This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel...This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex scenarios.In such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations.This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers.Subsequently,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies.Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input.Further,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions.The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision outcomes.Additionally,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.展开更多
The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper inves...The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.展开更多
The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability ...The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.展开更多
To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers ...To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.展开更多
Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration...Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration.However,the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations.In this paper,an improved method is proposed based on Z-numbers and the graded mean integration representation(GMIR)to deal with the uncertain information in FMEA.First,Z-numbers are constructed based on the evaluations of risk factors O,S,D for each failure mode by different experts.Second,weights of the three risk factors and experts are determined.Third,the integration representations of Z-numbers are obtained by a newmethod based on the GMIRmethod.Finally,risk priorities of the failure modes are derived considering the weights of experts and risk factors.Two examples and a case study are given to show the use of the proposed method and comparison with other methods.The results show that the proposed method is more reasonable,universal and simple in calculation.展开更多
Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certain...Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.展开更多
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
Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable ...Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.展开更多
Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on th...Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.展开更多
For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be ...For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.展开更多
The output of the fuzzy set is reduced by one for the defuzzification procedure.It is employed to provide a comprehensible outcome from a fuzzy inference process.This page provides further information about the defuzzi...The output of the fuzzy set is reduced by one for the defuzzification procedure.It is employed to provide a comprehensible outcome from a fuzzy inference process.This page provides further information about the defuzzifica-tion approach for quadrilateral fuzzy numbers,which may be used to convert them into discrete values.Defuzzification demonstrates how useful fuzzy ranking systems can be.Our major purpose is to develop a new ranking method for gen-eralized quadrilateral fuzzy numbers.The primary objective of the research is to provide a novel approach to the accurate evaluation of various kinds of fuzzy inte-gers.Fuzzy ranking properties are examined.Using the counterexamples of Lee and Chen demonstrates the fallacy of the ranking technique.So,a new approach has been developed for dealing with fuzzy risk analysis,risk management,indus-trial engineering and optimization,medicine,and artificial intelligence problems:the generalized quadrilateral form fuzzy number utilizing centroid methodology.As you can see,the aforementioned scenarios are all amenable to the solution pro-vided by the generalized quadrilateral shape fuzzy number utilizing centroid methodology.It’s laid out in a straightforward manner that’s easy to grasp for everyone.The rating method is explained in detail,along with numerical exam-ples to illustrate it.Last but not least,stability evaluations clarify why the Gener-alized quadrilateral shape fuzzy number obtained by the centroid methodology outperforms other ranking methods.展开更多
A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary jud...A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.展开更多
In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.
The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representat...The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.展开更多
This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual par...This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.展开更多
Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the li...Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the literature, there is no single measure that is universally applicable to a wide variety of situations. This paper suggested a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0,1] reflecting the decision makers’ risk taking attitude. The method is simple, but has many comparative advantages.展开更多
In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.
文摘This study aims to establish an expert consensus and enhance the efficacy of decision-making processes by integrating Spherical Fuzzy Sets(SFSs)and Z-Numbers(SFZs).A novel group expert consensus technique,the PHImodel,is developed to address the inherent limitations of both SFSs and the traditional Delphi technique,particularly in uncertain,complex scenarios.In such contexts,the accuracy of expert knowledge and the confidence in their judgments are pivotal considerations.This study provides the fundamental operational principles and aggregation operators associated with SFSs and Z-numbers,encompassing weighted geometric and arithmetic operators alongside fully developed operators tailored for SFZs numbers.Subsequently,a case study and comparative analysis are conducted to illustrate the practicality and effectiveness of the proposed operators and methodologies.Integrating the PHI model with SFZs numbers represents a significant advancement in decision-making frameworks reliant on expert input.Further,this combination serves as a comprehensive tool for decision-makers,enabling them to achieve heightened levels of consensus while concurrently assessing the reliability of expert contributions.The case study results demonstrate the PHI model’s utility in resolving complex decision-making scenarios,showcasing its ability to improve consensus-building processes and enhance decision outcomes.Additionally,the comparative analysis highlights the superiority of the integrated approach over traditional methodologies,underscoring its potential to revolutionize decision-making practices in uncertain environments.
基金funded by King Khalid University through a large group research project under Grant Number R.G.P.2/449/44.
