Fermatean Hesitant Fuzzy Prioritized Heronian Mean Operator and Its Application in Multi-Attribute Decision Making

In real life,incomplete information,inaccurate data,and the preferences of decision-makers during qualitative judgment would impact the process of decision-making.As a technical instrument that can successfully handle uncertain information,Fermatean fuzzy sets have recently been used to solve the multi-attribute decision-making(MADM)problems.This paper proposes a Fermatean hesitant fuzzy information aggregation method to address the problem of fusion where the membership,non-membership,and priority are considered simultaneously.Combining the Fermatean hesitant fuzzy sets with Heronian Mean operators,this paper proposes the Fermatean hesitant fuzzy Heronian mean(FHFHM)operator and the Fermatean hesitant fuzzyweighted Heronian mean(FHFWHM)operator.Then,considering the priority relationship between attributes is often easier to obtain than the weight of attributes,this paper defines a new Fermatean hesitant fuzzy prioritized Heronian mean operator(FHFPHM),and discusses its elegant properties such as idempotency,boundedness and monotonicity in detail.Later,for problems with unknown weights and the Fermatean hesitant fuzzy information,aMADM approach based on prioritized attributes is proposed,which can effectively depict the correlation between attributes and avoid the influence of subjective factors on the results.Finally,a numerical example of multi-sensor electronic surveillance is applied to verify the feasibility and validity of the method proposed in this paper.

INFINITELY MANY SOLUTIONS OF DIRICHLET PROBLEM FOR p-MEAN CURVATURE OPERATOR

The existence of infinitely many solutions of the following Dirichlet problem for p-mean curvature operator:-div((1+|u| 2) p-22u)=f(x,u),\ x∈Ω, u∈W 1,p 0(Ω),is considered, where Ω is a bounded domain in R n(n>p>1) with smooth boundary Ω.Under some natural conditions together with some conditions weaker than (AR) condition,we prove that the above problem has infinitely many solutions by a symmetric version of the Mountain Pass Theorem if f(x,u)|u| p-2u→+∞ as u→∞.

BEST APPROXIMATION FOR WEIERSTRASS TRANSFORM CONNECTED WITH SPHERICAL MEAN OPERATOR

Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.

Cubic q-Rung Orthopair Fuzzy Linguistic Set and Their Application to Multiattribute Decision-making with Muirhead Mean Operator

The objective of this paper is to present a new concept,named cubic q-rung orthopair fuzzy linguistic set(Cq-ROFLS),to quantify the uncertainty in the information.The proposed Cq-ROFLS is a qualitative form of cubic q-rung orthopair fuzzy set,where membership degrees and nonmembership degrees are represented in terms of linguistic variables.The basic notions of Cq-ROFLS have been introduced and study their basic operations and properties.Furthermore,to aggregate the different pairs of preferences,we introduce the Cq-ROFL Muirhead mean-(MM),weighted MM-,dual MM-based operators.The major advantage of considering the MM is that it considers the interrelationship between more than two arguments at a time.On the other hand,the Cq-ROFLS has the ability to describe the qualitative information in terms of linguistic variables.Several properties and relation of the derived operators are argued.In addition,we also investigate multiattribute decision-making problems under the Cq-ROFLS environment and illustrate with a numerical example.Finally,the effectiveness and advantages of the work are established by comparing with other methods.

Novel Complex T-Spherical Dual Hesitant Uncertain Linguistic Muirhead Mean Operators and Their Application in Decision-Making

In this manuscript,the theory of complex T-spherical dual hesitant uncertain linguistic set is discovered,which is the mixture of three different ideas like the complex T-spherical fuzzy set,dual hesitant fuzzy set,and uncertain linguistic set.The complex T-spherical dual hesitant uncertain linguistic set composes the uncertain linguistic set,truth grade,abstinence grade,and falsity grade.Whose real and imaginary parts are the subset of a unit interval,and some of their operational laws are also presented.The theory of complex T-spherical dual hesitant uncertain linguistic Muirhead mean operator,complex T-spherical dual hesitant uncertain linguistic weighted Muirhead mean operator,complex T-spherical dual hesitant uncertain linguistic dual Muirhead mean operator and complex T-spherical dual hesitant uncertain linguistic weighted dual Muirhead mean operator are discovered.Some exceptional cases of the proposed operators are also examined.A multi-attribute decision making technique is further utilized based on explored operators.Moreover,an enterprise informatization level evaluation issue is resolved by using the presented operators to verify the proficiency and capability of the discovered approaches.Finally,some comparative analysis and advantages of the explored works are further developed to express that it is more flexible and effective than the existing methods.

