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Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks. [ABSTRACT FROM AUTHOR]

As generalize of the hesitant fuzzy sets, hesitant interval-valued fuzzy sets (HIVFSs), which permits the memberships of an element to a given set having a few different interval values in [0,1] rather than real numbers, can be considered as a powerful tool to express uncertain information in the human decision making process. Based on the traditional Hamming distance, Euclidean distance, Hausdorff distance, and generalized distance, in this paper, we propose a variety of distance measures for hesitant interval-valued fuzzy sets, based on which the corresponding similarity measures can be obtained. We investigate the connections of the aforementioned distance measures and further develop a number of hesitant interval-valued ordered weighted distance measures and hesitant interval-valued ordered weighted similarity measures. They can alleviate the influence of unduly large (or small) deviations on the aggregation results by assigning them low (or high) weights. Finally, we shall present a numerical example to show potential evaluation of emerging technology commercialization with hesitant interval-valued fuzzy information in order to illustrate the method proposed in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new fuzzy decision making technique called the fuzzy induced heavy ordered weighted averaging distance (FIHOWAD) operator. It is an extension of the ordered weighted averaging (OWA) operator that uses the main characteristics of the induced OWA (IOWA), the Hamming distance, the heavy OWA (HOWA) and uncertain information represented as fuzzy numbers. A key feature of the FIHOWAD operator is that it generalizes a wide range of aggregation operators such as the fuzzy minimum distance, the fuzzy weighted Hamming distance (FWHD), the fuzzy OWA distance (FOWAD), the fuzzy IOWA distance (FIOWAD) and the fuzzy heavy OWA distance (FHOWAD) operators. We studied some of its main properties and different particular cases. Finally, we present a numerical example to illustrate the new approach in a financial decision making problem. [ABSTRACT FROM AUTHOR]