Non-probabilistic Measure Research Articles

Logarithmic Entropy Measures for Fuzzy Rough Set and their Application in Decision Making Problem

Decision-making is a critical problem in various circumstances where some vagueness and ambiguity is found in information. To handle these types of problems, entropy is an important measure of information theory which is exploited to evaluate the uncertain degree of any data. There are two methodologies to determine the entropy, one is probabilistic in nature and other is non-probabilistic. It is shown that for every probabilistic measure there is a corresponding non-probabilistic measure. In this article, some logarithmic non-probabilistic entropy measures have been proposed for the fuzzy rough set corresponding to existing probabilistic entropy measures. The proposed measures are employed in a decision-making problem, which is related to the agriculture. Finally, these proposed measures are compared with the existing trigonometric entropy measures for fuzzy rough sets.

3D Terrain Multiobjective Deployment Optimization of Heterogeneous Directional Sensor Networks in Security Monitoring

The traditional deployment research on wireless sensor networks (WSNs) has mainly focused on 2D plane and 3D full space; also, the sensors considered are almost always omni-directional sensors and are usually homogeneous. However, this type of research cannot fulfill the diverse requirements required for practical 3D environment. We study the deployment problem of heterogeneous directional sensor networks (HDSNs) on 3D terrain, which is more suitable for practical security monitoring requirements and has more practical significance. In this paper, we propose a novel uncertain comprehensive coverage model: a modified 3D directional sensing model is presented, and a non-probabilistic measure based fusion operator is utilized. We transform the deployment problem into a multiobjective optimization problem by comprehensively considering Coverage , Connectivity Uniformity and Deployment Cost , and we use various state-of-the-art multiobjective optimization algorithm based deployment approaches to address it. We conduct deployment experiments on three types of real-world 3D terrain data (plain, hill and mountain). Through the analysis of the deployment results, we obtain a deeper understanding and insight into the multiobjective deployment problem of HDSN. Meanwhile, we more clearly recognize the characteristics of the deployment approaches.

Knightian Uncertainty Meets Ranking Theory

Knightian uncertainty is not a special kind of uncertainty; it’s just uncertainty. And it raises the issue how we may model uncertainty. The paper gives a brief overview over non-probabilistic measures of uncertainty, starting with Shackle’s functions of potential surprise and mentioning non-additive probabilities, Dempster–Shafer belief functions, etc. It arrives at an explanation of ranking theory as a further uncertainty model and emphasizes its additional epistemological virtues, which consist in a representation of belief, i.e., of taking something to be true (which is the basic notion of traditional epistemology and admits of degrees as well) and a full dynamic account of those degrees. The final section addresses the issue how these uncertainty measures and in particular ranking theory may be used within a decision theoretic context.

Time-Dependent Reliability Modeling and Analysis Method for Mechanics Based on Convex Process

The objective of the present study is to evaluate the time-dependent reliability for dynamic mechanics with insufficient time-varying uncertainty information. In this paper, the nonprobabilistic convex process model, which contains autocorrelation and cross-correlation, is firstly employed for the quantitative assessment of the time-variant uncertainty in structural performance characteristics. By combination of the set-theory method and the regularization treatment, the time-varying properties of structural limit state are determined and a standard convex process with autocorrelation for describing the limit state is formulated. By virtue of the classical first-passage method in random process theory, a new nonprobabilistic measure index of time-dependent reliability is proposed and its solution strategy is mathematically conducted. Furthermore, the Monte-Carlo simulation method is also discussed to illustrate the feasibility and accuracy of the developed approach. Three engineering cases clearly demonstrate that the proposed method may provide a reasonable and more efficient way to estimate structural safety than Monte-Carlo simulations throughout a product life-cycle.

A Non-Probabilistic Measure of Structural Reliability Based on Convex Model

The problem of the non-probabilistic reliability is investigated in this paper, in which the convex model is used to deal with uncertainties in structural analysis and design. The limitation on the current non-probabilistic reliability is discussed. Then a novel non-probabilistic reliability model is proposed, and its computational procedure is given. Two numerical examples are conducted to illustrate the feasibility and validity of the proposed non-probabilistic reliability model.

Scalar Measures of Performance in Rare-Event Situations

A set of 14 scalar, nonprobabilistic measures—some old, some new—is examined in the rare-event situation. The set includes measures of accuracy, association, discrimination, bias, and skill. It is found that all measures considered herein are inequitable in that they induce under- or overforecasting. One condition under which such bias is not induced (for some of the measures) is when the underlying class-conditional distributions are Gaussian (normal) and equivariant.

A Neural Network for Damaging Wind Prediction

A neural network is developed to diagnose which circulations detected by the National Severe Storms Laboratory’s Mesocyclone Detection Algorithm yield damaging wind. In particular, 23 variables characterizing the circulations are selected to be used as the input nodes of a feed-forward, supervised neural network. The outputs of the network represent the existence/nonexistence of damaging wind, based on ground observations. A set of 14 scalar, nonprobabilistic measures and a set of two multidimensional, probabilistic measures are employed to assess the performance of the network. The former set includes measures of accuracy, association, discrimination, skill, and the latter consists of reliability and refinement diagrams. Two classification schemes are also examined. It is found that a neural network with two hidden nodes outperforms a neural network with no hidden nodes when performance is gauged with any of the 14 scalar measures, except for a measure of discrimination where the results are opposite. The two classification schemes perform comparably to one another. As for the performance of the network in terms of reliability diagrams, it is shown that the process by which the outputs are converted to probabilities allows for the forecasts to be completely reliable. Refinement diagrams complete the representation of the calibration-refinement factorization of the joint distribution of forecasts and observations.

A non-probabilistic measure of reliability of linear systems based on expansion of convex models

In this paper we develop a rigorous quantitative alternative to the probabilistic theory of reliability. The intuitive concept of reliability which underlies our analysis is that a system is reliable if it is robust with respect to uncertainty. That is, a system is reliable if it can tolerate a large amount of uncertainty before failure can occur. Conversely, a system is unreliable if it is fragile with respect to uncertainty. We model uncertainty with non-probabilistic convex models, and measure the amount of uncertainty with the expansion parameters of the convex models. The measure of reliability developed here is the amount of uncertainty the system can tolerate before failure. We consider linear dynamic systems with uncertain inputs and uncertain output failure states. The reliability of these systems hinges on the disjointness of convex sets. Using the hyperplane separation theorem for convex sets, we introduce a concept of modal reliability.

Generalized information theory

Generalized information theory is viewed in this paper as an information theory that is liberated from the boundaries of probability theory. After overviewing classical (probabilistic) information theory, the paper examines recent developments regarding nonprobabilistic measures and principles of uncertainty-based information, which form a nucleus of the emerging generalized information theory.

Information Theory and Identification – An Account of an Effective Interaction

An account is given of useful and effective applications of information theory in identification and some new problems are indicated, which can be solved within an information-theoretic framework. In the first part of the paper a brief survey is presented of information measures and their mutual relations. Restriction has been made to probabilistic information measures. Non-probabilistic measures did not find any application in identification so far.The second part of the paper deals with the practical applications of information theory in identification. Special attention is paid to problems, the solution of which in the information-theoretic framework seems to be the most effective or perhaps even the only possible one*).