SET VALUE MAPPING AND ITS APPLICATION

The dynamics of set value mapping is considered. For the upper semi-continuous set value maps, the existence of attractors under some conditions and the upper semi-continuity of attractors under the perturbation are proved. Its application in numerical simulation of differential equation is also considered. The upper semi-continuity of attractors in set value maps under the perturbation is used to show the reasonable of subdivision algorithm and interval arithmetic in numerical simulation of differential equation.

Set Valued Vitali-Hahn-Saks-Nikodym Theorem

In this paper, we establish the set valued Vitali-Hahn-Saks-Nikodym Theorem.

Note on the Paper “Representation of Set Valued Operators” *

The aim of this paper is to show that one main theorem in is not correct by a counterexample and to give its correction.

STRICT STABILITY OF IMPULSIVE SET VALUED DIFFERENTIAL EQUATIONS

In this paper, we develop strict stability concepts of ODE to impulsive hybrid set valued differential equations. By Lyapunov’s original method, we get some basic strict stability criteria of impulsive hybrid set valued equations.

Criterion Theorems of Set Valued Martingales With Values in a Banach Space

In this paper, by means of support functions and distance functions, we give tow criterion theorems ofset valued martingales with values in a Banach space.

THE EXISTENCE THEOREM OF THE CONE-WEAK SUBDIFFERENTIAL OF SET-VALUED MAPPING

In this paper, the existence theorem of the cone weak subdifferential of set valued mapping in locally convex topological vector space is proved. Received March 30,1998. 1991 MR Subject Classification: 47H17,90C29.

Cartesian product over interval valued intuitionistic fuzzy sets

The intuitionistic fuzzy set(IFS) based on fuzzy theory,which is of high efficiency to solve the fuzzy problem, has been introduced by Atanassov. Subsequently, he pushed the research one step further from the IFS to the interval valued intuitionistic fuzzy set(IVIFS). On the basis of fuzzy set(FS), the IFS is a generalization concept. And the IFS is generalized to the IVIFS.In this paper, the definition of the sixth Cartesian product over IVIFSs is first introduced and its some properties are explored.We prove some equalities based on the operation and the relation over IVIFSs. Finally, we present one geometric interpretation and a numerical example of the sixth Cartesian product over IVIFSs.

Self-organizing Map Method Based on Real Rough Sets Space and Its Application of Pattern Recognition

This paper presents a real rough sets space and corresponding concepts of real lower and upper approximation sets which correspond to the real-valued attributes. Therefore, the real rough sets space can be investigated directly. A rhombus neighborhood for SOM is proposed, and the combination of SOM and rough sets theory is explored. According to the distance between the weight of winner node and the input vector in the real rough sets space, new weight learning rules are defined. The modified method makes the classification of the output of SOM clearer and the intervals of different classes larger. Finally, an example based on fault identification of an aircraft actuator is presented, The result of the simulation shows that this method is right and effective.

A Note on Normal Families of Meromorphic Functions and Sharing Set

In the paper,we prove the main result:Let k(≥2)be an integer,and a,b and c be three distinct complex numbers.Let F be a family of functions holomorphic in a domain D in complex plane,all of whose zeros have multiplicity at least k.Suppose that for each f∈F,f(z)and f(k)(z)share the set{a,b,c}.Then F is a normal family in D.

Existence of solutions for fourth-order boundary value problem with parameter

This paper is a sequel to a previous paper （Yang, Y. and Zhang, J. H. Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69（2）, 1364-1375 （2008）） in which the nontrivial solutions to the fourthorder boundary value problems were studied. In the current work with the same conditions near infinity but different near zero, the positive, negative, and sign-changing solutions are obtained by the critical point theory, retracting property, and invariant sets.

The Coset Group and Com ove Group

Based on the concepts of set value map and power group,the definitions of comove relation,coset group and comove group were given,their properties were discussed and meaningful results were obtained.

