In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis...In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.展开更多
Efficient quantum circuits for arithmetic operations are vital for quantum algorithms.A fault-tolerant circuit is required for a robust quantum computing in the presence of noise.Quantum circuits based on Clifford+T g...Efficient quantum circuits for arithmetic operations are vital for quantum algorithms.A fault-tolerant circuit is required for a robust quantum computing in the presence of noise.Quantum circuits based on Clifford+T gates are easily rendered faulttolerant.Therefore,reducing the T-depth and T-Count without increasing the qubit number represents vital optimization goals for quantum circuits.In this study,we propose the fault-tolerant implementations for TR and Peres gates with optimized T-depth and T-Count.Next,we design fault-tolerant circuits for quantum arithmetic operations using the TR and Peres gates.Then,we implement cyclic and complete translations of quantum images using quantum arithmetic operations,and the scalar matrix multiplication.Comparative analysis and simulation results reveal that the proposed arithmetic and image operations are efficient.For instance,cyclic translations of a quantum image produce 50%T-depth reduction relative to the previous best-known cyclic translation.展开更多
Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Mos...Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Most numeral systems make use of a base,typically 10,less commonly 20,followed by a wide range of other possibilities.Higher numerals are formed from primitive lower numerals by applying the processes of addition and multiplication,in many languages also exponentiation;sometimes,however,numerals are formed from a higher numeral,using subtraction or division.Numerous complexities and idiosyncrasies are discussed,as are numeral systems that fall outside this general characterization,such as restricted numeral systems with no internal arithmetic structure,and some New Guinea extended body-part counting systems.展开更多
Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester...Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.展开更多
Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their...Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.展开更多
Purpose-The aim of this study as to find out an approach for emergency program selection.Design/methodology/approach-The authors have generated six aggregation operators(AOs),namely picture fuzzy Yager weighted averag...Purpose-The aim of this study as to find out an approach for emergency program selection.Design/methodology/approach-The authors have generated six aggregation operators(AOs),namely picture fuzzy Yager weighted average(PFYWA),picture fuzzy Yager ordered weighted average,picture fuzzy Yager hybrid weighted average,picture fuzzy Yager weighted geometric(PFYWG),picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.Findings-First of all,the authors defined the score and accuracy function for picture fuzzy set(FS),and some fundamental operational laws for picture FS using the Yager aggregation operation.After that,using the developed operational laws,developed some AOs,namely PFYWA,picture fuzzy Yager ordered weighted average,picture fuzzy Yager hybrid weighted average,PFYWG,picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators,have been proposed along with their desirable properties.A decision-making(DM)approach based on these operators has also been presented.An illustrative example has been given for demonstrating the approach.Finally,discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.Originality/value-To find the best alternative for emergency program selection.展开更多
A neutrosophic number(NN)(d=μ+vI)can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I.Regarding the hybrid concept of intuitionistic fuzzy set(IFS)and NN,this stu...A neutrosophic number(NN)(d=μ+vI)can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I.Regarding the hybrid concept of intuitionistic fuzzy set(IFS)and NN,this study presents an orthopair indeterminate set(OIS),an orthopair indeterminate element weighted arithmetic averaging(OIEWAA)operator and an orthopair indeterminate element weighted geometric averaging(OIEWGA)operator to simplify and generalise the existing IFS and interval-valued IFS expressions and aggregation forms.Thus,a multiattribute decision making(DM)approach with indeterminate ranges of decision makers is developed based on the OIEWAA and OIEWGA operators and the score and accuracy functions of orthopair indeterminate elements in OIS setting.Finally,the proposed DM approach is applied to a multi-attribute DM example of manufacturing schemes(alternatives)in OIS setting to demonstrate the applicability and flexibility of the proposed DM approach in OIS setting.展开更多
文摘In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.
基金supported by the National Natural Science Foundation of China(Grant Nos.61762012,and 61763014)the Science and Technology Project of Guangxi(Grant No.2018JJA170083)+3 种基金the National Key Research and Development Plan(Grant Nos.2018YFC1200200,and 2018YFC1200205)the Fund for Distinguished Young Scholars of Jiangxi Province(Grant No.2018ACB2101)the Natural Science Foundation of Jiangxi Province of China(Grant No.20192BAB207014)the Science and Technology Research Project of Jiangxi Provincial Education Department(Grant No.GJJ190297)。
文摘Efficient quantum circuits for arithmetic operations are vital for quantum algorithms.A fault-tolerant circuit is required for a robust quantum computing in the presence of noise.Quantum circuits based on Clifford+T gates are easily rendered faulttolerant.Therefore,reducing the T-depth and T-Count without increasing the qubit number represents vital optimization goals for quantum circuits.In this study,we propose the fault-tolerant implementations for TR and Peres gates with optimized T-depth and T-Count.Next,we design fault-tolerant circuits for quantum arithmetic operations using the TR and Peres gates.Then,we implement cyclic and complete translations of quantum images using quantum arithmetic operations,and the scalar matrix multiplication.Comparative analysis and simulation results reveal that the proposed arithmetic and image operations are efficient.For instance,cyclic translations of a quantum image produce 50%T-depth reduction relative to the previous best-known cyclic translation.
