Topic
Fuzzy number
About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.
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TL;DR: A novel risk decision-making method with the aid of HFDTRSs is developed and investigates the ranking and resource allocation by utilizing the associated costs of alternatives and multiobjective 0-1 integer programming.
Abstract: Decision-theoretic rough sets (DTRSs) play a crucial role in risk decision-making problems. With respect to the minimum expected risk, DTRSs deduce the rules of three-way decisions. Considering the new expression of evaluation information with hesitant fuzzy sets (HFSs), we introduce HFSs into DTRSs and explore their decision mechanisms. More specifically, we take into account the losses of DTRSs with hesitant fuzzy elements and propose a new model of hesitant fuzzy decision-theoretic rough sets (HFDTRSs). Some properties of the expected losses and their corresponding scores are carefully investigated under the hesitant fuzzy information. Three-way decisions and the associated cost of each object are further derived. With the above analysis, a novel risk decision-making method with the aid of HFDTRSs is developed. Besides the three-way decisions with DTRSs, the method investigates the ranking and resource allocation by utilizing the associated costs of alternatives and multiobjective 0–1 integer programming. Our study also offers a solution in the aspect of determining losses of DTRS and extends the range of applications.
166 citations
TL;DR: A new fuzzy membership function is proposed to the nonlinear fuzzy support vector machine that gives good performance on reducing the effects of outliers and significantly improves the classification accuracy and generalization.
Abstract: It is known that with a proper fuzzy membership function, a fuzzy support vector machine can effectively reduce the effects of outliers when solving the classification problem. In this paper, a new fuzzy membership function is proposed to the nonlinear fuzzy support vector machine. The fuzzy membership is calculated in the feature space and is represented by kernels. This method gives good performance on reducing the effects of outliers and significantly improves the classification accuracy and generalization.
166 citations
TL;DR: A numerical experiment on real data indicates that the proposed multiple tree induction is superior to the single tree induction based on the individual reduct or on the entire feature set for learning problems with many attributes.
165 citations
TL;DR: Criteria for a fuzzy matrix to be regular is given and it is proved that the row and column rank of any regular fuzzy matrix are equal, and the cardinality of any two bases are equal.
165 citations
TL;DR: The structure of fuzzy binary relations of indifference and preference is studied and the general notion of a relative ‘degree of fuzziness’ is defined in connection with a study of the quantitative description of preservation properties under fuzzy mappings.
165 citations