Identification of mental disorders in South Africa using complex probabilistic hesitant fuzzy N-soft aggregation information.

This paper aims to address the challenges faced by medical professionals in identifying mental disorders. These mental health issues are an increasing public health concern, and middle-income nations like South Africa are negatively impacted. Mental health issues pose a substantial public health concern in South Africa, putting forth extensive impacts on both individuals and society broadly. Insufficient funding for mental health remains the greatest barrier in this country. In order to meet the diverse and complex requirements of patients effective decision making in the treatment of mental disorders is crucial. For this purpose, we introduced the novel concept of the complex probabilistic hesitant fuzzy N-soft set (CPHFNSS) for modeling the unpredictability and uncertainty effectively. Our approach improves the precision with which certain traits connected to different types of mental conditions are recognized by using the competence of experts. We developed the fundamental operations (like extended and restricted intersection, extended and restricted union, weak, top, and bottom weak complements) with examples. We also developed the aggregation operators and their many features, along with their proofs and theorems, for CPHFNSS. By implementing these operators in the aggregation process, one could choose a combination of characteristics. Further, we introduced the novel score function, which is used to determine the optimal choice among them. In addition, we created an algorithm with numerical illustrations for decision making in which physicians employ CPHFNS data to diagnose a specific condition. Finally, comparative analyses confirm the practicability and efficacy of the technique that arises from the model developed in this paper.

Evaluation of economic development policies using a spherical fuzzy extended TODIM model with Z̆-numbers.

Zadeh's Z̆-numbers are able to more effectively characterize uncertain information. Combined with "constraint" and "reliability". It is more powerful at expressing human knowledge. While the reliability of data can have a direct impact on the precision of decisions. The key challenge in solving a Z̆-number issue is reasoning about both fuzzy and probabilistic uncertainty. Existing research on the Z̆-number measure is only some, and most studies cannot adequately convey the benefits of Z̆-information and the properties of Z̆-number. Considering this study void, this work concurrently investigated the randomness and fuzziness of Z̆-number with Spherical fuzzy sets. We first introduced the spherical fuzzy Z-numbers (SFZNs), whose elements are pairwise comparisons of the decision-maker's options. It can be used effectively to make true ambiguous judgments, reflecting the fuzzy nature, flexibility, and applicability of decision making data. We developed the operational laws and aggregation operators such as the weighted averaging operator, the ordered weighted averaging operator, the hybrid averaging operator, the weighted geometric operator, the ordered weighted geometric operator, and the hybrid geometric operator for SFZ̆Ns. Furthermore, two algorithm are developed to tackle the uncertain information in the form of spherical fuzzy Z̆-numbers based to the proposed aggregation operators and TODIM methodology. Finally, we developed the relative comparison and discussion analysis to show the practicability and efficacy of the suggested operators and approach.

Early infectious diseases identification based on complex probabilistic hesitant fuzzy N-soft information.

This paper aims to assess and deal with the challenges experienced by medical professionals caring for infectious diseases. In Pakistan, public health is still a serious concern and the main contributor to morbidity and mortality is infectious diseases. The major issue is a resemblance in the clinical symptoms of infectious diseases such as tuberculosis, hepatitis, COVID-19, dengue, and malaria. Early detection of infectious disease is crucial in order to start treatment with counseling and medication. This can only be done if several infections with similar clinical traits can be diagnosed depending on several criteria, including the availability of various kits, the ability to carry out diagnostic procedures, money, and technical staff. But woefully Pakistan's economy is badly battered due to several circumstances. Therefore, we are unable to provide patients with enough diagnostic testing kits and broadly accessible therapy choices, which makes diagnosis more difficult and create hesitancy with fuzziness and randomness. For this purpose, we introduced the new concept of the complex probabilistic hesitant fuzzy N-soft set. We defined its fundamental operations (like restricted and extended union, restricted and extended intersection, weak, top and bottom weak complements, as well as soft max-AND or soft min-OR) with examples. We also discussed their many properties with their proofs and theorems. Furthermore, we developed the algorithms for decision-making where doctors use the complex probabilistic hesitant fuzzy N-soft information to identify a particular disease. Furthermore, we explained numerical illustration of two case studies. Moreover, a sensitive and comparative analysis is discussed. In the last, we conclude the whole study.

