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
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
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
The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence ...The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (<i>λ</i>, <i>μ</i>)-ideal statistical convergence and strongly weighted (<i>λ</i>, <i>μ</i>)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.展开更多
Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging op...Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.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
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 the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and e...In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.展开更多
In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and...In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and give some correlation theorem. It is shown that <em>x</em> = {<em>x<sub>ijk</sub></em>} is ideal statistically pre-Cauchy if and only if <img src="Edit_0f9eaa1e-440b-4bac-8bae-c50bb5e5c244.bmp" alt="" /> <em>D </em>(<em>x<sub>ijk</sub></em>, <em>x<sub>pqr</sub></em>) ≥ <em>ε</em>, <em>i</em> ≤ <em>m</em>,<em> j </em>≤ <em>n</em>, <em>t </em>≤ <em>k</em>}| ≥ <em>δ</em>} ∈<em>I</em>. At the same time, we have proved <em>x</em> = {<em>x<sub>ijk</sub></em>} is ideal statistically convergent to <em>x</em><sub>0</sub> if and only if <img src="Edit_343f4dfc-82c3-4985-aebc-95c52795bb2f.bmp" alt="" />. Also, some properties of these new sequence spaces are investigated.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.
The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy rand...The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.展开更多
In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fu...In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.展开更多
The numerical characteristics of fuzzy numbers include the optimistic value, pessimistic value, expected value, and the variance. We mainly provide the calculation formulae of several numerical characteristics of fuzz...The numerical characteristics of fuzzy numbers include the optimistic value, pessimistic value, expected value, and the variance. We mainly provide the calculation formulae of several numerical characteristics of fuzzy numbers based on credibility measure. Especially, the variance of symmetric fuzzy numbers is formulated, and a super bound for the variance of fuzzy numbers is presented. Meanwhile, some conclusions relative to credibility measure, optimistic and pessimistic values are also given.展开更多
In this paper a fuzzy transportation problem under a fuzzy environment is solved using octagonal fuzzy numbers.The transportation problem is significant and has been widely studied in the field of applied mathematics ...In this paper a fuzzy transportation problem under a fuzzy environment is solved using octagonal fuzzy numbers.The transportation problem is significant and has been widely studied in the field of applied mathematics to solve a system of linear equations in many applications in science.Systems of concurrent linear equations play a vital major role in operational research.The main perspective of this research paper is to find out the minimum amount of transportation cost of some supplies through a capacitated network formerly the availability and the demand notes are octagonal fuzzy numbers.Octagonal fuzzy numbers are used and showed a membership function.To illustrate this method,a fuzzy transportation problem is solved by using octagonal fuzzy numbers using the ranking technique.It is shown that it is the best optimal solution and it is demonstrated with a numerical example.展开更多
The evaluation of thesis by undergraduate has the characteristics of multi-factor, multi-layer and easy to be affected by subjective factors. To reduce the subjectivity, triangular fuzzy number is used as index set to...The evaluation of thesis by undergraduate has the characteristics of multi-factor, multi-layer and easy to be affected by subjective factors. To reduce the subjectivity, triangular fuzzy number is used as index set to give weight, and on this basis, fuzzy comprehensive evaluation is used to evaluate the quality of graduation thesis. The empirical analysis shows that the combination of triangular fuzzy number and fuzzy comprehensive evaluation has certain practical value in the quality evaluation of graduation thesis.展开更多
Context and Motivation: The notion of goal and goal models is ideal for the alternative systems. Goal models provide us different alternatives during goal oriented requirements engineering. Question/Problem: Once we f...Context and Motivation: The notion of goal and goal models is ideal for the alternative systems. Goal models provide us different alternatives during goal oriented requirements engineering. Question/Problem: Once we find different alternatives, we need to evaluate these alternatives to select the best one. Ideas: The selection process consists of two main parts. In first part of the selection process among alternatives, we will use techniques in which we establish some evaluation criteria. The evaluation criteria are based on leaf level goals. Stakeholders are involved to contribute their opinions about the evaluation criteria. The input provided by various stakeholders is then converted into quantifiable numbers using fuzzy triangle numbers. After applying the defuzzification process on fuzzy triangle numbers we get scores (weights) for each criteria. In second part, these scores are used in the selection process to select the best alternative. Contribution: The two steps selection process helps us to select the best alternative among many alternatives. We have described the process and applied it to “cyclecomputer” selection case study.展开更多
Purpose–The purpose of this paper is to develop a multi-attribute group decision-making(MAGDM)method under the q-rung orthopair trapezoidal fuzzy environment,which calculates the interaction between the criteria depe...Purpose–The purpose of this paper is to develop a multi-attribute group decision-making(MAGDM)method under the q-rung orthopair trapezoidal fuzzy environment,which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral(q-ROTrFACI)and employ TODIM(an acronym in Portuguese of Interactive and Multi-criteria Decision Making)to consider the risk psychology of decision-makers,to determine the optimal ranking of alternatives.Design/methodology/approach–In MAGDM,q-rung orthopair trapezoidal fuzzy numbers(q-ROTrFNs)are efficient to indicate the quantitative vagueness of decision-makers.The q-ROTrFACI operator is defined and some properties are proved.Then,a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function.Based on the above,a Choquet integral-based TODIM(CI-TODIM)method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.Findings–The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria.Then,an approach is proposed to determine the center point of q–ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed.Furthermore,CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context.The illustration example of business models’solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.Originality/value–Thepaperdevelops a novelCI-TODIMmethodthat effectivelysolves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers,which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.展开更多
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
The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fu...The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.展开更多
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.
