Adjustable Security Proportions in the Fuzzy Portfolio Selection under Guaranteed Return Rates

Based on the concept of high returns as the preference to low returns, this study discusses the adjustable security proportion for excess investment and shortage investment based on the selected guaranteed return rates in a fuzzy environment, in which the return rates for selected securities are characterized by fuzzy variables. We suppose some securities are for excess investment because their return rates are higher than the guaranteed return rates, and the other securities whose return rates are lower than the guaranteed return rates are considered for shortage investment. Then, we solve the proposed expected fuzzy returns by the concept of possibility theory, where fuzzy returns are quantified by possibilistic mean and risks are measured by possibilistic variance, and then we use linear programming model to maximize the expected value of a portfolio’s return under investment risk constraints. Finally, we illustrate two numerical examples to show that the expected return rate under a lower guaranteed return rate is better than a higher guaranteed return rates in different levels of investment risks. In shortage investments, the investment proportion for the selected securities are almost zero under higher investment risks, whereas the portfolio is constructed from those securities in excess investments.

A General Mathematical Approach Based on the Possibility Theory for Handling Measurement Results and All Uncertainties

The concept of measurement uncertainty was introduced in the 1990s by the “Guide to the expression of uncertainty in measurement”, known as GUM. The word uncertainty has a lexical meaning and reflects the lack of exact knowledge or lack of complete knowledge about the value of the measurand. Thanks to the suggestions in the GUM and following the mathematical probabilistic approaches therein proposed, an uncertainty value can be found and be associated to the measured value. In the last decades, however, other methods have been proposed in the literature, which try to encompass the definitions of the GUM, thus overcoming its limitations. Some of these methods are based on the possibility theory, such as the one known as the RFV method. The aim of this paper is to briefly recall the RFV method, starting from the very beginning and the initial motivations, and summarize in a unique paper the most relevant obtained results.

Uncertainty modelling and computational aspects of data association

A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. In order to account for the lack of information about the different aspects of this type of complex system, an alternative representation of uncertainty based on possibility theory is considered. It is shown how analogues of usual concepts such as Markov chains and hidden Markov models (HMMs) can be introduced in this context. In particular, the considered statistical model for multiple dynamical objects can be formulated as a hierarchical model consisting of conditionally independent HMMs. This structure is leveraged to propose an efficient method in the context of Markov chain Monte Carlo (MCMC) by relying on an approximate solution to the corresponding filtering problem, in a similar fashion to particle MCMC. This approach is shown to outperform existing algorithms in a range of scenarios.

A Redundancy Metric Set within Possibility Theory for Multi-Sensor Systems

In intelligent technical multi-sensor systems, information is often at least partly redundant—either by design or inherently due to the dynamic processes of the observed system. If sensors are known to be redundant, (i) information processing can be engineered to be more robust against sensor failures, (ii) failures themselves can be detected more easily, and (iii) computational costs can be reduced. This contribution proposes a metric which quantifies the degree of redundancy between sensors. It is set within the possibility theory. Information coming from sensors in technical and cyber–physical systems are often imprecise, incomplete, biased, or affected by noise. Relations between information of sensors are often only spurious. In short, sensors are not fully reliable. The proposed metric adopts the ability of possibility theory to model incompleteness and imprecision exceptionally well. The focus is on avoiding the detection of spurious redundancy. This article defines redundancy in the context of possibilistic information, specifies requirements towards a redundancy metric, details the information processing, and evaluates the metric qualitatively on information coming from three technical datasets.