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Atanassov presented the dominant notion of intuitionistic fuzzy sets which brought revolution in different fields of science since their inception. The operations of t-norm and t-conorm introduced by Dombi were known as Dombi operations and Dombi operational parameter possesses natural flexibility with the resilience of variability. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision-making. This study aims to propose intuitionistic fuzzy rough TOPSIS method based on Dombi operations. For this, first we propose some new operational laws based on Dombi operations to aggregate averaging and geometric aggregation operators under the hybrid study of intuitionistic fuzzy sets and rough sets. On the proposed concept, we present intuitionistic fuzzy rough Dombi weighted averaging, intuitionistic fuzzy rough Dombi ordered weighted averaging, and intuitionistic fuzzy rough Dombi hybrid averaging operators. Moreover, on the developed concept, we present intuitionistic fuzzy rough Dombi weighted geometric, intuitionistic fuzzy rough Dombi ordered weighted geometric, and intuitionistic fuzzy rough Dombi hybrid geometric operators. The basic related properties of the developed operators are presented in detailed. Then the algorithm for MCGDM based on TOPSIS method for intuitionistic fuzzy rough Dombi averaging and geometric operators is presented. By applying accumulated geometric operator, the intuitionistic fuzzy rough numbers are converted into the intuitionistic fuzzy numbers. The massive outbreak of the pandemic COVID-19 promoted the challenging scenario for the world organizations including scientists, laboratories, and researchers to conduct special clinical treatment strategies to prevent the people from COVID-19 pandemic. Additionally, an illustrative example is proposed to solve MCGDM problem to diagnose the most severe patient of COVID-19 by applying TOPSIS. Finally, a comparative analysis of the developed model is presented with some existing methods which show the applicability and superiority of the developed model. [ABSTRACT FROM AUTHOR]

Recently, some improvement has been made in the dominant notion of fuzzy set that is Yager investigated the generalized concept of fuzzy set, Intuitionistic fuzzy set (IFS) and Pythagorean fuzzy set (PFS) and called it q-rung orthopair fuzzy (q-ROF) set (q-ROFS). The aim of this manuscript is to present the concept of q-ROF soft (q-ROFSt) set (q-ROFStS) based on the Dombi operations. Since Dombi operational parameter possess natural flexibility with the resilience of variability. Some new operational laws are defined based on hybrid study of soft sets and q-ROFS. The advantage of Dombi operational parameter is very important to express the experts' attitude in decision making. In this paper, we present q-ROFSt Dombi average (q-ROFSt DA) aggregation operators including q-ROFSt Dombi weighted average (q-ROFSt DWA), q-ROFSt Dombi ordered weighted average (q-ROFSt DOWA) and q-ROFSt Dombi hybrid average (q-ROFSt DHA) operators. Moreover, we investigate q-ROFSt Dombi geometric (q-ROFSt DG) aggregation operators including q-ROFSt Dombi weighted geometric (q-ROFSt DWG), q-ROFSt Dombi ordered weighted geometric (q-ROFSt DOWG), and q-ROFSt Dombi hybrid geometric (q-ROFSt DHG) operators. The basic properties of these operators are presented with detail such us Idempotency, Boundedness, Monotonicity, Shift invariance, and Homogeneity. Thus from the analysis and advantages of proposed model, it is clear that the investigated q-ROFSt DWA operator is the generalized form of IF St DWA, PFSt DWA and q-ROFDWA operators. Similarly, the investigated q-ROFSt DWG operator is the generalized form of IF St DWG, PFSt DWG and q-ROFDWG operators. By applying the develop approach, this manuscript contains the technique and algorithm for multicriteria decision making (MCDM). Further a numerical example is developed to illustrate the flexibility and applicability of the developed operators. [ABSTRACT FROM AUTHOR]

Industrial control system (ICS) attacks are usually targeted attacks that use the ICS entry approach to get a foothold within a system and move laterally throughout the organization. In recent decades, powerful attacks such as Stuxnet, Duqu, Flame, and Havex have served as wake-up calls for industrial units. All organizations are faced with the rise of security challenges in technological innovations. This paper aims to develop aggregation operators that can be used to address the decision-making problems based on a spherical fuzzy rough environment. Meanwhile, some interesting properties of idempotence, boundedness, and monotonicity for the proposed operators are analyzed. Moreover, we use this newly constructed framework to select ICS security suppliers and validate its acceptability. Furthermore, a different test has been performed based on a new operator to strengthen the suggested approach. Additionally, comparative analysis based on the novel extended TOPSIS method is presented to demonstrate the superiority of the proposed technique. The results show that the conventional approach has a larger area for information representation, better adaptability to the evaluation environment, and higher reliability of the evaluation results. [ABSTRACT FROM AUTHOR]

The purpose of writing this manuscript is to point out some limitations of existing associated immediate probability intuitionistic fuzzy geometric aggregation operators as these existing operators fail under some conditions such as the existing operators cannot handle the information given in Pythagorean fuzzy sets, picture fuzzy sets, spherical fuzzy sets, and T-spherical fuzzy sets and the existing aggregation operators also cannot aggregate the membership value when membership value of anyone intuitionistic fuzzy number become zero. To overcome these shortcomings associated immediate probability geometric aggregation operators have been developed for T-spherical fuzzy sets and associated immediate probability interactive geometric aggregation operators are proposed. Then a comparison between these operators is developed with the help of an example. The existing score function for T-spherical fuzzy sets does not involve abstinence so a new score function is developed which provides a better comparison between any two T-spherical fuzzy numbers. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. The advantages of the proposed work are also discussed in which it is shown that under some conditions the proposed operators can be reduced to other tools of uncertainty. The comparison between existing and proposed work is also developed with the help of an example. [ABSTRACT FROM AUTHOR]

