A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making

The aim of this paper is to introduce the concept of a generalized Pythagorean fuzzy soft set(GPFSS),which is a combination of the generalized fuzzy soft sets and Pythagorean fuzzy sets.Several of important operations of GPFSS including complement,restricted union,and extended intersection are discussed.The basic properties of GPFSS are presented.Further,an algorithm of GPFSSs is given to solve the fuzzy soft decision-making.Finally,a comparative analysis between the GPFSS approach and some existing approaches is provided to show their reliability over them.

Generalized Soft Expert Set and Its Applications

The expert set theory performs an important part in making decisions. It can successfully convey the opinions of every expert since it includes several experts. In this study, generalizations and soft expert sets are combined. First, the generalized soft expert set notion is presented, then follows the definition of operation approaches and characteristics as the complement, union, intersection, AND and OR. The application of the generalized soft expert set concept to decision issues is then presented with an example. The study also introduces the idea of a generalized soft expert matrix and demonstrates how it may be used to solve decision-making issues. The most striking aspect of this paper is to present the concepts of generalized soft expert sets and generalized soft expert matrices and to apply them to the same decision-making scenario.

Dynamic weighted voting for multiple classifier fusion:a generalized rough set method

To improve the performance of multiple classifier system, a knowledge discovery based dynamic weighted voting （KD-DWV） is proposed based on knowledge discovery. In the method, all base classifiers may be allowed to operate in different measurement/feature spaces to make the most of diverse classification information. The weights assigned to each output of a base classifier are estimated by the separability of training sample sets in relevant feature space. For this purpose, some decision tables （DTs） are established in terms of the diverse feature sets. And then the uncertainty measures of the separability are induced, in the form of mass functions in Dempster-Shafer theory （DST）, from each DTs based on generalized rough set model. From the mass functions, all the weights are calculated by a modified heuristic fusion function and assigned dynamically to each classifier varying with its output. The comparison experiment is performed on the hyperspectral remote sensing images. And the experimental results show that the performance of the classification can be improved by using the proposed method compared with the plurality voting （PV）.

Generalized dominance-based rough set approach to security evaluation with imprecise information

The model of grey multi-attribute group decision-making （MAGDM） is studied, in which the attribute values are grey numbers. Based on the generalized dominance-based rough set approach （G-DR- SA）, a synthetic security evaluation method is presented. With-the grey MAGDM security evaluation model as its foundation, the extension of technique for order performance by similarity to ideal solution （TOPSIS） integrates the evaluation of each decision-maker （DM） into a group＇s consensus and obtains the expected evaluation results of information system. Via the quality of sorting （QoS） of G-DRSA, the inherent information hidden in data is uncovered, and the security attribute weight and DMs＇ weight are rationally obtained. Taking the computer networks in a certain university as objects, the example illustrates that this method can effectively remove the bottleneck of the grey MAGDM model and has practical significance in the synthetic security evaluation.

Category of Generalized Intuitionistic Fuzzy Sets

In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS are studied. Firstly, it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers, Secondly, it is proved that the category GIFS has middle object and consequently GIFS is a weak topos. Thirdly, by the use of theory of weak topos GIFS, the power object of an object in GIFS is studied.

The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets

We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.

α-Input and α-Unit Resolution Methods for Generalized Horn Clause Set in L_(V(n×2))F(X)

a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncertain linguistic values-based information. Firstly the concepts of a-input resolution and a.unit resolution are presented, and the equivalence of them is shown. Then α-input （a-unit） resolution is equivalently transformed from Lv（ n × 2） F（X） into that of LnP（X）, and their soundness and completeness are also established. Finally an algorithm for a-unit resolution is contrived in LnP（ X）.

MULTI-GRAY EDGE DETECTION BASED ON GENERALIZED FUZZY SET

In this letter, drawbacks of the classical algorithm to enhance the fuzzy contrast among adjacent regions are analyzed. Based on it, a new fuzzy enhancement algorithm and a linear fuzzy distribution that maps the gray images to corresponding generalized fuzzy set are proposed. Results of two examples illustrate that the algorithm is more effective and faster when used to detect the multi-level edges of images.

A NOTE ON GENERALIZED MORAN SET

Let E be a generallied Moran set. The authors determine the dim E and get the sufficient and necessary condition for E being a s-set.

Nonlinear Dynamic Characteristic Analysis of the Shaft System in Water Turbine Generator Set

A 3D finite element vibration model of water turbine generator set is constructed considering the coupling with hydropower house foundation. The method of determining guide bearing dynamic characteristic coefficients according to the swing of the shaft is proposed, which can be used for studying the self-vibration characteristic and stability of the water turbine generator set. The method fully considers the complex supporting boundary and loading conditions; especially the nonlinear variation of guide bearing dynamic characteristic coefficients and the coupling effect of the whole power-house foundation. The swing and critical rotating speed of an actual generator set shaft system are calculated. The simulated results of the generator set indicate that the coupling vibration model and calculation method presented in this paper are suitable for stability analysis of the water turbine generator set.

Lagrange-Maxwell equation and magnetic saturation parametric resonance of generator set

Lagrange-Maxwell＇s equation is extended firstly. With the theory of electromechanical analytical dynamics, the magnetic complement energy in air gap of generator is acquired. The torsional vibration differential equations with periodic coefficients of rotor shafting of generator which is in the state of.magnetic saturation are established. It is shown that the magnetic saturation may cause double frequency electromagnetic moment. By means of the averaging method, the first approximate solution and corresponding solution of the primary parametric resonance is obtained. The characteristics and laws of the primary parametric resonance excited by the electromagnetism are analyzed and some of new phenomena are revealed.

