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Aggregation of q-rung orthopair fuzzy information serves as an important branch of the q-rung orthopair fuzzy set theory, where operations on q-rung orthopair fuzzy values (q-ROFVs) play a crucial role. Recently, aggregation operators on q-ROFVs were established by employing the Einstein operations rather than the algebraic operations. In this paper, we give a further investigation on operations and aggregation operators for q-ROFVs based on the Einstein operational laws. We present the operational principles of Einstein operations over q-ROFVs and compare them with those built on the algebraic operations. The properties of the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator and q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator are investigated in detail, such as idempotency, monotonicity, boundedness, shift-invariance and homogeneity. Then, the developed operators are applied to multiattribute decision making problems under the q-rung orthopair fuzzy environment. Finally, an example for selecting the design scheme for a blockchain-based agricultural product traceability system is presented to illustrate the feasibility and effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

The four fundamental operations of arithmetic for real (and complex) numbers are well known to everybody and quite often used in our daily life. And they have been extended to classical and generalized fuzzy environments with the demand of practical applications. In this paper, we present the arithmetic operations, including addition, subtraction, multiplication, and division operations, over q‐rung orthopair membership grades, where subtraction and division operations are both defined in two different ways. One is by solving the equation involving addition or multiplication operations, whereas the other is by determining the infimum or supremum of solutions of the corresponding inequality. Not all of q‐rung orthopairs can be performed by the former method but by the latter method, and it is proved that the former is a special case of the latter. Moreover, the elementary properties of arithmetic operations as well as mixed operations are extensively investigated. Finally, these arithmetic operations are pointwise defined on q‐rung orthopair fuzzy sets in which the membership degree of each element is a q‐rung orthopair. [ABSTRACT FROM AUTHOR]

Generalized orthopair fuzzy sets are extensions of ordinary fuzzy sets by relaxing restrictions on the degrees of support for and support against. Correlation analysis is to measure the statistical relationships between two samples or variables. In this paper, we propose a function measuring the interrelation of two q‐rung orthopair fuzzy sets, whose range is the unit interval [0,1]. First, the correlation and correlation coefficient of q‐rung orthopair membership grades are presented, and their basic properties are investigated. Second, these concepts are extended to q‐rung orthopair fuzzy sets on discrete universes. Then, we discuss their applications in cluster analysis under generalized orthopair fuzzy environments. And, a real‐world problem involving the evaluation of companies is used to illustrate the detailed processes of the clustering algorithm. Finally, we introduce the correlation and correlation coefficient of q‐rung orthopair fuzzy sets on both bounded and unbounded continuous universes and provide some numerical examples to substantiate such arguments. [ABSTRACT FROM AUTHOR]

Abstract: The generalized orthopair fuzzy set inherits the virtues of intuitionistic fuzzy set and Pythagorean fuzzy set in relaxing the restriction on the support for and support against. The very lax requirement provides decision makers great freedom in expressing their beliefs about membership grades, which makes generalized orthopair fuzzy sets having a wide scope of application in practice. In this paper, we present the Minkowski‐type distance measures, including Hamming, Euclidean, and Chebyshev distances, for q‐rung orthopair fuzzy sets. First, we introduce the Minkowski‐type distances of q‐rung orthopair membership grades, based on which we can rank orthopairs. Second, we propose several distances over q‐rung orthopair fuzzy sets on a finite discrete universe and subsequently discuss their applications to multiattribute decision‐making problems. Then we extend these results to a continuous universe, both bounded and unbounded cases are considered. Some illustrative examples are employed to substantiate the conceptual arguments. [ABSTRACT FROM AUTHOR]

Various distance and similarity measures in Atanassov’s intuitionistic fuzzy sets (IFSs) are applied to practical problems. However, it is difficult to decide which one is the most suitable for measuring the degree of distance or similarity, especially in the case of the occurrence of conflict results in practice. In this paper, we propose the concept of aggregation distance measure for IFSs based on aggregation functions without zero divisors to help decision makers to make final decisions. Furthermore, a novel technique is introduced to construct similarity measures from a given distance measure with respect to non-filling fuzzy negations, which gives a new direction for the construction method for similarity measures of IFSs. Some illustrative examples in applications such as pattern recognition, fuzzy clustering and decision making are used to investigate the effectiveness of the proposed measures. [ABSTRACT FROM AUTHOR]