Medical Diagnosis Based on Multi-Attribute Group Decision-Making Using Extension Fuzzy Sets,Aggregation Operators and Basic Uncertainty Information Granule

Accurate medical diagnosis,which involves identifying diseases based on patient symptoms,is often hindered by uncertainties in data interpretation and retrieval.Advanced fuzzy set theories have emerged as effective tools to address these challenges.In this paper,new mathematical approaches for handling uncertainty in medical diagnosis are introduced using q-rung orthopair fuzzy sets(q-ROFS)and interval-valued q-rung orthopair fuzzy sets(IVq-ROFS).Three aggregation operators are proposed in our methodologies:the q-ROF weighted averaging(q-ROFWA),the q-ROF weighted geometric(q-ROFWG),and the q-ROF weighted neutrality averaging(qROFWNA),which enhance decision-making under uncertainty.These operators are paired with ranking methods such as the similarity measure,score function,and inverse score function to improve the accuracy of disease identification.Additionally,the impact of varying q-rung values is explored through a sensitivity analysis,extending the analysis beyond the typical maximum value of 3.The Basic Uncertain Information(BUI)method is employed to simulate expert opinions,and aggregation operators are used to combine these opinions in a group decisionmaking context.Our results provide a comprehensive comparison of methodologies,highlighting their strengths and limitations in diagnosing diseases based on uncertain patient data.

Effect of continuous nursing on treatment compliance and side effect management of coronary heart disease

BACKGROUND There are relatively few studies on continuing care of coronary heart disease(CHD),and its research value needs to be further clarified.AIM To investigate the effect of continuous nursing on treatment compliance and side effect management in patients with CHD.METHODS This is a retrospective study with patients from January 2021 to 2023.The study was divided into two groups with 30 participants in each group.Self-rating anxiety scale(SAS)and Self-rating depression scale(SDS)were used to assess patients'anxiety and depression,and medical coping questionnaire was used to assess patients'coping styles.The pelvic floor dysfunction questionnaire(PFDI-20)was used to assess the status of pelvic floor function,including bladder symptoms,intestinal symptoms,and pelvic symptoms.RESULTS SAS score decreased from 57.33±3.01before treatment to 41.33±3.42 after treatment,SDS score decreased from 50.40±1.45 to 39.47±1.57.The decrease of these two indexes was statistically significant(P<0.05).PFDI-20 scores decreased from the mean 16.83±1.72 before treatment to 10.47±1.3the mean after treatment,which was statistically significant(P<0.05).CONCLUSION The results of this study indicate that pioneering research in continuous care of CHD has a positive impact on improving patients'treatment compliance,reducing anxiety and depression levels,and improving coping styles and pelvic floor functional status.

MAXIMAL FUNCTION CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH BOTH NON-NEGATIVE SELF-ADJOINT OPERATORS SATISFYING GAUSSIAN ESTIMATES AND BALL QUASI-BANACH FUNCTION SPACES

Assume that L is a non-negative self-adjoint operator on L^(2)(ℝ^(n))with its heat kernels satisfying the so-called Gaussian upper bound estimate and that X is a ball quasi-Banach function space onℝ^(n) satisfying some mild assumptions.Let HX,L(ℝ^(n))be the Hardy space associated with both X and L,which is defined by the Lusin area function related to the semigroup generated by L.In this article,the authors establish various maximal function characterizations of the Hardy space HX,L(ℝ^(n))and then apply these characterizations to obtain the solvability of the related Cauchy problem.These results have a wide range of generality and,in particular,the specific spaces X to which these results can be applied include the weighted space,the variable space,the mixed-norm space,the Orlicz space,the Orlicz-slice space,and the Morrey space.Moreover,the obtained maximal function characterizations of the mixed-norm Hardy space,the Orlicz-slice Hardy space,and the Morrey-Hardy space associated with L are completely new.

