Due to apparent flexibility of Intuitionistic Fuzzy Set (IFS) concepts in dealing with the imprecision or uncertainty, these are proving to be quite useful in many application areas for a more human consistent reasoning under imperfectly defined facts and imprecise knowledge. In this paper, we apply notions of entropy and intuitionistic fuzzy sets to present a new fuzzy decision-making approach called intuitionistic fuzzy entropy measure for selection and ranking the suppliers with respect to the attributes. An entropy-based model is formulated and applied to a real case study aiming to examine the rankings of suppliers. Furthermore, the weights for each alternative, with respect to the criteria, are calculated using intuitionistic fuzzy entropy measure. The supplier with the highest weight is selected as the best alternative. This proposed model helps the decision-makers in better understanding of the weight of each criterion without relying on the mere expertise.

The Shannon interval entropy function as a useful dynamic measure of uncertainty for two sided truncated random variables has been proposed in the literature of reliability. In this paper, we show that interval entropy can uniquely determine the distribution function. Furthermore, we propose a measure of discrepancy between two lifetime distributions at the interval of time in base of Kullback-Leibler discrimination information. We study various properties of this measure, including its connection with residual and past measures of discrepancy and interval entropy, and we obtain its upper and lower bounds.

This paper derives a new family of Burr-type distributions as new Burr distribution. This particular skewed distribution that can be used quite effectively in analyzing lifetime data. It is observed that the new distribution has modified unimodal hazard function. Various properties of the new Burr distribution, such that moments, quantile functions, hazard function, and Shannon’s entropy are obtained. The exact form of the probability density function and moments of \(i{\mathrm{th}}\)-order statistics in a sample of size n from new Burr distribution are derived. Estimation of parameters and change-point of hazard function by the maximum likelihood method are discussed. Change-point of hazard function is usually of great interest in medical or industrial applications. The flexibility of the new model is illustrated with an application to a real data set. In addition, a goodness-of-fit test statistic based on the Rényi Kullback–Leibler information is used.

Estimation of lifetime parameters such as reliability and hazard rate is necessary in many systems. Each method of estimation suffers from its own problems such as complexity of computations, high risk and etc. Toward this end, this study employed a new method, E-Bayesian, for estimating the parameters based on exponential distribution and record data. Furthermore, the asymptotic behaviours of E-Bayesian estimations and relations among them have been investigated. Finally, a comparison among the E-Bayesian estimations and older methods are made, using a real data and the Monte Carlo simulation. The computations show that the new method is more efficient than previous methods and is also easy to operate.