets to formally define correlation between decision making attributes. Then we propose linguistic intuitionistic fuzzy reducible weighted Maclaurin symmetric mean (LIFRWMSM) operator and linguistic intuitionistic fuzzy reducible weighted dual Maclaurin symmetric mean (LIFRWDMSM) operator to aggregate linguistic intuitionistic fuzzy value decision information of correlational decision making attributes, and analyze several important properties of the two operator. Inspired by evaluation based on distance from average solution (EDAS) method, we design a solution scheme and decision steps to deal with large-scale linguistic intuitionistic fuzzy decision making problems. To show the effectiveness and usefulness of the proposed decision method, we employ the choice of buying a house and the selection of travel destination to demonstrate our method and make comparative analysis with others aggregation operators or methods.

Abstract The notable characteristic of large-scale linguistic decision-making problems is that there are so many decision makers who provide linguistic assessments by using fuzzy linguistic representation models. In real-world applications, fuzzy linguistic terms mean different things for different people, and linguistic assessments based on different linguistic representation models may be simultaneous in the same large-scale linguistic decision-making problems. To this end, a novel linguistic decision-making method based on the voting model is proposed in the paper to deal with multi-linguistic assessments provided by decision makers. In large-scale linguistic decision process, evaluation-based voting is defined and multi-linguistic decision matrix is designed to represent multi-linguistic assessments provided by decision makers by using different linguistic representation models, and properties of the decision matrix are analyzed to show that linguistic assessments based on different linguistic representation models can be simultaneously represented. Based on multi-linguistic decision matrix, a new linguistic decision-making framework is developed to deal with large-scale linguistic decision-making problems with multi-linguistic assessments, in which normalization of multi-linguistic decision matrix and trust degrees of linguistic terms are contained, and more important, based on trust degrees of linguistic terms and 2-tuple fuzzy linguistic aggregation operators, an uniform fusion method of multi-linguistic assessments is proposed to aggregate multi-linguistic assessments of large-scale linguistic decision-making problems. Finally, user experiences of shared bikes, which are a large-scale linguistic decision-making problem in real-world applications, are employed to show the new decision-making framework and the uniform fusion method of multi-linguistic assessments, and furthermore, compared with existing linguistic decision-making methods analyzed in the example, it seems that multi-linguistic decision matrix and the uniform fusion method are useful and effective tools to deal with large-scale linguistic decision-making problems with multi-linguistic assessments.

This essay designs an innovate approach to work out linguistic multiattribute group decision-making (MAGDM) issues with complex q-rung orthopair fuzzy 2-tuple linguistic (Cq-ROF2TL) evaluation information. To begin with, the conception of Cq-ROF2TL set is propounded to express uncertain and fuzzy assessment information. Meanwhile, the score and accuracy function, a comparison approach, Cq-ROF2TL weighted averaging, and Cq-ROF2TL weighted geometric operator are put forward. Furthermore, to take into consideration the correlation among multiple input data, the Cq-ROF2TL Maclaurin symmetric mean (MSM) operator, the Cq-ROF2TL dual MSM operator and their weighted forms are presented. Several attractive characteristics and particular instances of the developed operators are also explored at length. Later, an innovative MAGDM methodology is designed based upon the propounded operators to settle the emergency program evaluation issue under the Cq-ROF2TL circumstance. Consequently, the efficiency and outstanding superiority of the created approach are severally substantiated by parameter exploration and detailed comparative analysis.