文摘The main goal of informal computing is to overcome the limitations of hypersensitivity to defects and uncertainty while maintaining a balance between high accuracy,accessibility,and cost-effectiveness.This paper investigates the potential applications of intuitionistic fuzzy sets(IFS)with rough sets in the context of sparse data.When it comes to capture uncertain information emanating fromboth upper and lower approximations,these intuitionistic fuzzy rough numbers(IFRNs)are superior to intuitionistic fuzzy sets and pythagorean fuzzy sets,respectively.We use rough sets in conjunction with IFSs to develop several fairly aggregation operators and analyze their underlying properties.We present numerous impartial laws that incorporate the idea of proportionate dispersion in order to ensure that the membership and non-membership activities of IFRNs are treated equally within these principles.These operations lead to the development of the intuitionistic fuzzy rough weighted fairly aggregation operator(IFRWFA)and intuitionistic fuzzy rough ordered weighted fairly aggregation operator(IFRFOWA).These operators successfully adjust to membership and non-membership categories with fairness and subtlety.We highlight the unique qualities of these suggested aggregation operators and investigate their use in the multiattribute decision-making field.We use the intuitionistic fuzzy rough environment’s architecture to create a novel strategy in situation involving several decision-makers and non-weighted data.Additionally,we developed a novel technique by combining the IFSs with quaternion numbers.We establish a unique connection between alternatives and qualities by using intuitionistic fuzzy quaternion numbers(IFQNs).With the help of this framework,we can simulate uncertainty in real-world situations and address a number of decision-making problems.Using the examples we have released,we offer a sophisticated and systematically constructed illustrative scenario that is intricately woven with the complexity ofmedical evaluation in order to thoroughly assess the relevance and efficacy of the suggested methodology.
文摘The primary goal of this research is to determine the optimal agricultural field selection that would most effectively support manufacturing producers in manufacturing production while accounting for unpredictability and reliability in their decision-making.The PFS is known to address the levels of participation and non-participation.To begin,we introduce the novel concept of a PFZN,which is a hybrid structure of Pythagorean fuzzy sets and the ZN.The PFZN is graded in terms of membership and non-membership,as well as reliability,which provides a strong advice in real-world decision support concerns.The PFZN is a useful tool for dealing with uncertainty in decision-aid problems.The PFZN is a practical way for dealing with such uncertainties in decision-aid problems.The list of aggregation operators:PFZN Einstein weighted averaging and PFZN Einstein weighted geometric,is established under the novel Pythagorean fuzzy ZNs.It is a more precise mathematical instrument for dealing with precision and uncertainty.The core of this research is to develop a numerical algorithmto tackle the uncertainty in real-life problems using PFZNs.To show the applicability and effectiveness of the proposed algorithm,we illustrate the numerical case study related to determining the optimal agricultural field.The main purpose of this work is to describe the extended EDAS approach,then compare the proposed methodology with many other methodologies now in use,and then demonstrate how the suggested methodology may be applied to real-world problems.In addition,the final ranking results that were obtained by the devised techniques weremore efficient and dependable in comparison to the results provided by other methods presented in the literature.
文摘To address the fuzziness and variability in determining customer demand importance,a dynamic analysis method based on intuitionistic fuzzy numbers is proposed.First,selected customers use intuitionistic fuzzy numbers to represent the importance of each demand.Then,the preference information is aggregated using customer weights and time period weights through the intuitionistic fuzzy ordered weighted average operator,yielding a dynamic vector of the subjective importance of the demand index.Finally,the feasibility of the proposed method is demonstrated through an application example of a vibrating sorting screen.
基金supported by Shanghai Rising-Star Program(Grant No.21QA1403400)Shanghai Natural Science Foundation(Grant No.19ZR1420700)Shanghai Key Laboratory of Power Station Automation Technology(Grant No.13DZ2273800).