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The paper aims to investigate different types of weighted ideal statistical convergence and strongly weighted ideal convergence of double sequences of fuzzy numbers. Relations connecting ideal statistical convergence and strongly ideal convergence have been investigated in the environment of the newly defined classes of double sequences of fuzzy numbers. At the same time, we have examined relevant inclusion relations concerning weighted (<i>λ</i>, <i>μ</i>)-ideal statistical convergence and strongly weighted (<i>λ</i>, <i>μ</i>)-ideal convergence of double sequences of fuzzy numbers. Also, some properties of these new sequence spaces are investigated.
基金supported by the National Natural Science Foundation of China (70771115).
文摘Intuitionistic trapezoidal fuzzy numbers and their operational laws are defined. Based on these operational laws, some aggregation operators, including intuitionistic trapezoidal fuzzy weighted arithmetic averaging operator and weighted geometric averaging operator are proposed. Expected values, score function, and accuracy function of intuitionitsic trapezoidal fuzzy numbers are defined. Based on these, a kind of intuitionistic trapezoidal fuzzy multi-criteria decision making method is proposed. By using these aggregation operators, criteria values are aggregated and integrated intuitionistic trapezoidal fuzzy numbers of alternatives are attained. By comparing score function and accuracy function values of integrated fuzzy numbers, a ranking of the whole alternative set can be attained. An example is given to show the feasibility and availability of the method.
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.
基金This project was partly supported bythe Key Programof the National Natural Science Foundation of China (79990580) .
文摘In the conceptual design stage of complex products, CBR（Case-Based Reasoning） tool is useful to offer a feasible set of schemes. Then the most adaptive scheme can be generated through a procedure of comparison and evaluation. The procedure is essentially a multiple criteria decision-making problem. The traditional multiple criteria programming is not flexible enough in executing the system evaluation algorithm due to both the limited experimental data and the lack of human experiences. To make the CBR tool to be more efficient, a new method for the best choice among the feasible schemes based on the Fuzzy AHP using Fuzzy numbers （FFAHP） is proposed. Since the final results become a problem of ranking the mean of fuzzy numbers by the optimism of decision-maker using the FFAHP, its execution is much more intuitive and effective than with the traditional method.
文摘In this paper, we extend the notions of ideal statistically convergence for sequence of fuzzy number. We introduce the notions ideal statistically pre-Cauchy triple sequences of fuzzy number about Orlicz function, and give some correlation theorem. It is shown that <em>x</em> = {<em>x<sub>ijk</sub></em>} is ideal statistically pre-Cauchy if and only if <img src="Edit_0f9eaa1e-440b-4bac-8bae-c50bb5e5c244.bmp" alt="" /> <em>D </em>(<em>x<sub>ijk</sub></em>, <em>x<sub>pqr</sub></em>) ≥ <em>ε</em>, <em>i</em> ≤ <em>m</em>,<em> j </em>≤ <em>n</em>, <em>t </em>≤ <em>k</em>}| ≥ <em>δ</em>} ∈<em>I</em>. At the same time, we have proved <em>x</em> = {<em>x<sub>ijk</sub></em>} is ideal statistically convergent to <em>x</em><sub>0</sub> if and only if <img src="Edit_343f4dfc-82c3-4985-aebc-95c52795bb2f.bmp" alt="" />. Also, some properties of these new sequence spaces are investigated.
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.
文摘The theory of metric spaces of fuzzy numbers has been established and found very convenient in many research fields on fuzzy analysis such as fuzzy integrals and differentials, fuzzy differential equations, fuzzy random variables and fuzzy stochastic processes etc.. But, a large part of this theory heavily depends on the condition that fuzzy number has to have compact support set and so fails to analyze and apply noncompact fuzzy numbers. The purpose of this paper is to introduce three classes of metrics on noncompact fuzzy number space and to discuss their basic properties, completeness and separability in detail.
基金The NSF (10971232,60673191,60873055) of Chinathe NSF (8151042001000005,9151026005000002) of Guangdong Province+1 种基金the Guangdong Province Planning Project of Philosophy and Social Sciences (09O-19)the Guangdong Universities Subject Construction Special Foundation
文摘In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.
