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
In this article, we introduce and examine some properties of new difference sequence spaces of fuzzy numbers defined using a sequence of modulus functions.
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
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
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 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 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
This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis...This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.展开更多
Building upon the concept of Dα operator introduced by Atanassov （1989）, thin article proposes an improved objective approach and a hybrid approach to operationalize Dα so that the hesitation in an intuitionistic ...Building upon the concept of Dα operator introduced by Atanassov （1989）, thin article proposes an improved objective approach and a hybrid approach to operationalize Dα so that the hesitation in an intuitionistic fuzzy number （IFN） can be further refined and characterized. Numerical experiments are carried out to demonstrate the features and novelty of the proposed approach compared to existing methods in the literature. The aim is to furnish an effective way to refine hesitations in intuitionistic fuzzy assessments for more reliable and confident decision aids.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
Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for grou...Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistie fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers＇ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.展开更多
In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by gene...In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers （GITFNs）. Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.展开更多
Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper...Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper, based on the level characteristic function and α-average of level cut sets of fuzzy number, we establish the IMα-metric method for measuring fuzzy number as a whole, and introduce the concept of IDα-difFerence that describes the reliability of IMα-metric value. Further, the basic properties and the separability of IMα-metric and IDα-difference are discussed. Finally, we give a mathematical model to solve fuzzy optimization problems by means of IMα-metric.展开更多
Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameter...Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameters.Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions.The first method eliminates the non-negativity constraint from the coefficient matrix while the second method eliminates the constraint of non-negativity on the solution vector.The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.Design/methodology/approach–The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system.Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.Findings–The results that are obtained reveal interesting properties of a FFLS.By using the proposed methods,the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions,i.e.trivial,unique or infinite.Further it is also seen that an n£n FFLS may yield finitely many solutions which may not be entirely feasible(strong).Also the methods successfully remove the non-negativity restriction on the coefficient matrix and the solution vector,respectively.Research limitations/implications–Evolving methods with better computational complexity and that which remove the non-negativity restriction jointly on all the parameters are left as an open problem.Originality/value–The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists.The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations.Heretofore,the usability of FFLS is largely dormant.展开更多
In this paper,we consider a modification of the well-known logistic family using a family of fuzzy numbers.The dynamics of this modified logistic map is studied by computing its topological entropy with a given accura...In this paper,we consider a modification of the well-known logistic family using a family of fuzzy numbers.The dynamics of this modified logistic map is studied by computing its topological entropy with a given accuracy.This computation allows us to characterize when the dynamics of the modified family is chaotic.Besides,some attractors that appear in bifurcation diagrams are explained.Finally,we will show that the dynamics induced by the logistic family on the fuzzy numbers need not be complicated at all.展开更多
Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. ...Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.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 distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platfor...The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platforms,there raises the concern over the validation of virtual product designs and their manufacturing procedures for novices as well as users with 3D printing experience before physical products are produced through the cloud platform.This paper presents a 3D model to help users validate their designs and requirements not only in the traditional digital 3D model properties like shape and size,but also in physical material properties and manufacturing properties when producing physical products like surface roughness,print accuracy and part cost.These properties are closely related to the process of 3D printing and materials.In order to establish the 3D model,the paper analyzes the model of the 3D printing process selection in the cloud platform.Triangular intuitionistic fuzzy numbers are applied to generate a set of 3D printers with the same process and material.Based on the 3D printing process selection model,users can establish the 3D model and validate their designs and requirements on physical material properties and manufacturing properties before printing physical products.展开更多
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.
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.
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.
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 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This study presents a new approach that advances the algorithm of similarity measures between generalized fuzzy numbers. Following a brief introduction to some properties of the proposed method, a comparative analysis based on 36 sets of generalized fuzzy numbers was performed, in which the degree of similarity of the fuzzy numbers was calculated with the proposed method and seven methods established by previous studies in the literature. The results of the analytical comparison show that the proposed similarity outperforms the existing methods by overcoming their drawbacks and yielding accurate outcomes in all calculations of similarity measures under consideration. Finally, in a numerical example that involves recommending cars to customers based on a nine-member linguistic term set, the proposed similarity measure proves to be competent in addressing fuzzy number recommendation problems.
基金financially supported by the funding(No.JA09291)from the Fujian Education Department,Chinathe Natural Sciences and Engineering Research Council of Canada(NSERC)under its Discovery Grant program the Natural Science Foundation of China(Nos.71272129 and 71271188)
文摘Building upon the concept of Dα operator introduced by Atanassov （1989）, thin article proposes an improved objective approach and a hybrid approach to operationalize Dα so that the hesitation in an intuitionistic fuzzy number （IFN） can be further refined and characterized. Numerical experiments are carried out to demonstrate the features and novelty of the proposed approach compared to existing methods in the literature. The aim is to furnish an effective way to refine hesitations in intuitionistic fuzzy assessments for more reliable and confident decision aids.
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.
基金supported by the National Natural Sciences Foundation of China(No.71221061)China Postdoctoral Science Foundation(No.2014M552169)Central South University Business Management Postdoctoral Research Station
文摘Considering the decision maker＇s risk psychological factors and information ambiguity under uncertainty, a novel TOPSIS based on prospect theory （PT） and trapezoidal intuitionistic fuzzy numbers （YrIFNs） for group decision making is investigated, in which the criteria values and the criteria weights take the form of TrIFNs, and weights of decision makers are unknown. Firstly, distance measures for TrIFNs are used to induce value function under trapezoidal intuitionistic fuzzy environment. Secondly, the concepts of distance measures and trapezoidal intuitionistie fuzzy weighted averaging operator are employed to induce the weights of decision makers and thus the decision makers＇ options can be aggregated. Then the PT-based separation measures and relative closeness coefficient are defined and an algorithm for ranking alternatives under trapezoidal intuitionistic fuzzy environment is proposed. Finally, a numerical example further illustrates the practicality and effectiveness of the proposed TOPSIS method.
