To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(...To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(CR) as benefit, and the maximum modification compared to the original pairwise comparison matrix(PCM) as cost, then the improvement of consistency is transformed to a benefit/cost analysis problem. According to the maximal marginal effect principle, the elements of PCM are modified by a fixed increment(or decrement) step by step till the consistency ratio becomes acceptable, which can ensure minimum adjustment to the original PCM so that the decision makers’ judgment is preserved as much as possible. The correctness of the proposed method is proved mathematically by theorem. Firstly, the marginal benefit/cost ratio is calculated for each single element of the PCM when it has been modified by a fixed increment(or decrement).Then, modification to the element with the maximum marginal benefit/cost ratio is accepted. Next, the marginal benefit/cost ratio is calculated again upon the revised matrix, and followed by choosing the modification to the element with the maximum marginal benefit/cost ratio. The process of calculating marginal effect and choosing the best modified element is repeated for each revised matrix till acceptable consistency is reached, i.e., CR<0.1. Finally,illustrative examples show the proposed method is more effective and better in preserving the original comparison information than existing methods.展开更多
The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new meth...The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale展开更多
The consistency measurement and weight estimation approach of the hybrid uncertain comparison matrix in the analytic hierarchy process （AHP） are studied. First, the decision-making satisfaction membership function i...The consistency measurement and weight estimation approach of the hybrid uncertain comparison matrix in the analytic hierarchy process （AHP） are studied. First, the decision-making satisfaction membership function is defined based on the decision making＇s allowable error. Then, the weight model based on the maximal satisfactory consistency idea is suggested, and the consistency index is put forward. Moreover, the weight distributing value model is developed to solve the decision making misleading problem since the multioptimization solutions in the former model. Finally, the weights are ranked based on the possibility degree approach to obtain the ultimate order.展开更多
The improvement of consistency index and the computation of priority values are studied by considering a vector of the comparison matrix in this paper.According to consistency weight index,the orderpreserving is discu...The improvement of consistency index and the computation of priority values are studied by considering a vector of the comparison matrix in this paper.According to consistency weight index,the orderpreserving is discussed while a new vector is let into the comparison matrix,the methods of identification and revision for dissatisfaction vector are proposed,the computational formula for the revised vector are given so that the consistency weight index is optimum.the revision of the vector make the consistency of comparison matrix get much improvement and relate directly to the computation of priority vector.展开更多
Matrix-assisted Laser Desorption/Ionization with Time-of-flight Mass Spectrometry (MALDI-TOFMS) was investigated as a method for the rapid identifica-tion of species. Current demand in microbial identi-fication is how...Matrix-assisted Laser Desorption/Ionization with Time-of-flight Mass Spectrometry (MALDI-TOFMS) was investigated as a method for the rapid identifica-tion of species. Current demand in microbial identi-fication is how to compare unknown strains to the known one quickly, semi-automatically and accurately. In this paper, we present a software tool that allows flexibly microbial matching in a user-friendly way, by letting the users to customize comparison parameters including: in vitro transcription enzyme, mass tolerance,minimum fragment length, intensity threshold and corresponding weights. We provide three spectral scoring functions to compute the affin-ity between the species. Therefore, the precision of microbial comparison increases. To test and verify this tool, we employed experimental spectral data based on MALDI-TOFMS and the gene sequences of E.coli and Salmonella. This software is written in Java for cross-platform intention.展开更多
Objective To establish a method for quantitative detection of the sulfate glycosaminoglycans ( GAG) content in extracellular matrix of in vitro cultured chondrocytes so as to evaluate the biological characteristics of...Objective To establish a method for quantitative detection of the sulfate glycosaminoglycans ( GAG) content in extracellular matrix of in vitro cultured chondrocytes so as to evaluate the biological characteristics of epiphyseal, articular and rib chondrocytes. Methods Sulfate GAG content in extracellular matrix of three chondrocytes was measured by the modified dimethylmethylene blue (DMB) method. The changes of the toluidine blue (TB) stain of chondrocytes were observed by light microscope. Results Primary chondrocytes had the highest content of sulfate GAG in the extracellular matrix, ie, epiphyseal chondrocytes reached ( 70. 12 ± 7. 72 )μg/cm2, articular chondrocytes (92.00 ± 10.15) μg/cm2 and rib chondrocytes (80.61 ± 11. 40) μg/cm2, respectively. On the third pasage chondrocytes, epiphyceal chondrocytes decreased to (53.27 ± 9. 50 ) μg/cm2, articular chondrocytes to (63.88 ± 11.92) μg/cm2 and rib chondrocytes to (58.94 ±8.21) μg/cm2, respectively. The change of TB in every passage展开更多
