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Divergence or relative information is a measure of information associated with two probability distributions of a discrete random variable which is based in Shannon entropy. In this paper a new divergence measure and corresponding fuzzy directed divergence measure have been proposed. Comparative study of the proposed divergence measure with some existing divergence measure has been done with the help of numerical example. Further, the application of proposed fuzzy directed divergence is illustrated in decision making problems. [ABSTRACT FROM AUTHOR]

Due to the digitization of information, organizations have abundant data in databases. Large-scale data are equally important and complex hence gathering, storing, understanding, and analyzing data is a problem for organizations. To extract information from this superfluous data, the need for dimensionality reduction increases. Soft set theory has been efficaciously applied and solved problems of dimensionality, which saves the cost of computation, reduces noise, and redundancy in data. Different methods and measures are developed by researchers for the reduction of dimensions, in which some are probabilistic, and some are non-probabilistic. In this paper, a non-probabilistic approach is developed by using soft set theory for dimensionality reduction. Further, an algorithm of dimensionality reduction through bipartite graphs is also described. Lastly, the proposed algorithm is applied to a case study, and a comparison of results indicates that the proposed algorithm is better than the existing algorithms. [ABSTRACT FROM AUTHOR]

Uncertainties and fuzziness are basic phenomena in human thinking and in many real-world objectives. In the existing literature of information theory various divergence measures are available for studying such phenomena in accordance to their ethos. In general, some are probabilistic and some are non-probabilistic by nature. In the present communication, an attempt is made to introduce non-probabilistic divergence measures for fuzzy matrices that are exponential in nature. In the present study, we prove their validity and study their properties. The different applications of proposed non-probabilistic measure are discussed in the amphitheater of decision making and feature selection. [ABSTRACT FROM AUTHOR]