基金supported by a grant from Natural Science Foundation in China(71171202, 71171201,71210003)the Science Foundation for National Innovation Research Group in China(71221061)Key Project for National Natural Science Foundation in China (71431006)
文摘In this paper, a new decision making approach is proposed for the multi-attribute large group emergency decision-making problem that attribute weights are unknown and expert preference information is expressed by generalized interval-valued trapezoidal fuzzy numbers （GITFNs）. Firstly, a degree of similarity formula between GITFNs is presented. Secondly, expert preference information on different alternatives is clustered into several aggregations via the fuzzy clustering method. As the clustering proceeds, an index of group preference consistency is introduced to ensure the clustering effect, and then the group preference information on different alternatives is obtained. Thirdly, the TOPSIS method is used to rank the alternatives. Finally, an example is taken to show the feasibility and effectiveness of this approach. These method can ensure the consistency degree of group preference, thus decision efficiency of emergency response activities can be improved.
基金This work was supported by the National Natural Science Foundation of China (Grant No. 60004010)China Postdoctoral Science Foundation.
文摘Ranking and comparing fuzzy numbers is an important part in many fuzzy optimization problems such as intelligent control and manufacturing system production line scheduling with uncertainty environments. In this paper, based on the level characteristic function and α-average of level cut sets of fuzzy number, we establish the IMα-metric method for measuring fuzzy number as a whole, and introduce the concept of IDα-difFerence that describes the reliability of IMα-metric value. Further, the basic properties and the separability of IMα-metric and IDα-difference are discussed. Finally, we give a mathematical model to solve fuzzy optimization problems by means of IMα-metric.
文摘Purpose–The purpose of this paper is to study a nascent theory and an emerging concept of solving a fully fuzzy linear system(FFLS)with no non negative restrictions on the triangular fuzzy numbers chosen as parameters.Two new simplified computational methods are proposed to solve a FFLS without any sign restrictions.The first method eliminates the non-negativity constraint from the coefficient matrix while the second method eliminates the constraint of non-negativity on the solution vector.The methods are introduced with an objective to broaden the domain of fuzzy linear systems to encompass a wide range of problems occurring in reality.Design/methodology/approach–The design of numerical methods is motivated by decomposing the fuzzy based linear system into its equivalent crisp linear form which can be further solved by variety of classical methods to solve a crisp linear system.Further the paper investigates Schur complement technique to solve the crisp equivalent of the FFLS.Findings–The results that are obtained reveal interesting properties of a FFLS.By using the proposed methods,the authors are able to check the consistency of the fuzzy linear system as well as obtain the nature of obtained solutions,i.e.trivial,unique or infinite.Further it is also seen that an n£n FFLS may yield finitely many solutions which may not be entirely feasible(strong).Also the methods successfully remove the non-negativity restriction on the coefficient matrix and the solution vector,respectively.Research limitations/implications–Evolving methods with better computational complexity and that which remove the non-negativity restriction jointly on all the parameters are left as an open problem.Originality/value–The proposed methods are new and conceptually simple to understand and apply in several scientific areas where fuzziness persists.The methods successfully remove several constraints that have been employed exhaustively by researchers and thus eventually tend to widen the breadth of applicability and usability of fuzzy linear models in real life situations.Heretofore,the usability of FFLS is largely dormant.
基金supported by the grant MTM2017-84079-P funded by MCIN/AEI/10.13039/501100011033by“ERDF A way of making Europe”by the European Union。
文摘In this paper,we consider a modification of the well-known logistic family using a family of fuzzy numbers.The dynamics of this modified logistic map is studied by computing its topological entropy with a given accuracy.This computation allows us to characterize when the dynamics of the modified family is chaotic.Besides,some attractors that appear in bifurcation diagrams are explained.Finally,we will show that the dynamics induced by the logistic family on the fuzzy numbers need not be complicated at all.
文摘Recently, the space bvp of real or complex numbers consisting of all sequences whose differences are in the space lp has been studied by Basar, Altay [Ukrainian Math. J. 55（1）（2003）, 136-147], where 1 ≤ p ≤ ∞. The main purpose of the present paper is to introduce the space bvp（F） of sequences of p-bounded variation of fuzzy numbers. Moreover, it is proved that the space bvp（F） includes the space lp（F） and also shown that the spaces bvp（F） and lp（F） axe isomorphic for 1 ≤ p ≤∞. Furthermore, some inclusion relations have been given.
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the National High-Tech Research and Development Plan of China under Grant No.2015AA042101 and Fund of State Key Laboratory of Intelligent Manufacturing System Technology in China.
文摘The distributed and customized 3D printing can be realized by 3D printing services in a cloud manufacturing environment.As a growing number of 3D printers are becoming accessible on various 3D printing service platforms,there raises the concern over the validation of virtual product designs and their manufacturing procedures for novices as well as users with 3D printing experience before physical products are produced through the cloud platform.This paper presents a 3D model to help users validate their designs and requirements not only in the traditional digital 3D model properties like shape and size,but also in physical material properties and manufacturing properties when producing physical products like surface roughness,print accuracy and part cost.These properties are closely related to the process of 3D printing and materials.In order to establish the 3D model,the paper analyzes the model of the 3D printing process selection in the cloud platform.Triangular intuitionistic fuzzy numbers are applied to generate a set of 3D printers with the same process and material.Based on the 3D printing process selection model,users can establish the 3D model and validate their designs and requirements on physical material properties and manufacturing properties before printing physical products.
