Generalized complex q-rung orthopair fuzzy Einstein averaging aggregation operators and their application in multi-attribute decision making

Multi-attribute group decision making method for sponge iron factory location selection problem using multi-polar fuzzy EDAS approach

This paper presents new averaging operators, such as mpF Einstein weighted averaging (mpFEWA), mpF Einstein ordered weighted averaging (mpFEOWA), mpF Einstein hybrid weighted averaging (mpFEHWA), mpF Einstein weighted geometric (mpFEWG), and mpF Einstein hybrid weighted geometric (mpFEHWG), as well as new Einstein operations (mpFNs) for handling multi-polar fuzzy numbers. We evaluate these operators for idempotency, boundedness, monotonicity, and commutativity, and we design them to deal with multi-polar fuzzy numbers (mpFNs). Furthermore, the study investigates the use of these operators in MAGDM settings, namely mpFEWA and mpFEWG operators, to expand on this. Additionally, it proposes a procedure for determining the best site for a sponge iron production plant by use of the created MAGDM method. The EDAS method, which stands for "Evaluation based on Distance from Average Solution," verifies that the solutions are effective. Finally, the suggested model highlights the benefits and possible improvements provided by these creative strategies by comparing the new approach to conventional methods and evaluating its efficiency and practicality.

An integrated group decision-making method for the evaluation of hypertension follow-up systems using interval-valued q-rung orthopair fuzzy sets

It is imperative to comprehensively evaluate the function, cost, performance and other indices when purchasing a hypertension follow-up (HFU) system for community hospitals. To select the best software product from multiple alternatives, in this paper, we develop a novel integrated group decision-making (GDM) method for the quality evaluation of the system under the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs). The design of our evaluation indices is based on the characteristics of the HFU system, which in turn represents the evaluation requirements of typical software applications and reflects the particularity of the system. A similarity is extended to measure the IVq-ROFNs, and a new score function is devised for distinguishing IVq-ROFNs to figure out the best IVq-ROFN. The weighted fairly aggregation (WFA) operator is then extended to the interval-valued q-rung orthopair WFA weighted average operator (IVq-ROFWFAWA) for aggregating information. The attribute weights are derived using the LINMAP model based on the similarity of IVq-ROFNs. We design a new expert weight deriving strategy, which makes each alternative have its own expert weight, and use the ARAS method to select the best alternative based on these weights. With these actions, a GDM algorithm that integrates the similarity, score function, IVq-ROFWFAWA operator, attribute weights, expert weights and ARAS is proposed. The applicability of the proposed method is demonstrated through a case study. Its effectiveness and feasibility are verified by comparing it to other state-of-the-art methods and operators.

Complex q-rung orthopair fuzzy Frank aggregation operators and their application to multi-attribute decision making

The complex q-rung orthopair fuzzy sets (Cq-ROFSs) can serve as a generalization of q-rung orthopair fuzzy sets (q-ROFSs) and complex fuzzy sets FS (CFSs). Cq-ROFSs provide more freedom for people handling uncertainty and vagueness by the truth and falsity grades on the condition that the sum of the q-powers of the real part and imaginary part is within the unit interval. Further, Frank operational laws are an extended form of Archimedes' T mode and Archimedes' S mode and Frank aggregation operators have a certain parameter which makes them more flexible and more generalized than many other aggregation operators in the process of information fusion. The objectives of this paper are to extend the Frank operations to the complex q-rung orthopair fuzzy environment and to introduce their score function and accuracy function. Meanwhile, some complex q-rung fuzzy Frank aggregation operators are developed, such as the complex q-rung orthopair fuzzy Frank weighted averaging (Cq-ROFFWA) operator, the complex q-rung orthopair fuzzy Frank weighted geometric (Cq-ROFFWG) operator, and the complex q-rung orthopair fuzzy Frank ordered weighted averaging (Cq-ROFFOWA) operator, and their special cases are discussed. In addition, an innovative MADM method is introduced according to the propounded operators to deal with multi-attribute decision-making problems under the complex q-rung orthopair fuzzy environment. Consequently, the practicability and effectiveness of the created methods are proposed by parameter exploration and comparative analysis.

