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Register a new userSimilarity measure for aggregated fuzzy numbers from interval-valued data
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Added by
Uwe Aickelin
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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This paper presents a method to compute the degree of similarity between two aggregated fuzzy numbers from intervals using the Interval Agreement Approach (IAA). The similarity measure proposed within this study contains several features and attributes, of which are novel to aggregated fuzzy numbers. The attributes completely redefined or modified within this study include area, perimeter, centroids, quartiles and the agreement ratio. The recommended weighting for each feature has been learned using Principal Component Analysis (PCA). Furthermore, an illustrative example is provided to detail the application and potential future use of the similarity measure.
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This paper primarily presents two methods of ranking aggregated fuzzy numbers from intervals using the Interval Agreement Approach (IAA). The two proposed ranking methods within this study contain the combination and application of previously proposed similarity measures, along with attributes novel to that of aggregated fuzzy numbers from interval-valued data. The shortcomings of previous measures, along with the improvements of the proposed methods, are illustrated using both a synthetic and real-world application. The real-world application regards the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) algorithm, modified to include both the previous and newly proposed methods.
In this paper, the interval-valued intuitionistic fuzzy matrix (IVIFM) is introduced. The interval-valued intuitionistic fuzzy determinant is also defined. Some fundamental operations are also presented. The need of IVIFM is explain by an example.
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods to analyze interval-valued data results in loss of information, and thus, several interval-valued data models have been proposed to gather reliable information from such data types. On the other hand, recent technological developments have led to high dimensional and complex data in many application areas, which may not be analyzed by traditional techniques. Functional data analysis is one of the most commonly used techniques to analyze such complex datasets. While the functional extensions of much traditional statistical techniques are available, the functional form of the interval-valued data has not been studied well. This paper introduces the functional forms of some well-known regression models that take interval-valued data. The proposed methods are based on the function-on-function regression model, where both the response and predictor/s are functional. Through several Monte Carlo simulations and empirical data analysis, the finite sample performance of the proposed methods is evaluated and compared with the state-of-the-art.
Ranking of intuitionsitic fuzzy number plays a vital role in decision making and other intuitionistic fuzzy applications. In this paper, we propose a new ranking method of intuitionistic fuzzy number based on distance measure. We first define a distance measure for interval numbers based on Lp metric and further generalize the idea for intuitionistic fuzzy number by forming interval with their respective value and ambiguity indices. Finally, some comparative results are given in tabular form.
This paper presents an original method of fuzzy approximate reasoning that can open a new direction of research in the uncertainty inference of Artificial Intelligence(AI) and Computational Intelligence(CI). Fuzzy modus ponens (FMP) and fuzzy modus tollens(FMT) are two fundamental and basic models of general fuzzy approximate reasoning in various fuzzy systems. And the reductive property is one of the essential and important properties in the approximate reasoning theory and it is a lot of applications. This paper suggests a kind of extended distance measure (EDM) based approximate reasoning method in the single input single output(SISO) fuzzy system with discrete fuzzy set vectors of different dimensions. The EDM based fuzzy approximate reasoning method is consists of two part, i.e., FMP-EDM and FMT-EDM. The distance measure based fuzzy reasoning method that the dimension of the antecedent discrete fuzzy set is equal to one of the consequent discrete fuzzy set has already solved in other paper. In this paper discrete fuzzy set vectors of different dimensions mean that the dimension of the antecedent discrete fuzzy set differs from one of the consequent discrete fuzzy set in the SISO fuzzy system. That is, this paper is based on EDM. The experimental results highlight that the proposed approximate reasoning method is comparatively clear and effective with respect to the reductive property, and in accordance with human thinking than existing fuzzy reasoning methods.
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