Unilateral global interval bifurcation for problem with mean curvature operator in Minkowski space and its applications

In this paper,we establish a unilateral global bifurcation result from interval for a class problem with mean curvature operator in Minkowski space with non-differentiable nonlinearity.As applications of the above result,we shall prove the existence of one-sign solutions to the following problem{−div(√∇v 1−|∇v|^(2))=α(x)v^(+)+β(x)v^(−)+λa(x)f(v),in B_(R)(0),v(x)=0,on∂B_(R)(0),whereλ≠=0 is a parameter,R is a positive constant and BR(0)={x∈RN:|x|<R}is the standard open ball in the Euclidean space RN(N≥1)which is centered at the origin and has radius R.v^(+)=max{v,0},v−=−min{v,0},a(x)∈C(BR(0),(0,+∞)),α(x),β(x)∈C(BR(0)),a(x),α(x)andβ(x)are radially symmetric with respect to x;f∈C(R,R),sf(s)>0 for s≠=0,and f_(0)∈[0,∞],where f0=lim_(|s|)→0 f(s)/s.We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.We also study the asymptotic behaviors of positive radial solutions asλ→+∞.

Method of accurately calculating mean field operator in multi-configuration time-dependent Hartree-Fock frame

The accurate theoretical expressions of the mean field operator associated with the multi-configuration time-dependent Hartree-Fock （MCTDHF） method are presented in this paper. By using a theoretical formula, derived without approxima- tion, we can study the multi-electron correlation dynamics accurately. Some illustrative calculations are carried out to check the accuracy of the expression of the mean field operator. The results of illustrative calculations indicate the reliability of the accurate expression of the mean field operator. This theoretical calculation method for the mean field operator may be of considerable help in future studies of the correlated dynamics of many-electron systems in strong laser fields.

NOTES ON THE SPECTRAL PROPERTIES OF THE WEIGHTED MEAN DIFFERENCE OPERATOR G(u,v;?) OVER THE SEQUENCE SPACE ?_1

In the study by Baliarsingh and Dutta [Internat. J.Anal., Vol.2014（2014）, Article ID 786437], the authors computed the spectrum and the fine spectrum of the product operator G （u, v; A） over the sequence space e1. The product operator G （u, v; △） over l1 is defined by （G（u,v;△）x）k=^k∑i=0ukvi（xi- xi-1） with xk = 0 for all k 〈 0, where x = （xk）∈e1,and u and v axe either constant or strictly decreasing sequences of positive real numbers satisfying certain conditions. In this article we give some improvements of the computation of the spectrum of the operator G （u, v; △） on the sequence space gl.

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.

EQUIVALENCE THEOREM ON WEIGHTED SIMULTANEOUS L-APPROXIMATION BY MEANS OF SZASZ-KANTOROVICH OPERATORS AND BASKAKOV-KANTOROVICH OPERATORS

The intention of this paper is to give direct and converse results on weighted simultaneous approximation by means of Sz(?)sz-Kantorovich operators and Baskakov-Kantorovich operators in L_p-norms using the weighted Ditzian-Totik modulus of smoothness.

Solving the Jaynes-Cummings Model with Shift Operators Constructed by Means of the Matrix-Diagonalizing Technique

The Jaynes-Cummings model is solved with the raising and lowering（shift） operators using the matrix-diagonalizing technique. Bell nonlocality is also found to be present ubiquitously in the excitation states of the model.

On an Axiomatic about Functional Means

In this paper, we introduce an axiomatic approach about functional means. This includes that of operator means already introduced in the literature.

A Novel Green Supplier Selection Method Based on the Interval Type-2 Fuzzy Prioritized Choquet Bonferroni Means

In view of the environment competencies,selecting the optimal green supplier is one of the crucial issues for enterprises,and multi-criteria decision-making(MCDM)methodologies can more easily solve this green supplier selection(GSS)problem.In addition,prioritized aggregation(PA)operator can focus on the prioritization relationship over the criteria,Choquet integral(CI)operator can fully take account of the importance of criteria and the interactions among them,and Bonferroni mean(BM)operator can capture the interrelationships of criteria.However,most existing researches cannot simultaneously consider the interactions,interrelationships and prioritizations over the criteria,which are involved in the GSS process.Moreover,the interval type-2 fuzzy set(IT2FS)is a more effective tool to represent the fuzziness.Therefore,based on the advantages of PA,CI,BM and IT2FS,in this paper,the interval type-2 fuzzy prioritized Choquet normalized weighted BM operators with fuzzy measure and generalized prioritized measure are proposed,and some properties are discussed.Then,a novel MCDM approach for GSS based upon the presented operators is developed,and detailed decision steps are given.Finally,the applicability and practicability of the proposed methodology are demonstrated by its application in the shared-bike GSS and by comparisons with other methods.The advantages of the proposed method are that it can consider interactions,interrelationships and prioritizations over the criteria simultaneously.