A model for emergency supply management under extended EDAS method and spherical hesitant fuzzy soft aggregation information.

Due to the frequent occurrence of numerous emergency events that have significantly damaged society and the economy, the need for emergency decision-making has been manifest recently. It assumes a controllable function when it is critical to limit property and personal catastrophes and lessen their negative consequences on the natural and social course of events. In emergency decision-making problems, the aggregation method is crucial, especially when there are more competing criteria. Based on these factors, we first introduced some basic concepts about SHFSS, and then we introduced some new aggregation operators such as the spherical hesitant fuzzy soft weighted average, spherical hesitant fuzzy soft ordered weighted average, spherical hesitant fuzzy weighted geometric aggregation, spherical hesitant fuzzy soft ordered weighted geometric aggregation, spherical hesitant fuzzy soft hybrid average, and spherical hesitant fuzzy soft hybrid geometric aggregation operator. The characteristics of these operators are also thoroughly covered. Also, an algorithm is developed within the spherical hesitant fuzzy soft environment. Furthermore, we extend our investigation to the Evaluation based on the Distance from Average Solution method in multiple attribute group decision-making with spherical hesitant fuzzy soft averaging operators. And a numerical illustration for "supply of emergency aid in post-flooding the situation" is given to show the accuracy of the mentioned work. Then a comparison between these operators and the EDAS method is also established in order to further highlight the superiority of the established work.

Novel Information Measures for Fermatean Fuzzy Sets and Their Applications to Pattern Recognition and Medical Diagnosis.

Fermatean fuzzy sets (FFSs) have piqued the interest of researchers in a wide range of domains. The striking framework of the FFS is keen to provide the larger preference domain for the modeling of ambiguous information deploying the degrees of membership and nonmembership. Furthermore, FFSs prevail over the theories of intuitionistic fuzzy sets and Pythagorean fuzzy sets owing to their broader space, adjustable parameter, flexible structure, and influential design. The information measures, being a significant part of the literature, are crucial and beneficial tools that are widely applied in decision-making, data mining, medical diagnosis, and pattern recognition. This paper aims to expand the literature on FFSs by proposing many innovative Fermatean fuzzy sets-based information measures, namely, distance measure, similarity measure, entropy measure, and inclusion measure. We investigate the relationship between distance, similarity, entropy, and inclusion measures for FFSs. Another achievement of this research is to establish a systematic transformation of information measures (distance measure, similarity measure, entropy measure, and inclusion measure) for the FFSs. To accomplish this aim, new formulae for information measures of FFSs have been presented. To demonstrate the validity of the measures, we employ them in pattern recognition, building materials, and medical diagnosis. Additionally, a comparison between traditional and novel similarity measures is described in terms of counter-intuitive cases. The findings demonstrate that the innovative information measures do not include any absurd cases.

Correction to: A new emergency response of spherical intelligent fuzzy decision process to diagnose of COVID19.

[This corrects the article DOI: 10.1007/s00500-020-05287-8.].

A new emergency response of spherical intelligent fuzzy decision process to diagnose of COVID19.

The control of spreading of COVID-19 in emergency situation the entire world is a challenge, and therefore, the aim of this study was to propose a spherical intelligent fuzzy decision model for control and diagnosis of COVID-19. The emergency event is known to have aspects of short time and data, harmfulness, and ambiguity, and policy makers are often rationally bounded under uncertainty and threat. There are some classic approaches for representing and explaining the complexity and vagueness of the information. The effective tool to describe and reduce the uncertainty in data information is fuzzy set and their extension. Therefore, we used fuzzy logic to develop fuzzy mathematical model for control of transmission and spreading of COVID19. The fuzzy control of early transmission and spreading of coronavirus by fuzzy mathematical model will be very effective. The proposed research work is on fuzzy mathematical model of intelligent decision systems under the spherical fuzzy information. In the proposed work, we will develop a newly and generalized technique for COVID19 based on the technique for order of preference by similarity to ideal solution (TOPSIS) and complex proportional assessment (COPRAS) methods under spherical fuzzy environment. Finally, an illustrative the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested method, along with a sensitivity analysis and comparative analysis, showing the feasibility and reliability of its results.

A wind power plant site selection algorithm based on q-rung orthopair hesitant fuzzy rough Einstein aggregation information.