Mobile Edge Computing (MEC) is providing cloud computing capabilities within the radio access networks and offering a new paradigm to liberate the mobile devices from heavy computational workloads. Importantly, MEC can effectively reduce latency, avoid congestion, and prolong the battery lifetime of mobile devices by offloading the computation tasks from the mobile devices to a physically proximal MEC servers. Particularly, Virtual Machines (VMs) scheduling is a critical issue for tasks offloading and computation in MEC. Regarding to the VMs scheduling problem in MEC environmnet, this paper pioneers the use of Formal Concept Analysis (FCA) methodology for identifying the mapping from tasks to VMs. Specifically, the VMs profile and tasks descriptions are initially characterized as the formal contexts, respectively. With the constructed formal contexts, the corresponding formal concepts which refer to the rules set, are then generated. To better infuse the rules set of VMs and tasks, this paper defines a similarity measurement between formal concepts of VMs and tasks. Consequently, the matching problem from a given task to a virtual machine is to return the expected virtual machine according to the principle of maximum similarity degree between formal concepts of virtual machine and task. Extensive simulations are conducted with a real dataset for the validation of feasibility and effectiveness of the proposed approach. Specifically, the proposed approach can significantly reduce the energy consumption around 28 percent comparing to the approach without consideration of energy consumption. Overall, It is demonstrated that FCA-based VMs scheduling is a novel solution for a sustainable VMs scheduling in MEC environment.

Rough set approach for knowledge discovery in incomplete information systems has been extensively studied. This paper conduct a further study of valued tolerance relation based rough approximations. We make an analysis of the existing rough approximabilities and propose a new approach for lower (up per) approximability, which is a generalization of Pawlak approximation operators for complete information system. The approach has also been generalized to fuzzy cases. Some basic properties of the approximation operators are examined.

Different linguistic aggregation methods have been proposed and applied in the linguistic decision making problems. Generally, weights for experts or criteria are considered in linguistic aggregation processes. In this paper, we provide a method to discovery new forms to compute weights and new interpretations in the linguistic ordered weighted averaging operator. In linguistic decision analysis, it can be noticed that some of initial linguistic values used by experts have priority over others linguistic values in evaluation processes. We formalize the priority over initial linguistic values as weights for linguistic values, by considering weights for linguistic values as well as weights for experts, we provide an alternative method to discovery weights information of the linguistic ordered weighted averaging operator, its properties show that such linguistic aggregation operator is extensions of the 2-tuple arithmetic mean, the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator. By an illustrative example, we compare the linguistic aggregation operator with the 2-tuple weighted aggregation operator and the 2-tuple ordered weighted averaging operator in a decision making problem. From the practical point of view, we provide an optimization model to obtain such weights information in linguistic aggregation processes, examples show the linguistic aggregation operator as an alternative linguistic ordered weighted averaging operator in practice.

In this paper, we used Chen and Tan's method for handling multi-criteria fuzzy decision-making problems, where the characteristic of the alternatives are represented by intuitionistic fuzzy sets. The method allows the degrees of membership and non-membership of each alternative with respect to a set of criteria to be represented by intuitionistic fuzzy sets, respectively. Based on the structure of a fuzzy statement, a new method to extract Q, S and T of a linguistic data summary is discussed. The proposed method uses a new function weighting ldquoreal degreerdquo, which not only due to the fact that it use intuitionistic fuzzy set theory rather fuzzy set theory, but also due to the fact that the function can deal with the uncertainty well. Some patterns, which can conduct the decision-making, can be obtained from the linguistic summaries. Two example are given to illustrate the process.

Under the framework of set-valued information system, based on application of quantifiers and OWA operator, the definition on upper and lower approximations is generalized to the common form associated with the parameter lambdaepsi [0, 1]. The advantage of such generalization is that it could be flexibly used by restriction of additional linguistic quantifier, and is favorable to the further discussion on knowledge reduction and rules extraction in such model.

Aggregation operators are crucial to multiple attribute decision makers when they make decisions. While minimum and maximum can only represent optimistic and pessimistic extremes, an Ordered Weighted Aggregation (OWA) operator is able to reflect varied human attitudes lying between the two extremes by using distinct weight vectors. However, the OWA operator has a disadvantage of overlooking the importance of given argument itself. By combining the given argument itself with the ordered position argument and considering their importance, the authors of this paper first present an induced ordered weighted geometric averaging (IOWGA) operator for aggregating data information, and then give an IOWGA operator-based method applying to multiple attribute decision making (MADM) problems. Both the theoretical analysis and the numerical results show that IOWGA can better reflect the real situations in practical applications, and finally an illustrative example is given.

