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In our previous papers, we proposed an analysis of the relations between information theory and observation theory. Referring to the parameters of the observation and using Shannon's formulation, we defined and calculated the information associated with a result of observation and the entropy of a random variable for a process of observation. This paper presents an extension of this theory for other definitions of entropy (Onicescu, hyperbolic). The method allows in particular to define Onicescu and hyperbolic entropies of continuous random variables. We examine the main properties of these new functions and propose a comparative analysis.

The real challenges in online crack detection testing based on guided waves are random noise as well as narrow-band coherent noise; and to achieve efficient structural health assessment methodology, magnificent extraction of noise and analysis of the signals are essential. The purpose of this paper is to provide optimal noise filtering technique for Lamb waves in the diagnosis of structural singularities.

Filtration of time-frequency information of guided elastic waves through the noisy signal is investigated in the present analysis using matched filtering technique which “sniffs” the signal buried in noise and most favorable mother wavelet based denoising methods. The optimal wavelet function is selected using Shannon’s entropy criterion and verified by the analysis of root mean square error of the filtered signal.

Wavelet matched filter method, a newly developed filtering technique in this work and which is a combination of the wavelet transform and matched filtering method, significantly improves the accuracy of the filtered signal and identifies relatively small damage, especially in enormously noisy data. A comparative study is also performed using the statistical tool to know acceptability and practicability of filtered signals for guided wave application.

The proposed filtering techniques can be utilized in online monitoring of civil and mechanical structures. The algorithm of the method is easy to implement and found to be successful in accurately detecting damage.

Although many techniques have been developed over the past several years to suppress random noise in Lamb wave signal but filtration of interferences of wave modes and boundary reflection is not in a much matured stage and thus needs further investigation. The present study contains detailed information about various noise filtering methods, newly developed filtration technique and their efficacy in handling the above mentioned issues.

The purpose of this paper is to contribute to the study of sustainable rural livelihoods by developing a model to measure vulnerability of subsistence communities in dryland regions and identifying the major determinants that contribute to the livelihood vulnerability of these communities.

The author conducted a household survey across three subsistence communities in West Timor (n=627), from June to November 2013. Based on the guideline of the OECD (2008), the author developed a series of indicators and constructed a composite index to measure the vulnerability of dryland communities. The author adapted the livelihood vulnerability index (LVI) measure from Hahn et al. (2009) but refined it by using Shannon’s entropy method in deciding the weights of indicators and statistically tested the correlation between indicators using Kendall’s correlations.

Six major determinants were identified: education (EDU), children’s participation in agriculture (CPA), agricultural income (AI), subsistence food reserve (SUBSIST), social-cultural participation (SCP) and access to water, health clinic and market (ACC). LVI in all communities shows significant and strong relationships with SCP (0.594, p<0.01), AI (0.545, p<0.01) and CPA (0.434, p<0.01). This signifies that constraints to engage in social gatherings, market the harvest and obtain additional labour input are currently the major contributor to the vulnerability in these communities.

Shannon’s entropy is one of the methods for assisting in making decision (ranking) objectively. The results may need to be tested further using other methods.

Using objective weight provides additional information useful for identifying and prioritising areas (sub-components) which require attention and appropriate solutions to prevent households from further impoverishment and increased vulnerability.

Livelihood vulnerability of subsistence community in dry region is closely related to local survival skills and customs. Differences in the level of vulnerability across communities are due not only to geographical location and physical infrastructure, but also the leadership of local customary leaders and village government in looking for ways to improve the livelihoods of community members.

This paper is based on part of the results of a PhD thesis supported and approved by Griffith University. It has not been published before.

The presence of random noise as well as narrow band coherent noise makes the structural health monitoring a really challenging issue and to achieve efficient structural health assessment methodology, very good extraction of noise and analysis of the signals are essential. The purpose of this paper is to provide optimal noise filtering technique for Lamb waves in the diagnosis of structural singularities.

Filtration of time-frequency information of multimode Lamb waves through the noisy signal is investigated in the present analysis using matched filtering technique and wavelet denoising methods. Using Shannon’s entropy criterion, the optimal wavelet function is selected and verification is made via the analysis of root mean square error of filtered signal.

The authors propose wavelet matched filter method, a combination of the wavelet transform and matched filtering method, which can significantly improve the accuracy of the filtered signal and identify relatively small damage, especially in enormously noisy data. Correlation coefficient and root mean square error are additionally computed for performance evaluation of the filters.