This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of deci...This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.展开更多
In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of ...In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of uncertainty comparison matrix and uncertainty weights are proposed in this paper. It also gives the uncertain variable method to calculate uncertainty weights from uncertainty comparison matrices, which can be either consistent or inconsistent. The proposed uncertain variable method (UVM) is also applicable to interval comparison matrices and fuzzy comparison ma-trices when they are transformed into uncertainty comparison matrices using linear uncertainty distribution or zigzag uncertainty distribution. The proposed approach is computationally efficient as it consists of solving only inverse uncertainty distribution. At the end of this paper, five numerical examples are given to illustrate the method.展开更多
This paper addresses a class of numerical solution problems for quaternion quadratic matrix equations arising from practical engineering applications.By transforming it into a special Riccati equation,a sufficient con...This paper addresses a class of numerical solution problems for quaternion quadratic matrix equations arising from practical engineering applications.By transforming it into a special Riccati equation,a sufficient condition for the existence of solutions to the corresponding M-matrix equation is derived using the theory of comparison matrices.This condition is then applied to investigate the existence of solutions for the quaternion quadratic matrix equation.Finally,numerical examples demonstrate an effective solution method for the quaternion quadratic matrix equation using fixed-point iteration.展开更多
基金supported by the National Natural Science Foundation of China(6160150161502521)
文摘To improve the inconsistency in the analytic hierarchy process(AHP), a new method based on marginal optimization theory is proposed. During the improving process, this paper regards the reduction of consistency ratio(CR) as benefit, and the maximum modification compared to the original pairwise comparison matrix(PCM) as cost, then the improvement of consistency is transformed to a benefit/cost analysis problem. According to the maximal marginal effect principle, the elements of PCM are modified by a fixed increment(or decrement) step by step till the consistency ratio becomes acceptable, which can ensure minimum adjustment to the original PCM so that the decision makers’ judgment is preserved as much as possible. The correctness of the proposed method is proved mathematically by theorem. Firstly, the marginal benefit/cost ratio is calculated for each single element of the PCM when it has been modified by a fixed increment(or decrement).Then, modification to the element with the maximum marginal benefit/cost ratio is accepted. Next, the marginal benefit/cost ratio is calculated again upon the revised matrix, and followed by choosing the modification to the element with the maximum marginal benefit/cost ratio. The process of calculating marginal effect and choosing the best modified element is repeated for each revised matrix till acceptable consistency is reached, i.e., CR<0.1. Finally,illustrative examples show the proposed method is more effective and better in preserving the original comparison information than existing methods.
基金This project was supported by Zhejiang Provincial Natural Science Foundation of China (No. 601076).
文摘The main faults existing in current scale methods are that the scales do not represent the real importance of alternatives and their relations. This paper presents a proportion judgment scale and introduces a new method based on the proportion scale for construction comparison matrix in the analytic hierarchy process (AHP). The proportion judgment scales do not have the faults existing in current scale methods and the comparison matrix constructed by the new scale
基金supported by the National Natural Science Foundation of China (70701017)Education Department Humanism and Social Project in China (07JC630064)
文摘The consistency measurement and weight estimation approach of the hybrid uncertain comparison matrix in the analytic hierarchy process （AHP） are studied. First, the decision-making satisfaction membership function is defined based on the decision making＇s allowable error. Then, the weight model based on the maximal satisfactory consistency idea is suggested, and the consistency index is put forward. Moreover, the weight distributing value model is developed to solve the decision making misleading problem since the multioptimization solutions in the former model. Finally, the weights are ranked based on the possibility degree approach to obtain the ultimate order.