Wind power is often recognized as one of the best clean energy solutions due to its widespread availability, low environmental impact, and great cost-effectiveness. The successful design of optimal wind power sites to create power is one of the most vital concerns in the exploitation of wind farms. Wind energy site selection is determined by the rules and standards of environmentally sustainable development, leading to a low, renewable energy source that is cost effective and contributes to global advancement. The major contribution of this research is a comprehensive analysis of information for the multi-attribute decision-making (MADM) approach and evaluation of ideal site selection for wind power plants employing q-rung orthopair hesitant fuzzy rough Einstein aggregation operators. A MADM technique is then developed using q-rung orthopair hesitant fuzzy rough aggregation operators. For further validation of the potential of the suggested method, a real case study on wind power plant site has been given. A comparison analysis based on the unique extended TOPSIS approach is presented to illustrate the offered method's capability. The results show that this method has a larger space for presenting information, is more flexible in its use, and produces more consistent evaluation results. This research is a comprehensive collection of information that should be considered when choosing the optimum site for wind projects.

Decision support model for the patient admission scheduling problem based on picture fuzzy aggregation information and TOPSIS methodology.

Health care systems around the world do not have sufficient medical services to immediately offer elective (e.g., scheduled or non-emergency) services to all patients. The goal of patient admission scheduling (PAS) as a complicated decision making issue is to allocate a group of patients to a limited number of resources such as rooms, time slots, and beds based on a set of preset restrictions such as illness severity, waiting time, and disease categories. This is a crucial issue with multi-criteria group decision making (MCGDM). In order to address this issue, we first conduct an assessment of the admission process and gather four (4) aspects that influence patient admission and design a set of criteria. Even while many of these indicators may be accurately captured by the picture fuzzy set, we use an advanced MCGDM approach that incorporates generalized aggregation to analyze patients' hospitalization. Finally, numerical real-world applications of PAS are offered to illustrate the validity of the suggested technique. The advantages of the proposed approaches are also examined by comparing them to various existing decision methods. The proposed technique has been proved to assist hospitals in managing patient admissions in a flexible manner.

A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19.

The emergency situation of COVID-19 is a very important problem for emergency decision support systems. Control of the spread of COVID-19 in emergency situations across the world is a challenge and therefore the aim of this study is to propose a q-linear Diophantine fuzzy decision-making model for the control and diagnose COVID19. Basically, the paper includes three main parts for the achievement of appropriate and accurate measures to address the situation of emergency decision-making. First, we propose a novel generalization of Pythagorean fuzzy set, q-rung orthopair fuzzy set and linear Diophantine fuzzy set, called q-linear Diophantine fuzzy set (q-LDFS) and also discussed their important properties. In addition, aggregation operators play an effective role in aggregating uncertainty in decision-making problems. Therefore, algebraic norms based on certain operating laws for q-LDFSs are established. In the second part of the paper, we propose series of averaging and geometric aggregation operators based on defined operating laws under q-LDFS. The final part of the paper consists of two ranking algorithms based on proposed aggregation operators to address the emergency situation of COVID-19 under q-linear Diophantine fuzzy information. In addition, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.

EDAS method for decision support modeling under the Pythagorean probabilistic hesitant fuzzy aggregation information.

The significance of emergency decision-making (EmDM) has been experienced recently due to the continuous occurrence of various emergency situations that have caused significant social and monetary misfortunes. EmDM assumes a manageable role when it is important to moderate property and live misfortunes and to reduce the negative effects on the social and natural turn of events. Genuine world EmDM issues are usually described as complex, time-consuming, lack of data, and the effect of mental practices that make it a challenging task for decision-makers. This article shows the need to manage the various types of vulnerabilities and to monitor practices to resolve these concerns. In clinical analysis, how to select an ideal drug from certain drugs with efficacy values for coronavirus disease has become a common problem these days. To address this issue, we are establishing a multi-attribute decision-making approach (MADMap) based on the EDAS method under Pythagorean probabilistic hesitant fuzzy information. In addition, an algorithm is developed to address the uncertainty in the selection of drugs in EmDM issues with regards to clinical analysis. The actual contextual analysis of the selection of the appropriate drug to treat coronavirus ailment is utilized to show the practicality of our proposed technique. Finally, with the help of a comparative analysis of the TOPSIS technique, we demonstrate the efficiency and applicability of the established methodology.

