As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication . Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. In this paper, a novel method to find the solutions in which 0 is not the ...

This paper presents an applicable health monitoring method for Li-ion batteries based on profust reliability theory. The word “profust” derives from “probability” and “fuzzy-state”, which means that the profust reliability theory is a kind of fuzzy reliability theory based on probability assumption and fuzzy-state assumption. It defines a concept of transition from fuzzy success to fuzzy failur...

The Bayesian reliability estimation under fuzzy environments is proposed in this paper. In order to apply the Bayesian approach, the fuzzy parameters are assumed to be fuzzy random variables with fuzzy prior distributions. The (conventional) Bayesian estimation method will be used to create the fuzzy Bayes point estimator of reliability by invoking the well-known theorem called ‘Resolution Iden...

Fuzzy extractors are a powerful tool to extract randomness from noisy data. A fuzzy extractor can extract randomness only if the source data is discrete while in practice source data is continuous. Using quantizers to transform continuous data into discrete data is a commonly used solution. However, as far as we know no study has been made of the effect of the quantization strategy on the perfo...

Fuzzy transform is a novel, mathematically well founded soft computing method with many applications. In this paper, we present this technique with applications to data analysis. First, we show how it can be used for detection and characterization of dependencies among attributes. Second, we apply it to mining associations that have a functional character. Moreover, the mined associations are c...

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Fuzzy measures and integrals have been used in multiple applications in the area of information fusion. They can be used to aggregate information when information sources are not independent. Fuzzy measures are used to represent our background knowledge on the information sources. In particular, they can be used to model the dependencies between the variables. One of the applications of Choquet...