文摘The improvement of consistency index and the computation of priority values are studied by considering a vector of the comparison matrix in this paper.According to consistency weight index,the orderpreserving is discussed while a new vector is let into the comparison matrix,the methods of identification and revision for dissatisfaction vector are proposed,the computational formula for the revised vector are given so that the consistency weight index is optimum.the revision of the vector make the consistency of comparison matrix get much improvement and relate directly to the computation of priority vector.
文摘Matrix-assisted Laser Desorption/Ionization with Time-of-flight Mass Spectrometry (MALDI-TOFMS) was investigated as a method for the rapid identifica-tion of species. Current demand in microbial identi-fication is how to compare unknown strains to the known one quickly, semi-automatically and accurately. In this paper, we present a software tool that allows flexibly microbial matching in a user-friendly way, by letting the users to customize comparison parameters including: in vitro transcription enzyme, mass tolerance,minimum fragment length, intensity threshold and corresponding weights. We provide three spectral scoring functions to compute the affin-ity between the species. Therefore, the precision of microbial comparison increases. To test and verify this tool, we employed experimental spectral data based on MALDI-TOFMS and the gene sequences of E.coli and Salmonella. This software is written in Java for cross-platform intention.
文摘Objective To establish a method for quantitative detection of the sulfate glycosaminoglycans ( GAG) content in extracellular matrix of in vitro cultured chondrocytes so as to evaluate the biological characteristics of epiphyseal, articular and rib chondrocytes. Methods Sulfate GAG content in extracellular matrix of three chondrocytes was measured by the modified dimethylmethylene blue (DMB) method. The changes of the toluidine blue (TB) stain of chondrocytes were observed by light microscope. Results Primary chondrocytes had the highest content of sulfate GAG in the extracellular matrix, ie, epiphyseal chondrocytes reached ( 70. 12 ± 7. 72 )μg/cm2, articular chondrocytes (92.00 ± 10.15) μg/cm2 and rib chondrocytes (80.61 ± 11. 40) μg/cm2, respectively. On the third pasage chondrocytes, epiphyceal chondrocytes decreased to (53.27 ± 9. 50 ) μg/cm2, articular chondrocytes to (63.88 ± 11.92) μg/cm2 and rib chondrocytes to (58.94 ±8.21) μg/cm2, respectively. The change of TB in every passage
文摘This paper deals with the calculation of a vector of reliable weights of decision alternatives on the basis of interval pairwise comparison judgments of experts. These weights are used to construct the ranking of decision alternatives and to solve selection problems, problems of ratings construction, resources allocation problems, scenarios evaluation problems, and other decision making problems. A comparative analysis of several popular models, which calculate interval weights on the basis of interval pairwise comparison matrices (IPCMs), was performed. The features of these models when they are applied to IPCMs with different inconsistency levels were identified. An algorithm is proposed which contains the stages for analyzing and increasing the IPCM inconsistency, calculating normalized interval weights, and calculating the ranking of decision alternatives on the basis of the resulting interval weights. It was found that the property of weak order preservation usually allowed identifying order-related intransitive expert pairwise comparison judgments. The correction of these elements leads to the removal of contradictions in resulting weights and increases the accuracy and reliability of results.
文摘In practical application of AHP, non-deterministic factors are frequently encountered. This paper employs uncertainty theory to deal with non-deterministic factors in problems of ranking alternatives. The concepts of uncertainty comparison matrix and uncertainty weights are proposed in this paper. It also gives the uncertain variable method to calculate uncertainty weights from uncertainty comparison matrices, which can be either consistent or inconsistent. The proposed uncertain variable method (UVM) is also applicable to interval comparison matrices and fuzzy comparison ma-trices when they are transformed into uncertainty comparison matrices using linear uncertainty distribution or zigzag uncertainty distribution. The proposed approach is computationally efficient as it consists of solving only inverse uncertainty distribution. At the end of this paper, five numerical examples are given to illustrate the method.
文摘This paper addresses a class of numerical solution problems for quaternion quadratic matrix equations arising from practical engineering applications.By transforming it into a special Riccati equation,a sufficient condition for the existence of solutions to the corresponding M-matrix equation is derived using the theory of comparison matrices.This condition is then applied to investigate the existence of solutions for the quaternion quadratic matrix equation.Finally,numerical examples demonstrate an effective solution method for the quaternion quadratic matrix equation using fixed-point iteration.