Emergency decision support modeling under generalized spherical fuzzy Einstein aggregation information.

Dominant emergency action should be adopted in the case of an emergency situation. Emergency is interpreted as limited time and information, harmfulness and uncertainty, and decision-makers are often critically bound by uncertainty and risk. This framework implements an emergency decision-making approach to address the emergency situation of COVID-19 in a spherical fuzzy environment. As the spherical fuzzy set (SFS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision-making problems (DMPs). Keeping in view the features of the SFSs, the purpose of this paper is to present some robust generalized operating laws in accordance with the Einstein norms. In addition, list of propose aggregation operators using Einstein operational laws under spherical fuzzy environment are developed. Furthermore, we design the algorithm based on the proposed aggregation operators to tackle the uncertainty in emergency decision making problems. Finally, numerical case study of COVID-19 as an emergency decision making is presented to demonstrate the applicability and validity of the proposed technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.

q-Rung Orthopair Fuzzy Rough Einstein Aggregation Information-Based EDAS Method: Applications in Robotic Agrifarming.

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.

Entropy Based Pythagorean Probabilistic Hesitant Fuzzy Decision Making Technique and Its Application for Fog-Haze Factor Assessment Problem.

The Pythagorean probabilistic hesitant fuzzy set (PyPHFS) is an effective, generalized and powerful tool for expressing fuzzy information. It can cover more complex and more hesitant fuzzy evaluation information. Therefore, based on the advantages of PyPHFSs, this paper presents a new extended fuzzy TOPSIS method for dealing with uncertainty in the form of PyPHFS in real life problems. The paper is divided into three main parts. Firstly, the novel Pythagorean probabilistic hesitant fuzzy entropy measure is established using generalized distance measure under PyPHFS information to find out the unknown weights information of the attributes. The second part consists of the algorithm sets of the TOPSIS technique under PyPHFS environment, where the weights of criteria are completely unknown. Finally, in order to verify the efficiency and superiority of the proposed method, this paper applies some practical examples of the selection of the most critical fog-haze influence factor and makes a detailed comparison with other existing methods.

Emergency decision support modeling for COVID-19 based on spherical fuzzy information.

Significant emergency measures should be taken until an emergency event occurs. It is understood that the emergency is characterized by limited time and information, harmfulness and uncertainty, and decision-makers are always critically bound by uncertainty and risk. This paper introduces many novel approaches to addressing the emergency situation of COVID-19 under spherical fuzzy environment. Fundamentally, the paper includes six main sections to achieve appropriate and accurate measures to address the situation of emergency decision-making. As the spherical fuzzy set (FS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision-making problems (DMPs). First, we discuss basic algebraic operational laws (AOLs) under spherical FS. In addition, elaborate on the deficiency of existing AOLs and present three cases to address the validity of the proposed novel AOLs under spherical fuzzy settings. Second, we present a list of Einstein aggregation operators (AgOp) based on the Einstein norm to aggregate uncertain information in DMPs. Thirdly, we are introducing two techniques to demonstrate the unknown weight of the criteria. Fourthly, we develop extended TOPSIS and Gray relational analysis approaches based on AgOp with unknown weight information of the criteria. In fifth, we design three algorithms to address the uncertainty and ambiguity information in emergency DMPs. Finally, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed three algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.

Spherical Fuzzy Logarithmic Aggregation Operators Based on Entropy and Their Application in Decision Support Systems.

Keeping in view the importance of new defined and well growing spherical fuzzy sets, in this study, we proposed a novel method to handle the spherical fuzzy multi-criteria group decision-making (MCGDM) problems. Firstly, we presented some novel logarithmic operations of spherical fuzzy sets (SFSs). Then, we proposed series of novel logarithmic operators, namely spherical fuzzy weighted average operators and spherical fuzzy weighted geometric operators. We proposed the spherical fuzzy entropy to find the unknown weights information of the criteria. We study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Finally, the detailed steps for the spherical fuzzy decision-making problems were developed, and a practical case was given to check the created approach and to illustrate its validity and superiority. Besides this, a systematic comparison analysis with other existent methods is conducted to reveal the advantages of our proposed method. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.