Some Theorems for Inverse Uncertainty Distribution of Uncertain Processes

In real life, indeterminacy and determinacy are symmetric, while indeterminacy is absolute. We are devoted to studying indeterminacy through uncertainty theory. Within the framework of uncertainty theory, uncertain processes are used to model the evolution of uncertain phenomena. The uncertainty distribution and inverse uncertainty distribution of uncertain processes are important tools to describe uncertain processes. An independent increment process is a special uncertain process with independent increments. An important conjecture about inverse uncertainty distribution of an independent increment process has not been solved yet. In this paper, the conjecture is proven, and therefore, a theorem is obtained. Based on this theorem, some other theorems for inverse uncertainty distribution of the monotone function of independent increment processes are investigated. Meanwhile, some examples are given to illustrate the results.

Social Support in the Treatment of Heroin Addicts

Heroin addiction impairs every aspect of physical and psychological health of the addict, and at the same time, it impairs all forms of social functioning of the addict, as well as of everyone who loves him/her and of society as a whole, so it's necessary to put a lot of effort into treating this disease successfully. Working with heroin addicts shows that the treatment is a long and uncertain process, as the treatment must simultaneously cover three segments: psychological traits of heroin addicts, the degree of social support they have, and their motivation for this treatment. The theoretical goal of this research was to find out whether there is a link between social support and motivation for addiction treatment. The practical goal is to provide the improvement of the motivational aspect of treating heroin addicts, as well as to determine the role of social support in evaluating treatment outcomes. The research was conducted on a sample of 227 heroin addicts under treatment. The perception of social support for heroin addicts is the greatest when it comes to their families. A positive correlation was found between persistence in treatment and perceived social support from family members.

Risk-Neutral Pricing Method of Options Based on Uncertainty Theory

In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options.

Set-Valued Uncertain Process: Definition and Some Properties

Some phenomena are developing over time, while they are uncertain sets at each moment. From an uncertain set, we mean an unsharp concept, such as “illness” and “recovery”, that is not exactly clear, even for an expert. The values of a parameter that are considered “recovery” would guide one to explain the underlying concept quantitatively. For instance, in recovering from some disease, different levels of health might be assumed. Particularly, at each specific time moment, being healthy to some degree would be measured by belonging parameter values to a set of numbers with a specific belief degree. This set might be extracted using imprecisely observed data, while an expert opinion completely expresses the belief degree. Such concepts would direct one to employ uncertainty theory as a strong axiomatic mathematical framework for modeling human reasoning. Another important feature of these sets is their variation over time. For instance, the set defining “recovery” at the beginning stage of recovery in a disease would be completely or partially different from that at other stages. These characteristics result in considering a sequence of evolving sets over time. Analyzing the behavior of such a sequence motivated us to define the set-valued uncertain process. This concept is a combination of uncertain set, uncertain process, and uncertain sequence. Here, we introduce the main concept. Some properties are extracted and clarified, along with some illustrative examples.

Adaptive Two-Step Bearing-Only Underwater Uncooperative Target Tracking with Uncertain Underwater Disturbances

The bearing-only tracking of an underwater uncooperative target can protect maritime territories and allows for the utilization of sea resources. Considering the influences of an unknown underwater environment, this work aimed to estimate 2-D locations and velocities of an underwater target with uncertain underwater disturbances. In this paper, an adaptive two-step bearing-only underwater uncooperative target tracking filter (ATSF) for uncertain underwater disturbances is proposed. Considering the nonlinearities of the target’s kinematics and the bearing-only measurements, in addition to the uncertain noise caused by an unknown underwater environment, the proposed ATSF consists of two major components, namely, an online noise estimator and a robust extended two-step filter. First, using a modified Sage-Husa online noise estimator, the uncertain process and measurement noise are estimated at each tracking step. Then, by adopting an extended state and by using a robust negative matrix-correcting method in conjunction with a regularized Newton-Gauss iteration scheme, the current state of the underwater uncooperative target is estimated. Finally, the proposed ATSF was tested via simulations of a 2-D underwater uncooperative target tracking scenario. The Monte Carlo simulation results demonstrated the reliability and accuracy of the proposed ATSF in bearing-only underwater uncooperative tracking missions.

A Web-based Tool for Automatically linking Clinical Trials to their Publications

Objective. Evidence synthesis teams, physicians, policy makers, and patients and their families all have an interest in following the outcomes of clinical trials and would benefit from being able to evaluate both the results posted in trial registries and in the publications that arise from them. Manual searching for publications arising from a given trial is a laborious and uncertain process. We sought to create a statistical model to automatically identify PubMed articles likely to report clinical outcome results from each registered trial in ClinicalTrials.gov. Materials and Methods. A machine learning-based model was trained on pairs (publications linked to specific registered trials). Multiple features were constructed based on the degree of matching between the PubMed article metadata and specific fields of the trial registry, as well as matching with the set of publications already known to be linked to that trial. Results. Evaluation of the model using NCT-linked articles as gold standard showed that they tend to be top ranked (median best rank = 1.0), and 91% of them are ranked in the top ten. Discussion. Based on this model, we have created a free, public web based tool at http://arrowsmith.psych.uic.edu/cgi-bin/arrowsmith_uic/TrialPubLinking/trial_pub_link_start.cgithat, given any registered trial in ClinicalTrials.gov, presents a ranked list of the PubMed articles in order of estimated probability that they report clinical outcome data from that trial. The tool should greatly facilitate studies of trial outcome results and their relation to the original trial designs.

An uncertain SEIR rumor model

In this paper, an uncertain SEIR rumor model driven by one uncertain process is formulated to investigate the influence of perturbation in the transmission of rumor. Firstly, the deduced process of the uncertain SEIR rumor model is presented. Then, we proposed the existence and uniqueness theorem for the solution of the model. Moreover, the study of the stability of the uncertain SEIR rumor model was carried out, and then we came to the conclusion that the model stable in mean. In addition, computer algorithm and numerical simulation is used to verify the accuracy of the theoretical results. The simulation results show that the proposed model can explain the trend of rumor propagation correctly and describe the rumor propagation accurately. Finally, we have compared the propagation process of the uncertain rumor model and the deterministic model according to the numerical algorithm, and drew the conclusion that the model with uncertain perturbation fluctuates around the deterministic model.