文摘Failuremode and effects analysis(FMEA)is a widely used safety assessmentmethod inmany fields.Z-number was previously applied in FMEA since it can take both possibility and reliability of information into consideration.However,the use of fuzzy weighted mean to integrate Z-valuations may have some drawbacks and is not suitable for some situations.In this paper,an improved method is proposed based on Z-numbers and the graded mean integration representation(GMIR)to deal with the uncertain information in FMEA.First,Z-numbers are constructed based on the evaluations of risk factors O,S,D for each failure mode by different experts.Second,weights of the three risk factors and experts are determined.Third,the integration representations of Z-numbers are obtained by a newmethod based on the GMIRmethod.Finally,risk priorities of the failure modes are derived considering the weights of experts and risk factors.Two examples and a case study are given to show the use of the proposed method and comparison with other methods.The results show that the proposed method is more reasonable,universal and simple in calculation.
基金funded by the Fundamental Research Grant Scheme under the Ministry of Higher Education Malaysia FRGS/1/2019/STG06/UMP/02/9.
文摘Intuitionistic fuzzy numbers incorporate the membership and non-membership degrees.In contrast,Z-numbers consist of restriction components,with the existence of a reliability component describing the degree of certainty for the restriction.The combination of intuitionistic fuzzy numbers and Z-numbers produce a new type of fuzzy numbers,namely intuitionistic Z-numbers(IZN).The strength of IZN is their capability of better handling the uncertainty compared to Zadeh's Z-numbers since both components of Z-numbers are charac-terized by the membership and non-membership functions,exhibiting the degree of the hesitancy of decision-makers.This paper presents the application of such numbers in fuzzy multi-criteria decision-making problems.A decision-making model is proposed using the trapezoidal intuitionistic fuzzy power ordered weighted average as the aggregation function and the ranking function to rank the alternatives.The proposed model is then implemented in a supplier selection problem.The obtained ranking is compared to the existing models based on Z-numbers.The results show that the ranking order is slightly different from the existing models.Sensitivity analysis is performed to validate the obtained ranking.The sensitivity analysis result shows that the best supplier is obtained using the proposed model with 80%to 100%consistency despite the drastic change of criteria weights.Intuitionistic Z-numbers play a very important role in describing the uncertainty in the decision makers’opinions in solving decision-making problems.
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.
文摘Up to now, the study on the cardinal number of fuzzy sets has advanced at on pace since it is very hard to give it an appropriate definition. Althrough for it in [1], it is with some harsh terms and is not reasonable as we point out in this paper. In the paper, we give a general definition of fuzzy cardinal numbers. Based on this definition, we not only obtain a large part of results with re spect to cardinal numbers, but also give a few of new properties of fuzzy cardinal numbers.
文摘Similarity measure is an essential tool to compare and determine the degree of similarity between intuitionistic fuzzy sets (IFSs). In this paper, a new similarity measure between intuitionistic fuzzy sets based on the mid points of transformed triangular fuzzy numbers is proposed. The proposed similarity measure provides reasonable results not only for the sets available in the literature but also gives very reasonable results, especially for fuzzy sets as well as for most intuitionistic fuzzy sets. To provide supportive evidence, the proposed similarity measure is tested on certain sets available in literature and is also applied to pattern recognition and medical diagnosis problems. It is observed that the proposed similarity measure provides a very intuitive quantification.
文摘For same cases the rules of monosource fuzzy numbers con be used into the solution of fuzzy stochastic finite element equations in engineering. This method can reduce the computing quantity of the solution. It can be proved that the amount of the solution is nearly as much as that with the general stochastic finite element method (SFEM). In addition, a new method to appreciate the structural fuzzy failure probability is presented for the needs of the modem engineering design.
文摘The output of the fuzzy set is reduced by one for the defuzzification procedure.It is employed to provide a comprehensible outcome from a fuzzy inference process.This page provides further information about the defuzzifica-tion approach for quadrilateral fuzzy numbers,which may be used to convert them into discrete values.Defuzzification demonstrates how useful fuzzy ranking systems can be.Our major purpose is to develop a new ranking method for gen-eralized quadrilateral fuzzy numbers.The primary objective of the research is to provide a novel approach to the accurate evaluation of various kinds of fuzzy inte-gers.Fuzzy ranking properties are examined.Using the counterexamples of Lee and Chen demonstrates the fallacy of the ranking technique.So,a new approach has been developed for dealing with fuzzy risk analysis,risk management,indus-trial engineering and optimization,medicine,and artificial intelligence problems:the generalized quadrilateral form fuzzy number utilizing centroid methodology.As you can see,the aforementioned scenarios are all amenable to the solution pro-vided by the generalized quadrilateral shape fuzzy number utilizing centroid methodology.It’s laid out in a straightforward manner that’s easy to grasp for everyone.The rating method is explained in detail,along with numerical exam-ples to illustrate it.Last but not least,stability evaluations clarify why the Gener-alized quadrilateral shape fuzzy number obtained by the centroid methodology outperforms other ranking methods.
