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In traditional finance, option prices are typically calculated using crisp sets of variables. However, as reported in the literature novel, these parameters possess a degree of fuzziness or uncertainty. This allows participants to estimate option prices based on their risk preferences and beliefs, considering a range of possible values for the parameters. This paper presents a comprehensive review of existing work on fuzzy fractional Brownian motion and proposes an extension in the context of financial option pricing. In this paper, we define a unified framework combining fractional Brownian motion with fuzzy processes, creating a joint product measure space that captures both randomness and fuzziness. The approach allows for the consideration of individual risk preferences and beliefs about parameter uncertainties. By extending Merton’s jump-diffusion model to include fuzzy fractional Brownian motion, this paper addresses the modelling needs of hybrid systems with uncertain variables. The proposed model, which includes fuzzy Poisson processes and fuzzy volatility, demonstrates advantageous properties such as long-range dependence and self-similarity, providing a robust tool for modelling financial markets. By incorporating fuzzy numbers and the belief degree, this approach provides a more flexible framework for practitioners to make their investment decisions.

Purpose - Data preparation plays an important role in data mining as most real life data sets contained missing data. This paper aims to investigate different treatment methods for missing data. Design/methodology/approach - This paper introduces, analyses and compares well-established treatment methods for missing data and proposes new methods based on naïve Bayesian classifier. These methods have been implemented and compared using a real life geriatric hospital dataset. Findings - In the case where a large proportion of the data is missing and many attributes have missing data, treatment methods based on naïve Bayesian classifier perform very well. Originality/value - This paper proposes an effective missing data treatment method and offers a viable approach to predict inpatient length of stay from a data set with many missing values. [ABSTRACT FROM AUTHOR]