Partial Certainty Research Articles

Q-INDETERMINATE CORRELATION COEFFICIENT BETWEEN SIMPLIFIED NEUTROSOPHIC INDETERMINATE SETS AND ITS MULTICRITERIA DECISION-MAKING METHOD

Owing to the indeterminacy, incompleteness, and inconsistency of decision makers’ arguments/cognitions regarding complicated decision-making problems, the truth, falsity, and indeterminacy degrees given by decision makers may imply the partial certainty and partial uncertainty information. In this case, a simplified neutrosophic set (SNS) cannot express the uncertainty degrees of the truth, falsity, indeterminacy arguments. To depict the hybrid information of SNS and neutrosophic (indeterminate) numbers (NNs) together, this study presents a simplified neutrosophic indeterminate set (SNIS) to describe the uncertainty degrees of the truth, falsity, indeterminacy, and then based on the de-neutrosophication technology using the parameterized SNSs of SNISs we introduce the q-indeterminate correlation coefficients of SNISs with a parameter q ∈ [0, 1]. Next, a simplified neutrosophic indeterminate multicriteria decision-making method using the qindeterminate correlation coefficients of SNISs is established along with decision makers’ risk attitudes, such as the small risk for q = 0, the moderate risk for q = 0.5, and the large risk for q = 1, to carry out multicriteria decision-making problems in SNIS setting. Eventually, the proposed decision-making approach is applied in an example of selecting a satisfactory slope design scheme for an open pit mine to indicate the practicality and flexibility in SNIS setting.

Probabilistic Model for Resource Demand Prediction in Cloud

Dynamic cloud infrastructure provisioning is possible with the virtualization technology. Cost, agility and time to market are the key elements of the cloud services. Virtualization is the software layer responsible for interaction with multiple servers, bringing entire IT resources together and provide standardized Virtual compute centers that drives the entire infrastructure. The increased pooling of shared resources helps in improving self-provisioning and automation of service delivery. Probabilistic model proposed in this article is based on the hypothesis that the accurate resource demand predictions can benefit in improving the virtualization layer efficiency. The probabilistic method, uses the laws of combinatorics. The probability space gives an idea about both the partial certainty and randomness of the variable. The method is popular in theoretical computer science. The probabilistic models provide the predictions considering the randomness of the variables. In the cloud environment there are multiple factors dynamically affecting the resource demand needs. The resource demand has a certain degree of certainty but the randomness of requirements. This further leads to decrease in risk related to leveraging cloud services. It accelerates development and implementation of cloud services that overall improves the services pertaining to SLA.

Introducing complexity to formal testing

A general theory introducing asymptotic complexity to testing is presented. Our goal is measuring how fast the effort of testing must increase to reach higher levels of partial certainty on the correctness of the implementation under test (IUT). By recent works it is known that, for many practical testing scenarios, any partial level of correctness certainty less than 1 (where 1 means full certainty) can be reached by some finite test suite. In this paper we address the problem of finding out how fast must these test suites grow as long as the target level gets closer to 1. More precisely, we want to study how test suites grow with α, where α is the inverse of the distance to 1 (e.g., if α=4 then our target level is 0.75=1−14). A general theory to measure this testing complexity is developed. We use this theory to analyze the testing complexity of some general testing problems, as well as the complexity of some specific testing strategies for these problems, and discover that they are within e.g., O(logα), O(log2α), O(α), O(αlogα), or O(α). Similarly as the computational complexity theory conceptually distinguishes between the complexity of problems and algorithms, tightly identifying the complexity of a testing problem will require reasoning about any testing strategy for the problem. The capability to identify testing complexities will provide testers with a measure of the productivity of testing, that is, a measure of the utility of applying the (n+1)-th planned test case (after having passed the n previous ones) in terms of how closer would that additional test case get us to the (ideal) complete certainty on the IUT (in-)correctness.

