Complex Pythagorean Dombi fuzzy graphs for decision making

Decision algorithm for picture fuzzy sets and Aczel Alsina aggregation operators based on unknown degree of wights

Aggregation operators (AOs) are well-known and efficient mathematical tools that are utilized to overcome the impact of imprecise and vague information during the aggregation process. The theoretical concepts of Aczel Alsina aggregation expressions are an extension of triangular norms and become a hot research topic in the environment of the fuzzy framework. The power operators provide a smooth approximation and are used to mitigate the influence of redundant or insufficient information on the attributes or criteria. Some robust aggregation approaches are developed by combining two different theories, like power operators and Aczel Alsina aggregation tools. This article aims to explore the theory of picture fuzzy sets (PFSs), an extended version of fuzzy sets, and intuitionistic fuzzy sets. Some robust operations of Aczel Alsina aggregation tools are also present in light of the picture fuzzy environment. We established a class of new methodologies in the light of picture fuzzy information, including picture fuzzy Aczel Alsina power weighted average (PFAAPWA) and picture fuzzy Aczel Alsina power ordered weighted average (PFAAPOWA) operators. We also developed an appropriate approach like picture fuzzy Aczel Alsina power weighted geometric (PFAAPWG) and picture fuzzy Aczel Alsina power ordered weighted geometric (PFAAPOWG) operators. Notable properties and characteristics of proposed methodologies are also demonstrated. Our invented approaches not only aggregate complicated information but can clearly define interrelationships among several arguments. Moreover, we establish an algorithm for the multi-attribute group decision-making (MAGDM) problem to handle the impact of redundant and vague information on human opinions. Finally, we study an experimental case study to evaluate an appropriate optimal option from available options. To reveal consistency and effectiveness of developed approaches, influence study by changing various parametric values and comparative study by comparing results of existing approaches.

Solving Pythagorean fuzzy partial fractional diffusion model using the Laplace and Fourier transforms

Many mathematical models describe the Corona virus disease 2019 (COVID-19) outbreak; however, they require advance mathematical skills. The need for this study is to determine the diffusion of the COVID-19 vaccine in humans. To this end, we first establish a Pythagorean fuzzy partial fractional differential equation using the Pythagorean fuzzy integral transforms to express the effects of COVID-19 vaccination on humans under the generalized Hukuhara partial differential conditions. We extract the analytical solution of the Pythagorean fuzzy partial fractional differential equation using the Pythagorean fuzzy Laplace transform under the generalized Hukuhara partial differential and the Pythagorean fuzzy Fourier transform using the Caputo generalized Hukuhara partial differential. Moreover, we present some essential postulates and results related to the Pythagorean fuzzy Laplace transform and the Pythagorean fuzzy Fourier transform. Furthermore, we develop the solution procedure to extract the solution of the Pythagorean fuzzy partial fractional differential equation. To grasp the considered approach, a mathematical model for the diffusion of the COVID-19 vaccination in the human body is provided and analyzed the behavior to visualize and support the proposed model. Our proposed method is efficient and has a great worth to discuss the bio-mathematical models in various fields of science and medicines.

q-Rung orthopair fuzzy soft aggregation operators based on Dombi t-norm and t-conorm with their applications in decision making

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.

New concepts of pentapartitioned neutrosophic graphs and applications for determining safest paths and towns in response to COVID-19

Pentapartitioned neutrosophic sets are a generalization of the single-valued and quadri-partitioned single-valued neutrosophic sets, and utilizes five symbol-valued neutrosophic logic. In this paper, we introduce some novel concepts regarding pentapartitioned neutrosophic graphs (PPNGs), and emphasize the effectiveness at interpreting extremely heterogeneous data that are prevalent in our daily life, particularly data gathered from various different sources which are becoming increasingly common place in the current times. The applicability of the proposed PPNG is demonstrated by applying the PPNGs on a potential real-life scenario on responding to the spread of COVID-19, where PPNGs are used to determine the safest path of travel and the safest place to stay to minimize the chances of getting infected. Both of this information have proven to be vital aspects in the efforts to combat the spread of the COVID-19 pandemic while providing the necessary support to the domestic economies, most of which are currently in recession due to the adverse effects brought upon by the pandemic. Hence, the PPNGs are applicable to all countries around the world and can be used under any circumstances such as pandemics or even in regular situations to optimize the travelling time and distance.