文摘Numeral systems in natural languages show astonishing variety,though with very strong unifying tendencies that are increasing as many indigenous numeral systems disappear through language contact and globalization.Most numeral systems make use of a base,typically 10,less commonly 20,followed by a wide range of other possibilities.Higher numerals are formed from primitive lower numerals by applying the processes of addition and multiplication,in many languages also exponentiation;sometimes,however,numerals are formed from a higher numeral,using subtraction or division.Numerous complexities and idiosyncrasies are discussed,as are numeral systems that fall outside this general characterization,such as restricted numeral systems with no internal arithmetic structure,and some New Guinea extended body-part counting systems.
基金supported by the National Natural Science Foundation of China (61703426)the National Social Science Foundation of China.
文摘Intelligent wars can take place not only in the physical domain and information domain but also in the cognitive domain.The cognitive domain will become the key domain to win in the future intelligent war.A Lanchester equation considering cognitive domain is proposed to fit the development tendency intelligent wars in this paper.One party is considered to obtain the exponential enhancement advantage on combat forces in combat if it can gain an advantage in the cognitive domain over the other party according to the systemic advantage function.The operational effectiveness of the cognitive domain in war is considered to consist of a series of indicators.Hesitant fuzzy sets and linguistic term sets are powerful tools when evaluating indicators,hence the indicators are scored by experts using hesitant fuzzy linguistic terms sets here.A unique hesitant fuzzy hybrid arithmetical averaging operator is used to aggregate the evaluation.
基金This study has received funding by the Science and Technology Plan Project of Keqiao District(No.2020KZ58).
文摘Since existing selection methods of surgical treatment schemes of renal cancer patients mainly depend on physicians’clinical experience and judgments,the surgical treatment options of renal cancer patients lack their scientifical and reasonable information expression and group decision-making model for renal cancer patients.Fuzzy multi-sets(FMSs)have a number of properties,which make them suitable for expressing the uncertain information of medical diagnoses and treatments in group decision-making(GDM)problems.To choose the most appropriate surgical treatment scheme for a patient with localized renal cell carcinoma(RCC)(T1 stage kidney tumor),this article needs to develop an effective GDM model based on the fuzzy multivalued evaluation information of the renal cancer patients.First,we propose a conversionmethod of transforming FMSs into entropy fuzzy sets(EFSs)based on the mean and Shannon entropy of a fuzzy sequence in FMS to reasonably simplify the information expression and operations of FMSs and define the score function of an entropy fuzzy element(EFE)for ranking EFEs.Second,we present the Aczel-Alsina t-norm and t-conorm operations of EFEs and the EFE Aczel-Alsina weighted arithmetic averaging(EFEAAWAA)and EFE Aczel-Alsina weighted geometric averaging(EFEAAWGA)operators.Third,we develop a multicriteria GDM model of renal cancer surgery options in the setting of FMSs.Finally,the proposed GDM model is applied to two clinical cases of renal cancer patients to choose the best surgical treatment scheme for a renal cancer patient in the setting of FMSs.The selected results of two clinical cases verify the efficiency and rationality of the proposed GDM model in the setting of FMSs.
基金supported by Higher Education Commission(HEC)under National Research Program for University(NRPU),Project title,Fuzzy Mathematical Modelling for Decision Support Systems and Smart Grid Systems(No.10701/KPK/NRPU/R&D/HEC/2017).
文摘Purpose-The aim of this study as to find out an approach for emergency program selection.Design/methodology/approach-The authors have generated six aggregation operators(AOs),namely picture fuzzy Yager weighted average(PFYWA),picture fuzzy Yager ordered weighted average,picture fuzzy Yager hybrid weighted average,picture fuzzy Yager weighted geometric(PFYWG),picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators.Findings-First of all,the authors defined the score and accuracy function for picture fuzzy set(FS),and some fundamental operational laws for picture FS using the Yager aggregation operation.After that,using the developed operational laws,developed some AOs,namely PFYWA,picture fuzzy Yager ordered weighted average,picture fuzzy Yager hybrid weighted average,PFYWG,picture fuzzy Yager ordered weighted geometric and picture fuzzy Yager hybrid weighted geometric aggregations operators,have been proposed along with their desirable properties.A decision-making(DM)approach based on these operators has also been presented.An illustrative example has been given for demonstrating the approach.Finally,discussed the comparison of the proposed method with the other existing methods and write the conclusion of the article.Originality/value-To find the best alternative for emergency program selection.
文摘A neutrosophic number(NN)(d=μ+vI)can flexibly represent the indeterminate information corresponding to values/ranges of the indeterminacy I.Regarding the hybrid concept of intuitionistic fuzzy set(IFS)and NN,this study presents an orthopair indeterminate set(OIS),an orthopair indeterminate element weighted arithmetic averaging(OIEWAA)operator and an orthopair indeterminate element weighted geometric averaging(OIEWGA)operator to simplify and generalise the existing IFS and interval-valued IFS expressions and aggregation forms.Thus,a multiattribute decision making(DM)approach with indeterminate ranges of decision makers is developed based on the OIEWAA and OIEWGA operators and the score and accuracy functions of orthopair indeterminate elements in OIS setting.Finally,the proposed DM approach is applied to a multi-attribute DM example of manufacturing schemes(alternatives)in OIS setting to demonstrate the applicability and flexibility of the proposed DM approach in OIS setting.