The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers' unknown weights as well as attributes' weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and EDAS methodology to handle the uncertainty in real-word decision-making problems (DMPs) under q-rung orthopair fuzzy rough information. To show the superiority and applicability of the developed technique, a numerical case study of a real-life DMP in agriculture farming is considered. Findings indicate that the suggested decision-making model is much more efficient and reliable to tackle uncertain information based on q-ROFR information. [ABSTRACT FROM AUTHOR]

The objective of this manuscript is to investigate the concept of generalized q-rung orthopair fuzzy sets (Gq- R O F Ss) and group generalized q-rung orthopair fuzzy sets (GGq- R O F Ss) by incorporating the concept of generalized parameter and group generalized parameters in q-rung orthopair fuzzy environment. The main advantage of generalized parameter in q-rung orthopair fuzzy environment is to reduce uncertain errors in the original information to ensure the expert's level of trust and improve the accuracy of final decision. On the base of generalized parameter, some aggregation operators are introduced such as generalized q-rung orthopair fuzzy average aggregation operators and group generalized q-rung orthopair fuzzy average aggregation operators and studied their related properties. Furthermore, a multi-criteria decision-making method technique based on proposed approach is presented. Finally, a numerical example is provided to illustrate the feasibility of the proposed methods and deliver the sensitivity analysis and comparative analysis, which show the superiority of developed approached than existing methods. [ABSTRACT FROM AUTHOR]

Recently, Yager presented the new concept of q-rung orthopair fuzzy (q-ROF) set (q-ROFS) which emerged as the most significant generalization of Pythagorean fuzzy set (PFS). From the analysis of q-ROFS, it is clear that the rung q is the most significant feature of this notion. When the rung q increases, the orthopair adjusts in the boundary range which is needed. Thus, the input range of q-ROFS is more flexible, resilient, and suitable than the intuitionistic fuzzy set (IFS) and PFS. The aim of this manuscript is to investigate the hybrid concept of soft set ( S t S) and rough set with the notion of q-ROFS to obtain the new notion of q-ROF soft rough (q-ROF S t R) set (q-ROF S t RS). In addition, some averaging aggregation operators such as q-ROF S t R weighted averaging (q-ROF S t RWA), q-ROF S t R ordered weighted averaging (q-ROF S t ROWA), and q-ROF S t R hybrid averaging (q-ROF S t RHA) operators are presented. Then, the basic desirable properties of these investigated averaging operators are discussed in detail. Moreover, we investigated the geometric aggregation operators, such as q-ROF S t R weighted geometric (q-ROF S t RWG), q-ROF S t R ordered weighted geometric (q-ROF S t ROWG), and q-ROF S t R hybrid geometric (q-ROF S t RHG) operators, and proposed the basic desirable characteristics of the investigated geometric operators. The technique for multicriteria decision-making (MCDM) and the stepwise algorithm for decision-making by utilizing the proposed approaches are demonstrated clearly. Finally, a numerical example for the developed approach is presented and a comparative study of the investigated models with some existing methods is brought to light in detail which shows that the initiated models are more effective and useful than the existing methodologies. [ABSTRACT FROM AUTHOR]

Molodtsov investigated the pioneer notion of soft set (SfS) which provides a general framework for mathematical problems by affix parameterization tools during the analysis as compared to fuzzy set and q‐rung orthopair fuzzy set (q‐ROFS). The aim of this manuscript is to investigate the notion of q‐rung orthopair fuzzy soft set (q‐ROFSfS), which provide a lay of foundation for those difficulties and complexities which the contemporary theories face during the study of uncertainty. Therefore, our main contribution in this manuscript is to investigate the q‐rung orthopair fuzzy soft weighted averaging, q‐rung orthopair fuzzy soft ordered weighted averaging and q‐rung orthopair fuzzy soft hybrid averaging operators in q‐ROF soft (q‐ROFSf) environment. Further, the fundamental properties of these aggregation operators are studied. On the base of developed approach an algorithm for multicriteria decision making method is being presented. An application of medical diagnosis problems is solved on the proposed algorithm under the q‐ROFSf environment. Finally, comparison between the developed operators with some existing operators are being presented showing the superiority and efficiency of the developed approach than the existing literature. [ABSTRACT FROM AUTHOR]

In this manuscript we develop a comprehensive model to tackle decision making problems where strong points of view are in the favor and against some projects, entities or plans. Therefore a new approach is adopted to hybrid q-rung orthopair fuzzy sets with notions of covering rough set and TOPSIS. This model has stronger capability than intuitionistic fuzzy set and Pythagorean fuzzy set to manage the uncertainty. Furthermore an example is given to demonstrate how the proposed method helps us in decision making problems. [ABSTRACT FROM AUTHOR]

The objective of this paper is to present new interactive averaging aggregation operators by assigning associate probabilities for T-spherical fuzzy sets (T-SFSs). T-SFS is a generalization of several existing theories such as intuitionistic fuzzy sets and picture fuzzy sets to handle imprecise information. Under such an environment, we developed a series of averaging interactive aggregation operators under the features that each element is represented with T-spherical fuzzy numbers. Various properties of the proposed operators are also investigated. Further, to rank the different T-SFSs, we exhibit the new score functions and state their some properties. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. To save non-renewable resources and to the protect environment, the use of renewable resources is important. Solar energy is one of the best renewable energy resources and is also environment-friendly and thus the selection of solar cells is typically a multi-attribute decision-making problem. Therefore, the applicability of the developed algorithm is demonstrated with a numerical example in the selection of the solar cells and comparison of their performance with the several existing approaches. [ABSTRACT FROM AUTHOR]