THE ABSENCE OF SINGULAR CONTINUOUS SPECTRUM FOR PERTURBED JACOBI OPERATORS

This paper is mainly about the spectral properties of a class of Jacobi operators(H_(c,b)u)(n)=c_(n)u(n+1)+c_(n-1)u(n-1)+b_(n)u(n),.where∣c_(n)−1∣=O(n^(−α))and b_(n)=O(n^(−1)).We will show that,forα≥1,the singular continuous spectrum of the operator is empty.

On the global L^(1)-boundedness of Fourier integral operators with rough amplitude and phase functions

Let T_(ϕ,a)be a Fourier integral operator with amplitude a and phase functions ϕ.In this paper,we study the boundedness of Fourier integral operator of rough amplitude a∈L^(∞)S_(ρ)^(m)and rough phase functionsϕ∈L^(m)ϕ^(2)with some measure condition.We prove the global L^(1)boundedness for T_(ϕ,a),when 1/<ρ≤1 and m<ρ-n+1/2.Our theorem improves some known results.

Effects of Continuous Precision Nursing Model on Knowledge, Attitudes, and Practices (KAP) Behavior and Cardiac Function in Patients after Percutaneous Coronary Angiography and Stent Implantation

Objective:To explore the impact of a continuous precision nursing model on patients’Knowledge,Attitudes,and Practices(KAP)and cardiac function during the nursing process of patients undergoing percutaneous coronary angiography and stent implantation.Methods:Ninety patients who underwent percutaneous coronary angiography and stent implantation in our hospital from April 2022 to April 2023 were selected and randomly divided into the control group(45 cases),in which routine nursing support was carried out during the treatment process,and the observation group(45 cases),in which continuous precision nursing model was carried out during the treatment process.Comparisons were made between the two groups of patients on their KAP,cardiac function,and quality of life during recovery.Results:There was no difference in the left ventricular ejection fraction(LVEF),cardiac output(CO),and cardiac index(CI)levels before intervention.After the intervention,the levels of cardiac function in the observation group were higher than those of the control group(P<0.05).There was no difference in the Exercise of Self-Care Agency(ESCA)self-care ability scale scores before the intervention.After the intervention,the observation group had higher ESCA scores than the control group(P<0.05).Conclusion:Implementation of a continuous precision nursing model in the care of patients undergoing percutaneous coronary angiography and stent implantation improved the patient’s cardiac function,and KAP,and promoted recovery.

EXACT CONTROLLABILITY AND CONTINUOUS DEPENDENCE OF FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY

In the present paper,with the help of the resolvent operator and some analytic methods,the exact controllability and continuous dependence are investigated for a fractional neutral integro-differential equations with state-dependent delay.As an application,we also give one example to demonstrate our results.

ESSENTIAL NORMS OF PRODUCTS OF WEIGHTED COMPOSITION OPERATORS AND DIFFERENTIATION OPERATORS BETWEEN BANACH SPACES OF ANALYTIC FUNCTIONS

We obtain several estimates of the essential norms of the products of differen- tiation operators and weighted composition operators between weighted Banach spaces of analytic functions with general weights. As applications, we also give estimates of the es- sential norms of weighted composition operators between weighted Banach space of analytic functions and Bloch-type spaces.

ENTIRE FUNCTIONS SHARING ONE SMALL FUNCTION CM WITH THEIR SHIFTS AND DIFFERENCE OPERATORS

In this article, we mainly devote to proving uniqueness results for entire functionssharing one small function CM with their shift and difference operator simultaneously. Letf（z） be a nonconstant entire function of finite order, c be a nonzero finite complex constant, and n be a positive integer. If f（z）, f（z＋c）, and △n cf（z） share 0 CM, then f（z＋c）≡Af（z）, where A（≠0） is a complex constant. Moreover, let a（z）, b（z）（ O） ∈ S（f） be periodic entire functions with period c and if f（z） - a（z）, f（z ＋ c） - a（z）, △cn f（z） - b（z） share 0 CM, then f（z ＋ c） ≡ f（z）.

