Abstract In this article, we introduce dual hesitant ‐rung orthopair fuzzy 2‐tuple linguistic set (DHq‐ROFTLS), a new strategy for dealing with uncertainty that incorporates a 2‐tuple linguistic term into dual hesitant ‐rung orthopair fuzzy set (DHq‐ROFS). DHq‐ROFTLS is a better way to deal with uncertain and imprecise information in the decision‐making environment. We elaborate the operational rules, based on which, the DHq‐ROFTL weighted averaging (DHq‐ROFTLWA) operator and the DHq‐ROFTL weighted geometric (DHq‐ROFTLWG) operator are presented to fuse the DHq‐ROFTL numbers (DHq‐ROFTLNs). As Maclaurin symmetric mean (MSM) aggregation operator is a useful tool to model the interrelationship between multi‐input arguments, we generalize the traditional MSM to aggregate DHq‐ROFTL information. Firstly, the DHq‐ROFTL Maclaurin symmetric mean (DHq‐ROFTLMSM) and the DHq‐ROFTL weighted Maclaurin symmetric mean (DHq‐ROFTLWMSM) operators are proposed along with some of their desirable properties and some special cases. Further, the DHq‐ROFTL dual Maclaurin symmetric mean (DHq‐ROFTLDMSM) and weighted dual Maclaurin symmetric mean (DHq‐ROFTLWDMSM) operators with some properties and cases are presented. Moreover, the assessment and prioritizing of the most important aspects in multiple attribute group decision‐making (MAGDM) problems is analysed by an extended novel approach based on the proposed aggregation operators under DHq‐ROFTL framework. At long last, a numerical model is provided for the selection of adequate medication to control COVID‐19 outbreaks to demonstrate the use of the generated technique and exhibit its adequacy. Finally, to analyse the advantages of the proposed method, a comparison analysis is conducted and the superiorities are illustrated.

Abstract A complex Pythagorean fuzzy set, an extension of Pythagorean fuzzy set, is a powerful tool to handle two dimension phenomenon. Dombi operators with operational parameters have outstanding flexibility. This article presents certain aggregation operators under complex Pythagorean fuzzy environment, including complex Pythagorean Dombi fuzzy weighted arithmetic averaging (CPDFWAA) operator, complex Pythagorean Dombi fuzzy weighted geometric averaging (CPDFWGA) operator, complex Pythagorean Dombi fuzzy ordered weighted arithmetic averaging (CPDFOWAA) operator and complex Pythagorean Dombi fuzzy ordered weighted geometric averaging (CPDFOWGA) operator. Moreover, this paper explores some fundamental properties of these operators with appropriate elaboration. A decision‐making numerical example related to the selection of bank to purchase loan is given to demonstrate the significance of our proposed approach. Finally, a comparative analysis with existing operators is given to demonstrate the peculiarity of our proposed operators.

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.

The aim of this note is to introduce the notion of fuzzy congruence relation on pseudo BE-algebras and investigate their properties. We show that the set of fuzzy congruence relations of a pseudo BE-algebra is a complete lattice. Moreover, the quotient structure induced by fuzzy congruence relations are studied.

In this note, by using the concept of vague sets, the notions of vague BCK/BCI-algebra is introduced. And the notions of alpha-cut and vague-cut is introduced and the relationship between these notions and crisp subalgebras are studied.

By using the concept of fuzzy points, we generalize the notion of hyper BCK-algebra and the notions of fuzzy point hyper BCK-(sub) algebras, fuzzy point (weak, strong) hyper BCK-ideals, quasi hyper BCK-(sub) algebras and quasi (weak, strong) hyper BCK-ideals are introduced. The relationship between these notions are stated and proved.