Attribute reduction plays an important role in rough set theory. It is an important application in data mining. In this paper, we focus on discussing the relation between set covering and attribute reduction in rough set theory. Based on the equivalence between minimal set covering and minimal attribute reduction sets, attribute reduction graph (ARG) is constructed. A novel algorithm to find the minimal attribute reduction sets, which is based on combination of binary discernibility matrix and graph theory is proposed in this paper. This algorithm demonstrates its efficiency and feasibility by an example.

Intuitionistic fuzzy special sets is a special case of intuitionistic fuzzy sets. In this paper, under the framework of information systems, based on the intuitionistic fuzzy special sets representation of rough sets, Hamming distance of association rule between condition and conclusion is discussed. By Hamming distance and the confidence of association rule, optimization model for extracting association rule are provided. The advantage of the optimization model is that it could be used to dynamically extract association rule from information systems and distinguish association rules with the same confidence by Hamming distance. Example shows that this paper’s method is an alternative method for extracting association rule.

Time series data is a series of observation data accord- ing to a certain time sequence. It has been penetrate various field. This paper applies Rough set to the knowledge dis- covery of time series. The process of knowledge discovery in time series includes preprocessing of time series data, at- tributes selection and similarity sequence searching. Then, the time series is partitioned to a set of pattern(each pattern represents a trend of time series)by mobile window method. An information table is formed by the most important pre- dicting attributes and target attribute which in the trend- ing structure sequence identified from each pattern. This information table is suitable for the Rough set to discover knowledge. The extracted rules can predict the time series behavior in the future. We demonstrate our method on time series stock market data.

Much information over the Internet is expressed by natural languages. The management of linguistic information involves an operation of comparison and aggregation. Based on the Ordered Weighted Averaging (OWA) operator and modifying indexes of linguistic terms (their indexes are fuzzy numbers on [0,T] ⊆ R+), new linguistic aggregating methods are presented and their properties are discussed. Also, based on a multi-agent system and new linguistic aggregating methods, gathering linguistic information over the Internet is discussed. Moreover, by fixing the threshold α, “soft filtering information” is proposed and better Web pages (or documents) that the user needs are obtained. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 435–453, 2007.

Clustering is one of major function in data mining. Social system appraisement is faced with random variable and fuzzy variable, in order to solve the clustering of the mix type variables, this paper puts forward a clustering application method. The major thought of this method as follows: on the foundation of screening in advance for data source, classifies data variable according to whether belong to random variable or fuzzy variable. Random variable is determined by posterior probability distribution through Bayes study theory, and made it carry out clustering with the method of not random variable with posterior probability distribution as the weight of random variable. For fuzzy variable, the equivalence matrix is established according to the system clustering method of fuzzy relation, and converted it into Equivalence matrix to carry out clustering.

In this paper, we propose a dynamic fuzzy neural-network structure, i.e., there are two classical fuzzy-neural network structures in dynamic fuzzy neural-network structure. In the practical identification processing, the function of the two classical fuzzy-neural networks is often changed. At the same time, one classical fuzzy-neural network can be used to estimate the model, and another classical fuzzy-neural network is used to learn. At the appropriate time, the role of the two classical fuzzy-neural networks is changed. The fuzzy-neural network that was used to estimate the model starts to learn, and the fuzzy-neural network that was learning is used to estimate the model, how to change is decided by a switching region. By using the method, the parameter adjustment of an adaptive fuzzy identification model and optimal parameters of the system can be obtained.

Filter is an algebraic structure, which has been widely applied to many branches of mathematics, especially to mathematical logic. Lattice implication algebra is a new kind of logical algebra proposed by Xu Yang. The concepts of filter, implicative filter, positive implicative filter, I-filter, involution filter, obstinate filter and ultra-filter in a lattice implication algebra were proposed and studied. By using the concept of truth functions, this paper is devoted to the study of the relation between filters and logical deductive rules. Further, the concept of G-filter based on deductive rules was proposed with its properties being discussed. The results of this paper provide the new methods for resolution based on filters.