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The concept of interval-valued Pythagorean fuzzy (IVPF) sets is capable of handling imprecise and ambiguous information and managing complex uncertainty in real-world applications. The focus of our this paper is to introduce some generalized operators, such as the generalized interval-valued Pythagorean fuzzy Einstein weighted averaging (abbreviated as GIVPFEWA) operator, the generalized interval-valued Pythagorean fuzzy Einstein ordered weighted averaging (abbreviated as GIVPFEOWA) operator, and the generalized interval-valued Pythagorean fuzzy Einstein hybrid averaging (abbreviated as GIVPFEHA) operator along with their some general properties, such as idempotency, commutativity, monotonicity and boundedness. Furthermore, the method for multiple attribute group decision making problems based on these operators was developed, and the operational processes were illustrated in detail. The main advantage of using the proposed methods and operators is that these operators and methods give a more complete view of the problem to the decision makers. These methods provide more general, more accurate and precise results as compared to the existing methods. Therefore these methods play a vital role in real world problems. Finally the proposed operators have been applied to decision-making problems to show the validity, practicality and effectiveness of the new approach. A systematic comparison between the existing work and the proposed work also has been given. [ABSTRACT FROM AUTHOR]

In this paper, we define aggregation operators for triangular cubic linguistic hesitant fuzzy sets which includes generalized triangular cubic linguistic hesitant fuzzy weighted averaging (GTCLHFWA) operator, generalized triangular cubic linguistic hesitant fuzzy weighted geometric (GTCHFWG) operator, generalized triangular cubic linguistic hesitant fuzzy ordered weighted average (GTCLHFOWA) operator, generalized triangular cubic linguistic hesitant fuzzy ordered weighted geometric (GTCLHFOWG) operator, generalized triangular cubic linguistic hesitant fuzzy hybrid averaging (GTCLHFHA) operator and generalized triangular cubic linguistic hesitant fuzzy hybrid geometric (GTCLHFHG) operator. Furthermore, we relate these aggregation operators to develop an approach to multiple attribute group decision-making with triangular cubic linguistic hesitant fuzzy information. Finally, a numerical example is providing to demonstrate the submission of the established approach. [ABSTRACT FROM AUTHOR]

The present study aims to introduce the notion of bipolar neutrosophic Hamacher aggregation operators and to also provide its application in real life. Then neutrosophic set (NS) can elaborate the incomplete, inconsistent, and indeterminate information, Hamacher aggregation operators, and extended Einstein aggregation operators to the arithmetic and geometric aggregation operators. First, we give the fundamental definition and operations of the neutrosophic set and the bipolar neutrosophic set. Our main focus is on the Hamacher aggregation operators of bipolar neutrosophic, namely, bipolar neutrosophic Hamacher weighted averaging (BNHWA), bipolar neutrosophic Hamacher ordered weighted averaging (BNHOWA), and bipolar neutrosophic Hamacher hybrid averaging (BNHHA) along with their desirable properties. The prime gain of utilizing the suggested methods is that these operators progressively provide total perspective on the issue necessary for the decision makers. These tools provide generalized, increasingly exact, and precise outcomes when compared to the current methods. Finally, as an application, we propose new methods for the multi-criteria group decision-making issues by using the various kinds of bipolar neutrosophic operators with a numerical model. This demonstrates the usefulness and practicality of this proposed approach in real life. [ABSTRACT FROM AUTHOR]