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Citations of paper extent analysis method on fuzzy AHP by chang 1996? 


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Chang (1996) introduced the Extent Analysis Method in the context of fuzzy AHP . This method has been widely used in fuzzy AHP applications but has faced criticism for potential misapplications and questionable reliability of group weights . Various fuzzy extensions of the eigenvector method have been introduced to address shortcomings in deriving priorities from fuzzy multiplicative pairwise comparison matrices . Additionally, new fuzzy AHP methods have been proposed to handle uncertainty and imprecision in multi-criteria decision-making processes, such as the Magnitude-based Fuzzy AHP and Total Difference-based Fuzzy AHP, which aim to improve accuracy and computational efficiency .

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What was done in this paper?4 answersThe paper described an image enhancement technique based on multispectral estimation (MSE) for detecting minor changes and boundaries of gastric mucosal lesions. Additionally, a paper-based method for browsing, retrieving, and viewing video programs using bar codes and a remote control device was presented. Furthermore, a review of research approaches in mathematics education in various countries was conducted through a satirical story involving a character named Odysseus and mathematical problem-solving scenarios. Moreover, the safety and efficacy of carotid artery stenting using a new generation self-expanding nitinol stent, Vascuflex SEC, with different types of embolic protection were evaluated, showing promising results in an unselected population referred for carotid revascularization. Lastly, a classification scheme of software reliability models and various methods for calculating software reliability were discussed in another paper.
What happens when fuzzy numbers doesn't intersect while applying extent analysis method by chang?4 answersWhen fuzzy numbers do not intersect during the application of the extent analysis method by Chang, it can lead to inaccuracies in extracting local weights from a fuzzy comparison matrix (FCM) and potentially result in incorrect ranking of alternatives. This issue was highlighted in the study by Arman and Hadi-Vencheh, where they proposed a revised extent analysis (REA) to address the flaws of the traditional extent analysis method. Additionally, Zhu, Shang, and Yang pointed out that the extent analysis method proposed by Chang in 1996 contained errors that could lead to issues such as zero-weight, poor robustness, and unreasonable priorities, making it unsuitable for fuzzy AHP applications. Therefore, when fuzzy numbers fail to intersect, it is crucial to use revised methods like REA to ensure accurate ranking and avoid potential errors in decision-making processes.
What is the fuzzy ranking methods?4 answersFuzzy ranking methods are techniques used to rank fuzzy numbers based on their ambiguous values. These methods are important in various fields such as decision-making and multi-criteria analysis. Several approaches have been proposed to address the challenges of ranking fuzzy numbers. One approach is the use of statistical techniques like multi-dimensional scaling and principal component analysis to rank triangular and trapezoidal fuzzy numbers. Another approach involves the use of ranking functions to convert fuzzy values into crisp values, allowing for easier comparison and ranking. Additionally, methods like Haar ranking and Yager's ranking have been proposed for ranking intuitionistic dense fuzzy sets. These ranking methods aim to provide accurate rankings while considering the complexity and computational load of the calculations.
What has been done in Fuzzy metric space, by who, when, where and why?4 answersFuzzy metric spaces have been studied by various authors in the field of mathematics. The concept of fuzzy metric space extends the idea of metric spaces by incorporating fuzziness characteristics and truth values in the interval [0,1]. Researchers have shown that every metric space can be considered as a fuzzy metric space. Additionally, the concept of fuzzy metric space has been applied to construct fuzzy Hausdorff spaces and fuzzy manifold spaces. These studies aim to extend the application of fuzzy metric spaces to union and product operations, as well as investigate the connection between manifolds and fuzzy metrics. The motivation behind these research efforts is to explore the relationship between fuzzy subsets and classical mathematics, and to develop new approaches in applied mathematics.
What is fuzzy boundary heuristic?4 answersA fuzzy boundary heuristic refers to a technique used to define boundaries in a way that allows for flexibility and imprecision. It is particularly useful in situations where traditional fixed boundaries are not suitable. The concept of fuzzy boundaries has been explored in various fields, including decision making, animal behavior studies, engineering systems analysis, and GIScience. In decision making, the concept of intuitionistic fuzzy soft sets has been introduced to solve problems using similarity measurement techniques. In animal behavior studies, a method has been described for confining animals within an experimenter-defined area using aversive noise, creating a fuzzy boundary that cannot be used as a spatial localizing cue. In engineering systems analysis, a fuzzy boundary element method has been developed to analyze systems with imprecisely defined parameters. In GIScience, fuzzy boundaries have been used to model geographic phenomena with smooth attribute variations.
What is Fuzzy SVM?4 answersFuzzy SVM is a classification model that combines fuzzy logic and support vector machines (SVM). It is used to handle uncertain and imbalanced data in machine learning tasks. Fuzzy SVM assigns fuzzy membership values to data samples, increasing the certainty of uncertain data. This is done in both the input space and feature space, with higher fuzzy membership assigned to minority samples compared to majority samples. By incorporating fuzzy logic, Fuzzy SVM improves the accuracy of traditional SVM models. It is particularly useful in applications such as cloth pattern recognition, where there are large intra-pattern variations. Fuzzy SVM has been shown to outperform traditional SVM-based methods in various experiments.

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