Implementation of Control Algorithms in Small Embedded Systems

This work describes how a control algorithm can be implemented in a small (8-bit) microcontroller for the main purpose of merging embedded systems and control theory in electrical engineering undergraduate classes. Two different methods for discretizing the control expression are compared: Euler transformation and bilinear transformation. The sampling rate’s impact on the algorithm is discussed and theoretical results are verified by an application to a temperature control system in a heating plant. Four control algorithms are compared: PID and PI algorithms discretized with Euler and bilinear transformation, respectively. It is shown that for the heating plant used in this work, a bilinear PI algorithm implemented in a small 8-bit microcontroller outperforms a commercial controller from Panasonic. It is also demonstrated that all the derived algorithms can be implemented using integer calculations only, obviating the need for expensive and time-consuming floating-point calculations. This work bridges the gap between control theory equations and the implementation of control systems in small embedded systems with no inherent floating-point processing power.

CALCULATION OF FUZZY RELIABILITY IN THE CASE OF RANDOM STRESS AND FUZZY FATIGUE STRENGTH

The fuzzy sets theory is introduced into the fatigue reliability analysis. The concepts of maximizing set and minimizing set are developed to decide the ordering value of each fuzzy number, and these values can be used to determine the order of the fuzzy numbers. On the basis of the works mentioned above, the membership function defining the fuzzy safety event can be calculated, and then the fuzzy reliability in the case of stress and fuzzy fatigue strength is deduced. An example is given to illustrate the method.

Degree of Compactness in I-fuzzy Topological Spaces

In this paper, the concept of degree of compactness is introduced in the general framework of I-fuzzy topological spaces, and its property is discussed. All good compactness are generalized to I-fuzzy topological spaces accordingly.

STABILITY AND STRICT POSITIVE REALNESS OF CONVEX POLYTOPES OF INTERVAL POLYNOMIALS

For an uncertain system described by convex combination of interval polynomials, its Hurwitz-stability can be guaranteed by, certain subset composed of vertices and edges. Furthermore, the testing set does not increase when the order of given system increases.

Entropy and Similarity Measure for T2SVNSs and Its Application

The objective of this paper is to present a new approach for solving the multicriteria group decision-making(MCGDM)problems in type-2 single valued neutrosophic set(T2SVNS)environment.Firstly,we give the concepts SVNS,T2SVNS and tangent similarity measure with T2SVN information.Secondly,we define a new entropy function for determining unknown attribute weights.In addition,a MCGDM method is developed based on entropy and tangent similarity measure of T2SVNSs.Finally,an illustrative example and comparative analysis are given to confirm the rationality and feasibility of the proposed method.

Zeros of Complete Symmetric Polynomials over Finite Fields

Wan and Zhang(2021) obtained a nontrivial lower bound for the number of zeros of complete symmetric polynomials over finite fields,and proposed a problem whether their bound can be improved.In this paper,the author improves Wan-Zhang's bound from three aspects.The proposed results are based on the estimates related to the number of certain permutations and the value sets of non-permutation polynomials associated to the complete symmetric polynomial.And the author believes that there are still possibilities to improve the bounds and hence Wan-Zhang's bound.

Some Generalized Single Valued Neutrosophic Linguistic Operators and Their Application to Multiple Attribute Group Decision Making

This paper proposes a group decision making method based on entropy of neutrosophic linguistic sets and generalized single valued neutrosophic linguistic operators. This method is applied to solve the multiple attribute group decision making problems under single valued neutrosophic liguistic environment, in which the attribute weights are completely unknown. First, the attribute weights are obtained by using the entropy of neutrosophic linguistic sets. Then three generalized single valued neutrosophic linguistic operators are introduced, including the generalized single valued neutrosophic linguistic weighted averaging(GSVNLWA) operator, the generalized single valued neutrosophic linguistic ordered weighted averaging(GSVNLOWA) operator and the generalized single valued neutrosophic linguistic hybrid averaging(GSVNLHA) operator, and the GSVNLWA and GSVNLHA operators are used to aggregate information. Furthermore, similarity measure based on single valued neutrosophic linguistic numbers is defined and used to sort the alternatives and obtain the best alternative. Finally,an illustrative example is given to demonstrate the feasibility and effectiveness of the developed method.

Degrees of Fuzzy Compactness in I-Fuzzy Topological Spaces

In this paper, the concept of degree of fuzzy compactness in I-fuzzy topological spaces is introduced by means of inequation. Its properties are discussed.