The present study provides detailed information about various noise filtering methods and a first attempt to apply the combination of the different techniques in signal processing for the structural health monitoring application. A comparative study is performed using the statistical tool to know whether filtered signals obtained through three different methods are acceptable and practicable for guided wave application or not.

To provide a simplified proof for Liu's results concerning the relationship between σ‐entropy and σ‐similarity measure.

First obtains Liu's clear and simple functional expression of σ‐similarity measures based on the structure of σ‐entropy by using expressions of equivalent functions of σ‐entropy. Then, by employing the general expression of equivalent functions of σ‐similarity measure of fuzzy sets, provides a different proof of Liu's results.

Here, the proof is much simpler than the original one provided by Liu. And, on the basis of Shannon's probability entropy as introduced by De Luca and Termini, a σ‐similarity measure is constructed, on which a No answer to an open question as proposed by Liu is provided.

Constructs a new approach to some known results and provides a definite answer to an open question.

This study aims to provide a method to assess the perceptual impact of the visual complexity of building façades.

The research identifies the number of design elements and the variation in their position and colour as variables of visual complexity. It introduces the concepts of vertices and corners as atomic indicators on which the measurement of these variables is built. It measures visual complexity and its variables in images of building façades and analyses their relationships with participants' reactions. It reports on the effect of visual complexity on preferences, the adequacy of different methods in measuring visual complexity and the perceptual impact of each of its variables.

The research demonstrates that visual complexity can be assessed through the measure of its variables and their statistical mapping to users' preferences.

The manuscript provides the foundation for a planning/assessment tool for the visual control of the built environment using computer systems based on the preferences of residents through the examination of the relationship between the users and their environment. It creates a paradigm, which introduces a robust concept in the visual analysis of urban design.

Knowledge of the dependence structure between financial assets is crucial to improve the performance in financial risk management. It is known that the copula completely summarizes the dependence structure among multiple variables. We propose a multivariate exponential series estimator (ESE) to estimate copula densities nonparametrically. The ESE has an appealing information-theoretic interpretation and attains the optimal rate of convergence for nonparametric density estimations in Stone (1982). More importantly, it overcomes the boundary bias of conventional nonparametric copula estimators. Our extensive Monte Carlo studies show the proposed estimator outperforms the kernel and the log-spline estimators in copula estimation. It also demonstrates that two-step density estimation through an ESE copula often outperforms direct estimation of joint densities. Finally, the ESE copula provides superior estimates of tail dependence compared to the empirical tail index coefficient. An empirical examination of the Asian financial markets using the proposed method is provided.

Each individual investor is different, with different financial goals, levels of risk tolerance and personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It is really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook – essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about 24 questions that each has to be answered with values from 1 to 5. The questions range from personal background to what the customer expects from an investment. A fuzzy logic system has been designed for the evaluation of the answers to the above questions. The notion of fuzziness with respect to funds allocation is investigated.

This paper is concerned with the problem of estimating the uncertainty associated with a variable in a finite population. The study of this problem leads to the following conclusion: The classical measure of uncertainty, Shannon's entropy, is not suitable for sampling from finite populations; nevertheless, by using the entropy of order ? = 2, proposed by Havrda and Charvat, one can define an unbiased estimator of the uncertainty associated with the variable in both, the sampling with replacement and the sampling without replacement. This conclusion will be illustrated by an example.

We replicate and extend the social history treatment of the Berg, Dickhaut, and McCabe (1995) investment game, to further document how the reporting of financial history influences how laboratory societies organize themselves over time. We replicate Berg et al. (1995) by conducting a No History and a Financial History session to determine whether a report summarizing the financial transactions of a previous experimental session will significantly reduce entropy in the amounts sent by Investors and returned by Stewards in the investment game, as Berg et al. (1995) found. We extend Berg et al. (1995) in two ways. First, we conduct a total of five sessions (one No History and four Financial History sessions). Second, we introduce Shannon’s (1948) measure of entropy from information theory to assess whether the introduction of financial transaction history reduces the amount of dispersion in the amounts invested and returned across generations of players. Results across sessions indicate that entropy declined in both the amounts sent by Investors and the percentage returned by Stewards, but these patterns are weaker and mixed compared to those in the Berg et al. (1995) study. Additional research is needed to test how initial conditions, path dependencies, actors’ strategic reasoning about others’ behavior, multiple sessions, and communication may mediate the impact of financial history. The study’s multiple successive Financial History sessions and entropy measure are new to the investment game literature.