GLOBAL STRUCTURE OF A NODAL SOLUTIONS SET OF MEAN CURVATURE EQUATION IN STATIC SPACETIME

By bifurcation and topological methods,we study the global structure of a radial nodal solutions set of the mean curvature equation in a standard static spacetime div {a∇u√1−a^(2)|∇u|^(2)+g(∇u,∇a)/√1−a^(2)|∇u|^(2)=λNH,with a 0-Dirichlet boundary condition on the unit ball.According to the behavior of H near 0,we obtain the global structure of sign-changing radial spacelike graphs for this problem.

Selecting suitable key supplier for core components during smart complex equipment central-private enterprises collaborative development process:from two different forms of evaluation information and matching perspective

With the development of central-private enterprises integration,selecting suitable key suppliers are able to provide core components for smart complex equipment.We consider selecting suitable key suppliers from matching perspective,for it not only satisfies natural development of smart complex equipment,it is also a good implementation of equipment project in central-private enterprises integration context.In in this paper,we carry out two parts of research,one is evaluation attributes based on comprehensive analysis,and the other is matching process between key suppliers and core components based on the matching attribute.In practical analysis process,we employ comprehensive evaluated analysis methods to acquire relevant attributes for the matching process that follows.In the analysis process,we adopt entropy-maximum deviation method(MDM)-decision-making trial and evaluation laboratory(DEMATEL)-technique for order preference by similarity to an ideal solution(TOPSIS)to obtain a comprehensive analysis.The entropy-MDM is applied to get weight value,DEMATEL is utilized to obtain internal relations,and TOPSIS is adopted to get ideal evaluated solution.We consider aggregating two types of evaluation information according to similarities of smart complex equipment based on the combination between geometric mean and arithmetic mean.Moreover,based on the aforementioned attributes and generalized power Heronian mean operator,we aggregate preference information to acquire relevant satisfaction degree,then combine the constructed matching model to get suitable key supplier.Through comprehensive analysis of selecting suitable suppliers,we know that two-sided matching and information aggregation can provide more research perspectives for smart complex equipment.Through analysis for relevant factors,we find that leading role and service level are also significant for the smart complex equipment development process.

Medical Waste Treatment Station Selection Based on Linguistic q-Rung Orthopair Fuzzy Numbers

During the COVID-19 outbreak,the use of single-use medical supplies increased significantly.It is essential to select suitable sites for establishing medical waste treatment stations.It is a big challenge to solve the medical waste treatment station selection problem due to some conflicting factors.This paper proposes a multi-attribute decision-making(MADM)method based on the partitioned Maclaurin symmetric mean(PMSM)operator.For the medical waste treatment station selection problem,the factors or attributes(these two terms can be interchanged.)in the same clusters are closely related,and the attributes in different clusters have no relationships.The partitioned Maclaurin symmetric mean function(PMSMF)can handle these complex attribute relationships.Hence,we extend the PMSM operator to process the linguistic q-rung orthopair fuzzy numbers(Lq-ROFNs)and propose the linguistic q-rung orthopair fuzzy partitioned Maclaurin symmetric mean(Lq-ROFPMSM)operator and its weighted form(Lq-ROFWPMSM).To reduce the negative impact of unreasonable data on the final output results,we propose the linguistic q-rung orthopair fuzzy partitioned dual Maclaurin symmetric mean(Lq-ROFPDMSM)operator and its weighted form(Lq-ROFWPDMSM).We also discuss the characteristics and typical examples of the above operators.A novel MADM method uses the Lq-ROFWPMSM operator and the Lq-ROFWPDMSM operator to solve the medical waste treatment station selection problem.Finally,the usability and superiority of the proposed method are verified by comparing it with previous methods.

Maps on Positive Cones of C^(*)-algebras

We prove that a surjective map(on the positive cones of unital C^(*)-algebras)preserves the minimum spectrum values of harmonic means if and only if it has a Jordan *-isomorphism extension to the whole algebra.We represent weighted geometric mean preserving bijective maps on the positive cones of prime C^(*)-algebras in terms of Jordan *-isomorphisms of the algebras.We also characterize order isomorphisms and orthoisomorphisms of the projection lattice of the von Neumann algebra of all bounded linear operators on a Hilbert space,answering an open question arisen by Dye.Finally,we give a description for Fuglede-Kadison determinant preserving maps on the positive cone of a finite von Neumann algebra and improve Gaal and Nayak’s work on this topic.

Weighted Inequalities in Martingale Spaces

We give a condition on the couple of weights（u,v） for Doob＇s operator to be a bounded one from martingale space Lp（u） to function space Lp（v） .Moreover,we also obtain necessary and sufficient conditions in order that the maximal geometric mean operator is bounded from martingale space Lp（u） to function space Lp（v） or Lp,∞（v） .