Selection and ranking of occupational safety indicators based on fuzzy AHP: A case study in road construction companies

In this article we give q-analogs of the Opial inequality for q-decreasing functions. Using a closed form of the restricted q-integral (see Gauchman in Comput. Math. Appl. 47:281–300, 2004), we establish a new integral inequality of the q-Opial type.

In recent decades, different definitions of conditional Rényi entropy (CRE) have been introduced. Thus, Arimoto proposed a definition that found an application in information theory, Jizba and Arimitsu proposed a definition that found an application in time series analysis and Renner-Wolf, Hayashi and Cachin proposed definitions that are suitable for cryptographic applications. However, there is still no a commonly accepted definition, nor a general treatment of the CRE-s, which can essentially and intuitively be represented as an average uncertainty about a random variable X if a random variable Y is given. In this paper we fill the gap and propose a three-parameter CRE, which contains all of the previous definitions as special cases that can be obtained by a proper choice of the parameters. Moreover, it satisfies all of the properties that are simultaneously satisfied by the previous definitions, so that it can successfully be used in aforementioned applications. Thus, we show that the proposed CRE is positive, continuous, symmetric, permutation invariant, equal to Rényi entropy for independent X and Y, equal to zero for $X=Y$ and monotonic. In addition, as an example for the further usage, we discuss the properties of generalized mutual information, which is defined using proposed CRE.

We will prove that when uniformly distributed random numbers are sorted by value, their successive differences are a exponentially distributed random variable Ex(λ). For a set of n random numbers, the parameters of mathematical expectation and standard deviation is λ = n⁻¹. The theorem was verified on four series of 200 sets of 101 random numbers each. The first series was obtained on the basis of decimals of the constant e = 2.718281…, the second on the decimals of the constant π = 3.141592…, the third on a Pseudo Random Number generated from Excel function RAND, and the fourth series of True Random Number generated from atmospheric noise. The obtained results confirm the application of the derived theorem in practice.

The increased use of urban technologies in smart cities brings new challenges and issues. Cyber security has become increasingly important as many critical components of information and communication systems depend on it, including various applications and civic infrastructures that use data-driven technologies and computer networks. Intrusion detection systems monitor computer networks for malicious activity. Signature-based intrusion detection systems compare the network traffic pattern to a set of known attack signatures and cannot identify unknown attacks. Anomaly-based intrusion detection systems monitor network traffic to detect changes in network behavior and identify unknown attacks. The biggest obstacle to anomaly detection is building a statistical normality model, which is difficult because a large amount of data is required to estimate the model. Supervised machine learning-based binary classifiers are excellent tools for classifying data as normal or abnormal. Feature selection and feature scaling are performed to eliminate redundant and irrelevant data. Of the 24 features of the Kyoto 2006+ dataset, nine numerical features are considered essential for model training. Min-Max normalization in the range [0,1] and [−1,1], Z-score standardization, and new hyperbolic tangent normalization are used for scaling. A hyperbolic tangent normalization is based on the Levenberg-Marquardt damping strategy and linearization of the hyperbolic tangent function with a narrow slope gradient around zero. Due to proven classification ability, in this study we used a feedforward neural network, decision tree, support vector machine, k-nearest neighbor, and weighted k-nearest neighbor models Overall accuracy decreased by less than 0.1 per cent, while processing time was reduced by more than a two-fold reduction. The results show a clear benefit of the TH scaling regarding processing time. Regardless of how accurate the classifiers are, their decisions can sometimes differ. Our study describes a conflicting decision detector based on an XOR operation performed on the outputs of two classifiers, the fastest feedforward neural network, and the more accurate but slower weighted k-nearest neighbor model. The results show that up to 6% of different decisions are detected.