Knowledge discovery method for feature-decision level fusion of multiple classifiers

To improve the performance of the multiple classifier system, a new method of feature-decision level fusion is proposed based on knowledge discovery. In the new method, the base classifiers operate on different feature spaces and their types depend on different measures of between-class separability. The uncertainty measures corresponding to each output of each base classifier are induced from the established decision tables （DTs） in the form of mass function in the Dempster-Shafer theory （DST）. Furthermore, an effective fusion framework is built at the feature-decision level on the basis of a generalized rough set model and the DST. The experiment for the classification of hyperspectral remote sensing images shows that the performance of the classification can be improved by the proposed method compared with that of plurality voting （PV）.

Applications of Generalized Rough Set Theory in Evaluation Index System of Radar Anti-Jamming Performance

Radar anti-jamming performance evaluation is a necessary link in the process of radar development,introduction and equipment. The applications of generalized rough set theory are proposed and discussed in this paper to address the problems of big data, incomplete data and redundant data in the construction of evaluation index system. Firstly, a mass of real-valued data is converted to some interval-valued data to avoid an unacceptable number of equivalence classes and classification rules, and the interval similarity relation is employed to make classifications of this interval-valued data. Meanwhile, incomplete data can be solved by a new definition of the connection degree tolerance relation for both interval-valued data and single-valued data, which makes a better description of rough set than the traditional limited tolerance relation. Then, E-condition entropy-based heuristic algorithm is applied to making attribute reduction to optimize the evaluation index system, and final decision rules can be extracted for system evaluation. Finally, the feasibility and advantage of the proposed methods are testified by a real example of radar anti-jamming performance evaluation.

THE RANKS OF CYCLIC AND NEGACYCLIC CODES OVER THE FINITE RING R

The ranks of cyclic and negacyclic codes over the finite chain ring R as well as their minimal generating sets are defined, and then the expression forms we presented by studying the structures of cyclic and negacyclic codes over the finite chain ring R. Through the paper, it is assumed that the length of codes n can not be divided by the characteristic of R.

Classification of Sitting States for the Humanoid Robot SJTU-HR1

The classification of sitting issues is investigated since detailed state classification for humanoid robots plays a key role in the practical application of humanoid robots, particularly for the humanoid robots doing complicated tasks. This paper presents the concept, the characteristics tree, and the prototype of the humanoid robot SJTU-HR1. The basic states lbr humanoid robots are proposed, including lying, sitting, standing, and handstanding. Moreover, the sitting states are classified into several states from the viewpoint of topology. The Gy （generalized function） set theory is applied to achieve the kinematic characteristics of the interested end-effectors of the humanoid robot SJTU-HR1. Finally, the results indicate that a large number of the sitting states can be represented by the meaningful notations systematically. Furthermore, the one-to-one correspondence between the state and kinematic characteristics of the interested end-effectors of the SJTU-HR 1 leads to deeper insight into the capabilities of the humanoid robot SJTU-HR1.

CYCLIC CODES OVER THE RING Z(_P^2) OF LENGTH p^e

The study of cyclic codes over rings has generated a lot of public interest.In this paper,we study cyclic codes and their dual codes over the ring Z P2 of length pe,and find a set of generators for these codes.The ranks and minimal generator sets of these codes are studied as well,which play an important role in decoding and determining the distance distribution of codes.

The Applications of Vague Soft Sets and Generalized Vague Soft Sets

The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definitions, some novel methods of object recognition from an imprecise multiobserver data has been presented. Moreover, we introduce the notion of generalized vague soft sets and study some of its properties. The similarity measure of generalized vague soft sets is also presented and an application of this measure in decision making problems has been shown.

Asynchronous Observer Design for Switched Linear Systems: A Tube-Based Approach

This paper proposes a tube-based method for the asynchronous observation problem of discrete-time switched linear systems in the presence of amplitude-bounded disturbances.Sufficient stability conditions of the nominal observer error system under mode-dependent persistent dwell-time(MPDT)switching are first established. Taking the disturbances into account, a novel asynchronous MPDT robust positive invariant(RPI) set and an asynchronous MPDT generalized RPI(GRPI)set are determined for the difference system between the nominal and disturbed observer error systems. Further, the global uniform asymptotical stability of the observer error system is established in the sense of converging to the asynchronous MPDT GRPI set, i.e., the cross section of the tube of the observer error system. Finally, the proposed results are validated on a space robot manipulator example.

Application of General Fractal Dimension to Coupling Fault Diagnosis

This paper presents the coucept of general and sensitive dimension, and also proposes the calculation formula of the general dimension least squares method. By calculating and analyzing the power spectrum and general dimension from the fault sample, the relationship is achieved between sample status and the general dimension from vibration signals of the equipment so as to provide reference to fault diagnosis. Furthermore, a correlation function of general dimension is proposed, and calculations are carried out for a monitor signal and samples signal. The diagnosis method based on fractal theory is effective through the concrete examples of the steam electric generating set fault diagnosis, and the correlation coefficient of general dimension between a monitor signal and samples signal can improve the accuracy for fault diagnosis.

SOME RESULTS ON GENERALIZED DIFFERENCE SETS

Sequences with ideal correlation functions have important applications in communications such as CDMA, FDMA, etc. It has been shown that difference sets can be used to construct such sequences. The author extends Pott and Bradley＇s method to a much broader case by proposing the concept of generalized difference sets. Some necessary conditions for the existence of generalized difference sets are established by means of some Diophantine equations. The author also provides an algorithm to determine the existence of generalized difference sets in the cyclic group Zv. Some examples are presented to illustrate that our method works.