ON THE BOUNDEDNESS AND THE NORM OF A CLASS OF INTEGRAL OPERATORS

The boundedness and the norm of a class of integral operators Ta,b,c on Lλ^P spaces are studied in this paper. The author not only gives the sufficient and necessary condition for the boundedness of Ta,b,c on Lλ^P,but also obtains its accurate norm on Lλ^P for some range under the condition of c = n ＋ a ＋ b.

PRODUCTS OF WEIGHTED COMPOSITION AND DIFFERENTIATION OPERATORS INTO WEIGHTED ZYGMUND AND BLOCH SPACES

We characterize boundedness and compactness of products of differentiation op- erators and weighted composition operators between weighted Banach spaces of analytic functions and weighted Zygmund spaces or weighted Bloch spaces with general weights.

The construction and approximation of some neural networks operators

In this paper, the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions. Using the modulus of continuity of function as a metric, the errors of the operators approximating continuous functions defined on a compact interval are estimated. Furthmore, Bochner-Riesz means operators of double Fourier series are used to construct networks operators for approximating bivariate functions, and the errors of approximation by the operators are estimated.

Elements and Experiments of Shenzhen Continuous Operating Reference Stations (SZCORS) System

Real-time kinematic GPS precise positioning has been playing an increasing role in both surveying and navigation. Based on the city’s fibre LAN network, Shenzhen Continuous Operating Reference Stations (SZCORS) system has been established and consists of GPS reference stations, system control center, user’s data center, and real-time datacom network. The SZCORS system provides users the real-time centimeter positioning or post-processing millimeter positioning. This paper makes discussion on the structure of SZCORS system. Some experiments have been made to test the usablity, and then the data has been analyzed.

SANDWICH-TYPE RESULTS FOR A CLASS OF CONVEX INTEGRAL OPERATORS

Let H（U） be the space of analytic functions in the unit disk U. For the integral operator

Composition Operators From B0 to QK and QK,0 Spaces

When φ is an analytic map of the unit disk D into itself,and X is a Banach space of analytic functions on D,define the composition operator Cφ by Cφ(f) = f οφ,for f ∈ X.In this paper,we study the boundedness and compactness of composition operators from the space B0 to QK and QK,0.

Toeplitz and Translation Operators on the q-Fock Spaces

In this work, we introduce a class of Hilbert spaces Fq of entire functions on the disk , , with reproducing kernel given by the q-exponential function eq(z);and we prove some properties concerning Toeplitz operators on this space. The definition and properties of the space extend naturally those of the well-known classical Fock space. Next, we study the multiplication operator Dq by and the q-Derivative operator on the Fock space Fq;and we prove that these operators are adjoint-operators and continuous from this space into itself. Lastly, we study a generalized translation operators and a Weyl commutation relations on Fq .

On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.

Modified approximation and error estimation for King’s type(p,q)-BBH operators

In this paper,the King’s type modification of(p,q)-Bleimann-Butzer and Hahn operators is defined.Some results based on Korovkin’s approximation theorem for these new operators are studied.With the help of modulus of continuity and the Lipschitz type maximal functions,the rate of convergence for these new operators are obtained.It is shown that the King’s type modification have better rate of convergence,flexibility than classical(p,q)-BBH operators on some subintervals.Further,for comparisons of the operators,we presented some graphical examples and the error estimation in the form of tables through MATLAB(R2015a)

A NOTE ON MEYER-KONIG AND ZELLER OPERATORS FOR FUNCTIONS OF BOUNDED VARIATION

In the present note we give the correct and improved estimate on the rate of convergence of integrated Meyer-Konig and Zetter operators for function of bounded variation.

LEIBNIZ′FORMULA OF GENERALIZED DIFFERENCE WITH RESPECT TO A CLASS OF DIFFERENTIAL OPERATORS AND RECURRENCE FORMULA OF THEIR GREEN′S FUNCTION

In this paper, Leibniz' formula of generalized divided difference with respect to a class of differential operators whose basic sets of solutions have power form, is considered. The recurrence formula of Green function about the operators is also given.