Complex T-spherical fuzzy Dombi aggregation operators and their applications in multiple-criteria decision-making

Complex fuzzy (CF) sets (CFSs) have a significant role in modelling the problems involving two-dimensional information. Recently, the extensions of CFSs have gained the attention of researchers studying decision-making methods. The complex T-spherical fuzzy set (CTSFS) is an extension of the CFSs introduced in the last times. In this paper, we introduce the Dombi operations on CTSFSs. Based on Dombi operators, we define some aggregation operators, including complex T-spherical Dombi fuzzy weighted arithmetic averaging (CTSDFWAA) operator, complex T-spherical Dombi fuzzy weighted geometric averaging (CTSDFWGA) operator, complex T-spherical Dombi fuzzy ordered weighted arithmetic averaging (CTSDFOWAA) operator, complex T-spherical Dombi fuzzy ordered weighted geometric averaging (CTSDFOWGA) operator, and we obtain some of their properties. In addition, we develop a multi-criteria decision-making (MCDM) method under the CTSF environment and present an algorithm for the proposed method. To show the process of the proposed method, we present an example related to diagnosing the COVID-19. Besides this, we present a sensitivity analysis to reveal the advantages and restrictions of our method.

Complex fuzzy aggregation operations with complex weights

Complex fuzzy aggregation operation (CFAO) is a formalized definition of combining several complex fuzzy sets into a single complex fuzzy set. It extends classical fuzzy aggregation operation (FAO) to the complex-valued domain retaining classical real-valued weight. CFAO was initially defined with complex weight by Ramot et al. However, there has been virtually no progress in developing CFAO with complex weight. In this paper, we study the CFAOs with complex weight. We first discuss how to define complex weights meeting the restriction that the sum of weights is equal to 1. We give a new natural type of complex weight which is different from Ramot et al.’s complex weight. Then we study various properties which include idempotency, homogeneity, rotational invariance and shift invariance for CFAOs with both types of complex weights.

Extensions of prioritized weighted aggregation operators for decision-making under complex q-rung orthopair fuzzy information

The complex q-rung orthopair fuzzy set (Cq-ROFS), an efficient generalization of complex intuitionistic fuzzy set (CIFS) and complex Pythagorean fuzzy set (CPFS), is potent tool to handle the two-dimensional information and has larger ability to translate the more uncertainty of human judgment then CPFS as it relaxes the constrains of CPFS and thus the space of allowable orthopair increases. To solve the multi-criteria decision making (MCDM) problem by considering that criteria are at the same priority level may affect the results because in realistic situations the priority level of criteria is different. In this manuscript, we propose some useful prioritized AOs under Cq-ROF environment by considering the prioritization among attributes. We develop two prioritized AOs, namely complex q-rung orthropair fuzzy prioritized weighted averaging (C-qROFPWA) operator and complex q-rung orthropair fuzzy prioritized weighted geometric (Cq-ROFPWG) operator. We also consider their desirable properties and two special cases with their detailed proofs. Moreover, we investigate a new technique to solve the MCDM problem by initiating an algorithm along with flowchart on the bases of proposed operators. Further, we solve a practical example to reveal the importance of proposed AOs. Finally, we apply the existing operators on the same data to compare our computed result to check the superiority and validity of our proposed operators.

Prioritized weighted aggregation operators under complex pythagorean fuzzy information

Complex Pythagorean fuzzy (CPF), a worthwhile generalization of Pythagorean fuzzy set, is a powerful tool to deal with two-dimensional or periodic information. In this paper, we develop two prioritized aggregation operators (AOs) under CPF environment, namely, complex Pythagorean fuzzy prioritized weighted averaging (CPFPWA) operator and complex Pythagorean fuzzy prioritized weighted geometric (CPFPWG) operator. We consider the prioritization relationship among criteria and decision makers (DMs) to make our result more accurate as in real decision making (DM) problems, the criteria and DMs have different priority level. Further, we discuss remarkable properties of our proposed AOs. Moreover, we promote the evolution of MCDM problem by investigating an algorithm in CPF environment with its flow chart. Finally, to check the superiority and validity of proposed operators, we compare the computed results with the different existing techniques.