Multiattribute Decision-Making Problems in terms of the Weighted Mean Operation of Two Aggregation Operators of Orthopair Z-Numbers

The Z number defined by Zadeh can depict the fuzzy restriction/value and reliability measure by an ordered pair of fuzzy values to strengthen the reliability of the fuzzy restriction/value. However, there exist truth and falsehood Z-numbers in real life. Thus, the Z number cannot reflect both. To indicate both, this study presents an orthopair Z-number (OZN) set to depict truth and falsehood values (intuitionistic fuzzy values) and their reliability levels in uncertain and incomplete cases. Next, we define the operations, score and accuracy functions, and sorting rules of OZNs. Further, the OZN weighted arithmetic mean (OZNWAM) and OZN weighted geometric mean (OZNWGM) operators are proposed based on the operations of OZNs. According to the weighted mean operation of the OZNWAM and OZNWGM operators, a multiattribute decision-making (MADM) model is established in the case of OZNs. Lastly, a numerical example is presented to reflect the flexibility and rationality of the presented MADM model. Comparative analysis indicates that the presented MADM model can indicate its superiority in the reliability and flexibility of decision results. Meanwhile, the resulting advantage of this study is that the presented MADM model can strengthen the reliability level of orthopair fuzzy values and make the decision results more reliable and flexible.

Sequential Interval Reliability for Discrete-Time Homogeneous Semi-Markov Repairable Systems

In this paper, a new reliability measure, named sequential interval reliability, is introduced for homogeneous semi-Markov repairable systems in discrete time. This measure is the probability that the system is working in a given sequence of non-overlapping time intervals. Many reliability measures are particular cases of this new reliability measure that we propose; this is the case for the interval reliability, the reliability function and the availability function. A recurrent-type formula is established for the calculation in the transient case and an asymptotic result determines its limiting behaviour. The results are illustrated by means of a numerical example which illustrates the possible application of the measure to real systems.

Unified Reliability Measure Method Considering Uncertainties of Input Variables and Their Distribution Parameters

Aleatoric and epistemic uncertainties can be represented probabilistically in mechanical systems. However, the distribution parameters of epistemic uncertainties are also uncertain due to sparsely available or inaccurate uncertainty information. Therefore, a unified reliability measure method that considers uncertainties of input variables and their distribution parameters simultaneously is proposed. The uncertainty information for distribution parameters of epistemic uncertainties could be as a result of insufficient data or interval information, which is represented with evidence theory. The probability density function of uncertain distribution parameters is constructed through fusing insufficient data and interval information based on a Gaussian interpolation algorithm, and the epistemic uncertainties are represented using a weighted sum of probability variables based on discrete distribution parameters. The reliability index considering aleatoric and epistemic uncertainties is calculated around the most probable point. The effectiveness of the proposed algorithm is demonstrated through comparison with the Monte Carlo method in the engineering example of a crank-slider mechanism and composite laminated plate.

Study of Quantile-Based Cumulative Renyi Information Measure

In this paper, we proposed a quantile version of cumulative Renyi entropy for residual and past lifetimes and study their properties. We also study quantile-based cumulative Renyi entropy for extreme order statistic when random variable untruncated or truncated in nature. Some characterization results are studied using the relationship between proposed information measure and reliability measure. We also examine it in relation to some applied problems such as weighted and equillibrium models.

Two Entropy Theory Wings as a New Trend for the Modern Means of Air Transport Operational Reliability Measure

The paper deals with the uncertainty of the operated system’s possible states hybrid combined optional functions. Traditionally, the probabilities of the system’s possible states are treated as the reliability measures. However, in the framework of the proposed doctrine, the optimality (for example, the maximal probability of the system’s state) is determined based upon a plausible assumption of the intrinsic objectively existing parameters. The two entropy theory wings consider on one hand the subjective preferences functions in subjective analysis, concerning the multi-alternativeness of the operational situation at an individual’s choice problems, and on the other hand the objectively existing characteristics used in theoretical physics. The discussed in the paper entropy paradigm proceeds with the objectively presented phenomena of the state’s probability and the probability’s maximum. The theoretical speculations and mathematical derivations are illustrated with the necessary plotted diagrams.

Many Labs 5: Registered Replication of Vohs and Schooler (2008), Experiment 1

Does convincing people that free will is an illusion reduce their sense of personal responsibility? Vohs and Schooler (2008) found that participants reading from a passage “debunking” free will cheated more on experimental tasks than did those reading from a control passage, an effect mediated by decreased belief in free will. However, this finding was not replicated by Embley, Johnson, and Giner-Sorolla (2015), who found that reading arguments against free will had no effect on cheating in their sample. The present study investigated whether hard-to-understand arguments against free will and a low-reliability measure of free-will beliefs account for Embley et al.’s failure to replicate Vohs and Schooler’s results. Participants ( N = 621) were randomly assigned to participate in either a close replication of Vohs and Schooler’s Experiment 1 based on the materials of Embley et al. or a revised protocol, which used an easier-to-understand free-will-belief manipulation and an improved instrument to measure free will. We found that the revisions did not matter. Although the revised measure of belief in free will had better reliability than the original measure, an analysis of the data from the two protocols combined indicated that free-will beliefs were unchanged by the manipulations, d = 0.064, 95% confidence interval = [−0.087, 0.22], and in the focal test, there were no differences in cheating behavior between conditions, d = 0.076, 95% CI = [−0.082, 0.22]. We found that expressed free-will beliefs did not mediate the link between the free-will-belief manipulation and cheating, and in exploratory follow-up analyses, we found that participants expressing lower beliefs in free will were not more likely to cheat in our task.