文摘The numerical characteristics of fuzzy numbers include the optimistic value, pessimistic value, expected value, and the variance. We mainly provide the calculation formulae of several numerical characteristics of fuzzy numbers based on credibility measure. Especially, the variance of symmetric fuzzy numbers is formulated, and a super bound for the variance of fuzzy numbers is presented. Meanwhile, some conclusions relative to credibility measure, optimistic and pessimistic values are also given.
文摘In this paper a fuzzy transportation problem under a fuzzy environment is solved using octagonal fuzzy numbers.The transportation problem is significant and has been widely studied in the field of applied mathematics to solve a system of linear equations in many applications in science.Systems of concurrent linear equations play a vital major role in operational research.The main perspective of this research paper is to find out the minimum amount of transportation cost of some supplies through a capacitated network formerly the availability and the demand notes are octagonal fuzzy numbers.Octagonal fuzzy numbers are used and showed a membership function.To illustrate this method,a fuzzy transportation problem is solved by using octagonal fuzzy numbers using the ranking technique.It is shown that it is the best optimal solution and it is demonstrated with a numerical example.
文摘The evaluation of thesis by undergraduate has the characteristics of multi-factor, multi-layer and easy to be affected by subjective factors. To reduce the subjectivity, triangular fuzzy number is used as index set to give weight, and on this basis, fuzzy comprehensive evaluation is used to evaluate the quality of graduation thesis. The empirical analysis shows that the combination of triangular fuzzy number and fuzzy comprehensive evaluation has certain practical value in the quality evaluation of graduation thesis.
基金support for the Article Processing Charge by the German Research Foundationthe Open Access Publication Fund of the Technische Universit Ilmenau.
文摘Context and Motivation: The notion of goal and goal models is ideal for the alternative systems. Goal models provide us different alternatives during goal oriented requirements engineering. Question/Problem: Once we find different alternatives, we need to evaluate these alternatives to select the best one. Ideas: The selection process consists of two main parts. In first part of the selection process among alternatives, we will use techniques in which we establish some evaluation criteria. The evaluation criteria are based on leaf level goals. Stakeholders are involved to contribute their opinions about the evaluation criteria. The input provided by various stakeholders is then converted into quantifiable numbers using fuzzy triangle numbers. After applying the defuzzification process on fuzzy triangle numbers we get scores (weights) for each criteria. In second part, these scores are used in the selection process to select the best alternative. Contribution: The two steps selection process helps us to select the best alternative among many alternatives. We have described the process and applied it to “cyclecomputer” selection case study.
基金This work is funded in part by Department of Shenzhen Local Science and Technology Development(No:2021Szvup052).
文摘Purpose–The purpose of this paper is to develop a multi-attribute group decision-making(MAGDM)method under the q-rung orthopair trapezoidal fuzzy environment,which calculates the interaction between the criteria depending on the proposed q-rung orthopair trapezoidal fuzzy aggregation Choquet integral(q-ROTrFACI)and employ TODIM(an acronym in Portuguese of Interactive and Multi-criteria Decision Making)to consider the risk psychology of decision-makers,to determine the optimal ranking of alternatives.Design/methodology/approach–In MAGDM,q-rung orthopair trapezoidal fuzzy numbers(q-ROTrFNs)are efficient to indicate the quantitative vagueness of decision-makers.The q-ROTrFACI operator is defined and some properties are proved.Then,a novel similarity measure is developed by fusing the area and coordinates of the q-rung orthopair trapezoidal fuzzy function.Based on the above,a Choquet integral-based TODIM(CI-TODIM)method to consider the risk psychology of decision-makers is proposed and two cases are provided to prove superiority of the method.Findings–The paper investigates q-ROTrFACI operator to productively solve problems with interdependent criteria.Then,an approach is proposed to determine the center point of q–ROTrFNs and a q-rung orthopair trapezoidal fuzzy similarity is constructed.Furthermore,CI-TODIM method is devised based on the proposed q-ROTrFACI operator and similarity in q-rung orthopair trapezoidal fuzzy context.The illustration example of business models’solutions and hypertension health management are given to demonstrate the effectiveness and superiority of proposed method.Originality/value–Thepaperdevelops a novelCI-TODIMmethodthat effectivelysolves the MAGDM problems under the premise of fully considering the priority of criteria and the risk preference of decision-makers,which provides guiding advantages for practical decision-making and enriches the application of decision-making theory.
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The objective is to develop a model considering demand dependent on selling price and deterioration occurs after a certain period of time, which follows two-parameter Weibull distribution. Shortages are allowed and fully backlogged. Fuzzy optimal solution is obtained by considering hexagonal fuzzy numbers and for defuzzification Graded Mean Integration Representation Method. A numerical example is provided for the illustration of crisp and fuzzy, both models. To observe the effect of changes in parameters, sensitivity analysis is carried out.
