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
This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly know...This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.展开更多
In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria tran...In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>展开更多
ISO9001:2000 and TS 16949 have become the major quality system management models in present traditional and Hi-tech industries. The Measurement System Analysis (MSA) Reference Manual, on the other hand, is one of the ...ISO9001:2000 and TS 16949 have become the major quality system management models in present traditional and Hi-tech industries. The Measurement System Analysis (MSA) Reference Manual, on the other hand, is one of the core tools in ISO/TS 16949. MSA aims to evaluate Gauge Repeatability and Reproducibility (GR&R) where the control, monitoring, and maintenance of the measurement process are required in measurement systems so that the measurement capability could be ensured under statistical control. An ideal measurement system should present the statistical characteristic of zero error on any measured product. Nevertheless, such an ideal measurement system hardly exists. Managers therefore have to adopt such measurement systems with unsatisfactory statistical characteristics. Traditional MSA indexes are constructed with definite observed values. Nevertheless, measurements with observed values are not entirely error-free. For this reason, this study proposes to research three cases in a case company and apply the integration of Fuzzy Theory and GR&R to discuss the differences in the evaluation index GR&R and the Number of Distinct Categories (NDC). Substituting fuzzy numbers for definite numbers found that the data of %GR&R were increased and NDC was decreased after fuzzification. Such results verify that the fuzzified %GR&R and NDC become stricter in the determination criterion. The research outcomes could assist the case company in improving the reference data of measurement systems and promoting the measurement quality.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
The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some p...The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some properties of them are given out and thus some relevant results are elucidated.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
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.
基金supported by the National Natural Science Foundation of China (70473037)the Key Project of National Development and Reform Commission (1009-213011)
文摘This paper is concerned with a technique for order performance by similarity to ideal solution（TOPSIS） method for fuzzy multi-attribute decision making,in which the information about attribute weights is partly known and the attribute values take form of triangular fuzzy numbers.Considering the fact that the triangular fuzzy TOPSIS results yielded by different distance measures are different from others,a comparative analysis of triangular fuzzy TOPSIS ranking from each distance measure is illustrated with discussion on standard deviation.By applying the most reasonable distance,the deviation degrees between attribute values are measured.A linear programming model based on the maximal deviation of weighted attribute values is established to obtain the attribute weights.Therefore,alternatives are ranked by using TOPSIS method.Finally,a numerical example is given to show the feasibility and effectiveness of the method.
文摘In this paper<i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> fuzzy techniques have been used to track the problem of malaria transmission dynamics. The fuzzy equilibrium of the proposed model was discussed for different amounts of parasites in the body. We proved that when the amounts of parasites are less than the minimum amounts required for disease transmission (<img src="Edit_bced8210-1c24-4e78-bb5b-60ea7d37361c.png" alt="" /></span><span></span><span style="font-family:Verdana;">)</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> we reach the model disease-free equilibrium. Using Choquet integral</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the fuzzy basic reproduction number through the expected value of fuzzy variable was introduced for the fuzzy Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Infected</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Recovered</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> susceptible-Susceptible</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> Exposed and Infected (SEIRS-SEI) malaria model. The fuzzy global stabilities were introduced and discussed. The disease-free equilibrium <img src="Edit_cc2d122d-7c04-4fb7-a96a-3eb919a3785d.png" alt="" /> </span><span style="font-family:Verdana;">is globally asymptotically stable if <img src="Edit_0974e52f-cf63-4bfa-9781-1ebce366a4a3.png" alt="" /></span><span></span><span style="font-family:Verdana;"> or if the basic reproduction number is less than one (<img src="Edit_dbffcb03-cd00-4213-b7e1-ada9a0cf5c98.png" alt="" /></span><span></span><span style="font-family:Verdana;">). When <img src="Edit_5fc38f3d-2561-4189-87c2-197e3ff30b2e.png" alt="" /></span><span></span><span style="font-family:Verdana;"> and <img src="Edit_bfe99d90-7e55-4466-96b2-ce107483f69b.png" alt="" /></span><span></span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> there exists a co-existing endemic equilibrium which is globally asymptotically stable in the interior of feasible set <img src="Edit_543608fd-d8c9-4109-a285-bcf9377f43cc.png" alt="" /></span><span></span><span style="font-family:Verdana;">. Finally</span><i><span style="font-family:Verdana;">,</span></i><span style="font-family:Verdana;"> the numerical simulation has been done for showing the effectiveness of our analytical results.</span>
文摘ISO9001:2000 and TS 16949 have become the major quality system management models in present traditional and Hi-tech industries. The Measurement System Analysis (MSA) Reference Manual, on the other hand, is one of the core tools in ISO/TS 16949. MSA aims to evaluate Gauge Repeatability and Reproducibility (GR&R) where the control, monitoring, and maintenance of the measurement process are required in measurement systems so that the measurement capability could be ensured under statistical control. An ideal measurement system should present the statistical characteristic of zero error on any measured product. Nevertheless, such an ideal measurement system hardly exists. Managers therefore have to adopt such measurement systems with unsatisfactory statistical characteristics. Traditional MSA indexes are constructed with definite observed values. Nevertheless, measurements with observed values are not entirely error-free. For this reason, this study proposes to research three cases in a case company and apply the integration of Fuzzy Theory and GR&R to discuss the differences in the evaluation index GR&R and the Number of Distinct Categories (NDC). Substituting fuzzy numbers for definite numbers found that the data of %GR&R were increased and NDC was decreased after fuzzification. Such results verify that the fuzzified %GR&R and NDC become stricter in the determination criterion. The research outcomes could assist the case company in improving the reference data of measurement systems and promoting the measurement quality.
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The concepts of quasi-cardinality, possibility and expectation of a fuzzy set on a measurable set, as a generalization of the quasi-cardinality of a fuzzy set on a finite universe of discourse is proposed. Also some properties of them are given out and thus some relevant results are elucidated.
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.