A new group decision-making framework based on 2-tuple linguistic complex q-rung picture fuzzy sets

The need for multi-attribute decision-making brings more and more complexity, and this type of decision-making extends to an ever wider range of areas of life. A recent model that captures many components of decision-making frameworks is the complex $ q $-rung picture fuzzy set (C$ q $-RPFS), a generalization of complex fuzzy sets and $ q $-rung picture fuzzy sets. From a different standpoint, linguistic terms are very useful to evaluate qualitative information without specialized knowledge. Inspired by the ease of use of the linguistic evaluations by means of 2-tuple linguistic term sets, and the broad scope of applications of C$ q $-RPFSs, in this paper we introduce the novel structure called 2-tuple linguistic complex $ q $-rung picture fuzzy sets (2TLC$ q $-RPFSs). We argue that this model prevails to represent the two-dimensional information over the boundary of C$ q $-RPFSs, thanks to the additional features of 2-tuple linguistic terms. Subsequently, some 2TLC$ q $-RPF aggregation operators are proposed. Fundamental cases include the 2TLC$ q $-RPF weighted averaging/geometric operators. Other sophisticated aggregation operators that we propose are based on the Hamacher operator. In addition, we investigate some essential properties of the new operators. These tools are the building blocks of a multi-attribute decision making strategy for problems posed in the 2TLC$ q $-RPFS setting. Furthermore, a numerical instance that selects an optimal machine is given to guarantee the applicability and effectiveness of the proposed approach. Finally, we conduct a comparison with other existing approaches.

Analyzing and controlling computer security threats based on complex q-rung orthopair fuzzy heronian mean operators

Certain intellectuals have generalized the principle of the fuzzy set (FS), but the theory of complex q-rung orthopair fuzzy set (Cq-ROFS) has received massive attraction from different scholars. The goal of this study is to combine the principle of Heronian mean (HM) operator with Cq-ROFS is to initiate the complex q-rung orthopair fuzzy HM (Cq-ROFHM) operator, complex q-rung orthopair fuzzy weighted HM (Cq-ROFWHM) operator, complex q-rung orthopair fuzzy geometric HM (Cq-ROFGHM) operator, complex q-rung orthopair fuzzy weighted geometric HM (Cq-ROFWGHM) operator, and their flexible and dominant properties. These operators can help to aggregate any number of attributes to determine the reliability and consistency of the investigated operators. Moreover, there are physical and non-physical threats. Physical threats cause damage to computer systems hardware and infrastructure. Examples include theft, vandalism through to natural disasters. Non-physical threats target the software and data on the computer systems. To manage such sort of troubles, we determine the analyzing and controlling computer security threats based on presented operators under the Cq-ROFS. Finally, to show the reliability and proficiency of the presented approaches, we resolved some numerical examples by using the explored operators. The comparative analysis, advantages, and graphical interpretations of the presented works are also discovered.

A further investigation on q-rung orthopair fuzzy Einstein aggregation operators

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.

A q-rung orthopair fuzzy non-cooperative game method for competitive strategy group decision-making problems based on a hybrid dynamic experts’ weight determining model

How to select the optimal strategy to compete with rivals is one of the hottest issues in the multi-attribute decision-making (MADM) field. However, most of MADM methods not only neglect the characteristics of competitors’ behaviors but also just obtain a simple strategy ranking result cannot reflect the feasibility of each strategy. To overcome these drawbacks, a two-person non-cooperative matrix game method based on a hybrid dynamic expert weight determination model is proposed for coping with intricate competitive strategy group decision-making problems within q-rung orthopair fuzzy environment. At the beginning, a novel dynamic expert weight calculation model, considering objective individual and subjective evaluation information simultaneously, is devised by integrating the superiorities of a credibility analysis scale and a Hausdorff distance measure for q-rung orthopair fuzzy sets (q-ROFSs). The expert weights obtained by the above model can vary with subjective evaluation information provided by experts, which are closer to the actual practices. Subsequently, a two-person non-cooperative fuzzy matrix game is formulated to determine the optimal mixed strategies for competitors, which can present the specific feasibility and divergence degree of each competitive strategy and be less impacted by the number of strategies. Finally, an illustrative example, several comparative analyses and sensitivity analyses are conducted to validate the reasonability and effectiveness of the proposed approach. The experimental results demonstrate that the proposed approach as a CSGDM method with high efficiency, low computation complexity and little calculation burden.