文摘A method for ranking complementary judgment matrixes with traspezoidal fuzzy numbers based on Hausdorff metric distance and fuzzy compromise decision approach is proposed. With regard to fuzzy number complementary judgment matrixes given by a decider group whose members have various weights, the expert＇s information was aggregated first by means of simple weight average（SWA） method and Bonissone calculational method. Hence a matrix including all the experts＇ preference information was got. Then the matrix＇ column members were added up and the fuzzy evaluation values of the alternatives were got. Lastly, the Hausdorff metric distance and fuzzy compromise decision approach were used to rank the fuzzy evaluation values and then the ranking values of all the alternatives were got. Because exact numbers and triangular fuzzy numbers could all be transformed into trapezoidal fuzzy numbers, the method developed can rank complementary judgment matrixes with trapezoidal fuzzy numbers, triangular fuzzy numbers and exact numbers as well. An illustrative example is also given to verify the developed method and to demonstrate its feasibility and practicality.
文摘In this paper,the pointwise characterizations of fuzzy mappings are given. Based of this definition,we give a few of new properties of fuzzy cardinal numbers.
基金supported by the Deanship of Scientific Research,Vice Presidency for Graduate Studies and Scientific Research,King Faisal University,Saudi Arabia[Grant No.GRANT3862].
文摘The idea of linear Diophantine fuzzy set(LDFS)theory with its control parameters is a strong model for machine learning and optimization under uncertainty.The activity times in the critical path method(CPM)representation procedures approach are initially static,but in the Project Evaluation and Review Technique(PERT)approach,they are probabilistic.This study proposes a novel way of project review and assessment methodology for a project network in a linear Diophantine fuzzy(LDF)environment.The LDF expected task time,LDF variance,LDF critical path,and LDF total expected time for determining the project network are all computed using LDF numbers as the time of each activity in the project network.The primary premise of the LDF-PERT approach is to address ambiguities in project network activity timesmore simply than other approaches such as conventional PERT,Fuzzy PERT,and so on.The LDF-PERT is an efficient approach to analyzing symmetries in fuzzy control systems to seek an optimal decision.We also present a new approach for locating LDF-CPM in a project network with uncertain and erroneous activity timings.When the available resources and activity times are imprecise and unpredictable,this strategy can help decision-makers make better judgments in a project.A comparison analysis of the proposed technique with the existing techniques has also been discussed.The suggested techniques are demonstrated with two suitable numerical examples.
文摘This study considers an MHD Jeffery-Hamel nanofluid flow with distinct nanoparticles such as copper,Al_(2)O_(3)and SiO_(2)between two rigid non-parallel plane walls with the fuzzy extension of the generalized dual parametric homotopy algorithm.The nanofluids have been formulated to enhance the thermophysical characteristics of fluids,including thermal diffusivity,conductivity,convective heat transfer coefficients and viscosity.Due to the presence of distinct nanofluids,a change in the value of volume fraction occurs that influences the velocity profiles of the flow.The short value of nanoparticles volume fraction is considered an uncertain parameter and represented in a triangular fuzzy number range among[0.0,0.1,0.2].A novel generalized dual parametric homotopy algorithm with fuzzy extension is used here to study the fuzzy velocities at various channel positions.Finally,the effectiveness of the proposed approach has been demonstrated through a comparison with the available results in the crisp case.
文摘Fuzzy numbers are convenient for representing imprecise numerical quantities in a vague environment, and their comparison or ranking is very important for application purposes. Despite many methods suggested in the literature, there is no single measure that is universally applicable to a wide variety of situations. This paper suggested a new method for comparing fuzzy numbers based on the combination of maximizing possibility and minimizing possibility using an index of optimism in [0,1] reflecting the decision makers’ risk taking attitude. The method is simple, but has many comparative advantages.
文摘In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.
