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Ineffective evaluation of open-source software learning management system (OSS-LMS) packages can negatively impact organizational effectiveness. Clients may struggle to select the best OSS-LMS package from a wide range of options, leading to a complex multi-criteria group decision-making (MCGDM) problem. This evaluates OSS-LMS packages based on several criteria like usability, functionality, e-learning standards, reliability, activity tracking, course development, assessment, backup and recovery, error reporting, efficiency, operating system compatibility, computer-managed instruction, authentication, authorization, troubleshooting, maintenance, upgrading, and scalability. Handling uncertain data is a vital aspect of OSS-LMS package evaluation. To tackle MCGDM issues, this study presents a consensus weighted sum product (c-WASPAS) method which is applied to an educational OSS-LMS package selection problem to evaluate four OSS-LMS packages, namely ATutor, eFront, Moodle, and Sakai. The findings indicate that the priority order of alternatives is Moodle > Sakai > eFront > ATutor and, therefore, MOODLE is the best OSS-LMS package for the case study. A sensitivity analysis of criteria weights is also conducted, as well as a comparative study, to demonstrate the effectiveness of the proposed method. It is essential to note that proper OSS-LMS package evaluation is crucial to avoid negative impacts on organizational performance. By addressing MCGDM issues and dealing with uncertain information, the c-WASPAS method presented in this study can assist clients in selecting the most appropriate OSS-LMS package from multiple alternatives. The findings of this study can benefit educational institutions and other organizations that rely on OSS-LMS packages to run their operations. [ABSTRACT FROM AUTHOR]

Cross entropy measure is one of the best way to calculate the divergence of any variable from the priori one variable. We define a new cross entropy measure under interval neutrosophic set (INS) environment, which we call IN-cross entropy measure and prove its basic properties. We also develop weighted IN-cross entropy measure and investigats its basic properties. Based on the weighted IN-cross entropy measure, we develop a novel strategy for multi attribute group decision making (MAGDM) strategy under interval neutrosophic environment. The proposed multi attribute group decision making strategy is compared with the existing cross entropy measure based strategy in the literature under interval neutrosophic set environment. Finally, an illustrative example of multi attribute group decision making problem is solved to show the feasibility, validity and efficiency of the proposed MAGDM strategy.

In this contribution, we mainly investigate how new entropy and cross entropy measures of hesitant fuzzy linguistic term sets (HFLTSs) can be designed by using the counterparts proposed for linguistic term sets (LTSs). In this circumstance, we intend to point out some drawbacks of the existing entropies, and then extend the theory of entropy and cross entropy measures of HFLTSs by constructing a number of new entropies. Furthermore, we compare the results of the approach being proposed based on the new entropy and cross entropy measures with that of the weight-determining method and the hesitant fuzzy linguistic alternative queuing method (HFL-AQM). [ABSTRACT FROM AUTHOR]

The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove their basic properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove their basic properties. Thereafter, we develop two novel multi-attribute decision-making strategies based on the proposed cross entropy measures. In the decision-making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision-making problems and compare the obtained result with the results of other existing strategies to show the applicability and effectiveness of the developed strategies. At the end, the main conclusion and future scope of research are summarized.

Synchronization provides an insight into underlying the interaction mechanisms among the bivariate time series and has recently become an increasing focus of interest. In this study, we proposed a new cross entropy measure, named cross fuzzy measure entropy (C-FuzzyMEn), to detect the synchronization of the bivariate time series. The performances of C-FuzzyMEn, as well as two existing cross entropy measures, i.e., cross sample entropy (C-SampEn) and cross fuzzy entropy (C-FuzzyEn), were first tested and compared using three coupled simulation models (i.e., coupled Gaussian noise, coupled MIX( p ) and coupled Henon model) by changing the time series length, the threshold value for entropy and the coupling degree. The results from the simulation models showed that compared with C-SampEn, C-FuzzyEn and C-FuzzyMEn had better statistical stability and compared with C-FuzzyEn, C-FuzzyMEn had better discrimination ability. These three measures were then applied to a cardiovascular coupling problem, synchronization analysis for RR and pulse transit time (PTT) series in both the normal subjects and heart failure patients. The results showed that the heart failure group had lower cross entropy values than the normal group for all three cross entropy measures, indicating that the synchronization between RR and PTT time series increases in the heart failure group. Further analysis showed that there was no significant difference between the normal and heart failure groups for C-SampEn (normal 2.13 ± 0.37 vs. heart failure 2.07 ± 0.16, P = 0.36). However, C-FuzzyEn had significant difference between two groups (normal 1.42 ± 0.25 vs. heart failure 1.31 ± 0.12, P < 0.05). The statistical difference was larger for two groups when performing C-FuzzyMEn analysis (normal 2.40 ± 0.26 vs. heart failure 2.15 ± 0.13, P < 0.01). [ABSTRACT FROM AUTHOR]

The bipolar neutrosophic set is an important extension of the bipolar fuzzy set. The bipolar neutrosophic set is a hybridization of the bipolar fuzzy set and neutrosophic set. Every element of a bipolar neutrosophic set consists of three independent positive membership functions and three independent negative membership functions. In this paper, we develop cross entropy measures of bipolar neutrosophic sets and prove their basic properties. We also define cross entropy measures of interval bipolar neutrosophic sets and prove their basic properties. Thereafter, we develop two novel multi-attribute decision-making strategies based on the proposed cross entropy measures. In the decision-making framework, we calculate the weighted cross entropy measures between each alternative and the ideal alternative to rank the alternatives and choose the best one. We solve two illustrative examples of multi-attribute decision-making problems and compare the obtained result with the results of other existing strategies to show the applicability and effectiveness of the developed strategies. At the end, the main conclusion and future scope of research are summarized. [ABSTRACT FROM AUTHOR]