How to fix a broken heart: Cardiac disease and the ‘multiverse’ of stem cell research in Canada

This article focuses on Canadian stem cell researchers working on therapeutic appli- cations of autologous stem cells for heart disease. Building on the concept of ‘multiverse’ – coined by William James and then further developed by Ernst Bloch – we are interested in the simultaneity of the certain and uncertain, sometimes contradictory arguments articulated by these scientists. In the first part of the article we illustrate some of the factors that provide certainty for researchers and clinicians. The second part analyzes the ways in which uncertain elements become integrated into a discourse of certainty. What we would like to show, using the concept of multiverse, is that a rela- tively new bio-technology such as stem cell treatments generally relies on both certain and uncertain reasoning. However, uncertainty has to give way to a platform of partial certainty, if crucial action is to be taken on issues as diverse as treatments and grant applications. The principle mechanisms we found that can make this kind of transformation possible target future developments (what we call ‘if only arguments’), including past encouraging results in need of further research.

Optimal number and allocation of data collection points for linear spline growth curve modeling

Spline growth modelling is a popular tool to model change processes with distinct phases and change points in longitudinal studies. Focusing on linear spline growth models with two phases and a fixed change point (the transition point from one phase to the other), we detail how to find optimal data collection designs that maximize the efficiency of detecting key parameters in the spline models, holding the total number of data points or sample size constant. We identify efficient designs for the cases where (a) the exact location of the change point is known (complete certainty), (b) only the interval that contains the change point is known (partial certainty), and (c) no prior knowledge on the location of the change point is available (zero certainty). We conclude with recommendations for optimal number and allocation of data collection points.

Dual Adaptive Controllers based on Partial Certainty Equivalence

AbstractThe article deals with the optimal control of a linear discrete stochastic state space system with uncertain parameters. The solution of this optimization problem leads to design of controllers with dual features. Because the closed-form solution is hardly attainable a suitable suboptimal approaches has to be used. Many of the simpler approaches restrict the control horizon only to one step ahead and thus suffer from the myopic behavior. One way how to overcome this restriction is to use the partial certainty equivalence approximation of the joint probability density functions. The goal of this paper is to present a comparison of suboptimal adaptive dual control methods employing this approximation.

Non-myopic Innovations Dual Controller

Optimal control of a linear discrete stochastic state space system with uncertain parameters is treated. The problem statement leads to design of a dual controllers. Unfortunately, except for few special cases it is not possible to obtain closed-form solution for such controller. Many suboptimal approaches were proposed to overcome this obstacle, however, mostly they restrict the control horizon only to one step ahead and thus suffer from myopic behaviour. This paper presents technique that makes it possible to derive suboptimal dual controller in closed-form for arbitrarily long control horizon. The design of the presented controller is based on the innovations dual controller and use of the partial certainty equivalence principle. The proposed dual controller is compared to other non-dual controllers in a numerical example.

Design of adaptive controllers using partial certainty equivalence principle

AbstractOptimal stochastic control problem for general non‐linear dynamic system with unknown parameters is considered. An approximative assumption, which has been named partial certainty equivalence (PCE) principle, is suggested for design of adaptive controllers of non‐linear and linear stochastic systems. For derivation of a suboptimal controller with the PCE principle the certainty equivalence (CE) assumption is used only for the part of the system states and unknown parameters. The PCE control policy has a simple form for linear systems with unknown parameters. It is suggested in the present paper to design adaptive dual control using the PCE assumption and bicriterial optimization to derive the adaptive controller with the optimal persistent excitation. Simulated examples are used to demonstrate the potential of the suggested method and its superiority over the generally used CE‐controllers. Copyright © 2004 John Wiley & Sons, Ltd.

Insurance Pricing and Regulation under Uncertainty: A Chance-Constrained Approach

A financial model of the non-life insurer under uncertainty is developed. The model recognizes the stochastic nature of both the insurer's underwriting and investment income. The total risk faced by the insurer, which includes both underwriting and investment risk, is considered. The impact of regulatory constraints on the insurer's profits also is analyzed. Moreover, the costs of regulation imposed on the insurer are assessed in a non-linear, chance-constrained, programming framework. In general, the model shows that economic tradeoffs must be considered when management or regulatory decisions are made because of the numerous interrelationships among variables in the model and in the real world. A simplified financial model of a non-life insurer's behavior under uncertainty is developed in this paper. It is an extension of an earlier paper by the authors (24) that examined insurer behavior under the simplified conditions of partial certainty where the assumption was that the insurer could accurately forecast its underwriting and investment results. In this paper, the stochastic nature of the insurer's underwriting and investment income is considered which greatly complicates the model, but makes it considerably more realistic.