VIKOR and TOPSIS framework with a truthful-distance measure for the (t, s)-regulated interval-valued neutrosophic soft set.

This article introduces the structure of the (t,s)-regulated interval-valued neutrosophic soft set (abbr. (t,s)-INSS). The structure of (t,s)-INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence (t,s)-regulated). Besides, a novel distance measure for the (t,s)-INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a Viekriterijumsko Kompromisno Rangiranje (VIKOR) algorithm that works on the (t,s)-INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of (t,s)-INSS. The parameters t and s in the (t,s)-INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The (t,s)-INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters t and s, thereby enabling the (t,s)-INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.

TOPSIS approach for MCGDM based on intuitionistic fuzzy rough Dombi aggregation operations

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.

Generalized plithogenic whole hypersoft set, PFHSS-Matrix, operators and applications as COVID-19 data structures

This article is a preliminary draft for initiating and commencing a new pioneer dimension of expression. To deal with higher-dimensional data or information flowing in this modern era of information technology and artificial intelligence, some innovative super algebraic structures are essential to be formulated. In this paper, we have introduced such matrices that have multiple layers and clusters of layers to portray multi-dimensional data or massively dispersed information of the plithogenic universe made up of numerous subjects their attributes, and sub-attributes. For grasping that field of parallel information, events, and realities flowing from the micro to the macro level of universes, we have constructed hypersoft and hyper-super-soft matrices in a Plithogenic Fuzzy environment. These Matrices classify the non-physical attributes by accumulating the physical subjects and further sort the physical subjects by accumulating their non-physical attributes. We presented them as Plithogenic Attributive Subjectively Whole Hyper-Super-Soft-Matrix (PASWHSS-Matrix) and Plithogenic Subjective Attributively Whole-Hyper-Super-Soft-Matrix (PSAWHSS-Matrix). Several types of views and level-layers of these matrices are described. In addition, some local aggregation operators for Plithogenic Fuzzy Hypersoft Set (PPFHS-Set) are developed. Finally, few applications of these matrices and operators are used as numerical examples of COVID-19 data structures. [ABSTRACT FROM AUTHOR] Copyright of Journal of Intelligent & Fuzzy Systems is the property of IOS Press and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Time-Leveled Hypersoft Matrix, Level Cuts, Operators, and COVID-19 Collective Patient Health State Ranking Model

This article is the first step to formulate such higher dimensional mathematical structures in the extended fuzzy set theory that includes time as a fundamental source of variation. To deal with such higher dimensional information, some modern data processing structures had to be built. Classical matrices (connecting equations and variables through rows and columns) are a limited approach to organizing higher dimensional data, composed of scattered information in numerous forms and vague appearances that differ on time levels. To extend the approach of organizing and classifying the higher dimensional information in terms of specific time levels, this unique plithogenic crisp time-leveled hypersoft-matrix (PCTLHS matrix) model is introduced. This hypersoft matrix has multiple parallel layers that describe parallel universes/realities/information on some specific time levels as a combined view of events. Furthermore, a specific kind of view of the matrix is described as a top view. According to this view, i-level cuts, sublevel cuts, and sub-sublevel cuts are introduced. These level cuts sort the clusters of information initially, subject-wise then attribute-wise, and finally time-wise. These level cuts are such matrix layers that focus on one required piece of information while allowing the variation of others, which is like viewing higher dimensional images in lower dimensions as a single layer of the PCTLHS matrix. In addition, some local aggregation operators are designed to unify i-level cuts. These local operators serve the purpose of unifying the material bodies of the universe. This means that all elements of the universe are fused and represented as a single body of matter, reflecting multiple attributes on different time planes. This is how the concept of a unified global matter (something like dark matter) is visualized. Finally, to describe the model in detail, a numerical example is constructed to organize and classify the states of patients with COVID-19.

A Study of the Neutrosophic Set Significance on Deep Transfer Learning Models: an Experimental Case on a Limited COVID-19 Chest X-ray Dataset.

Coronavirus, also known as COVID-19, has spread to several countries around the world. It was announced as a pandemic disease by The World Health Organization (WHO) in 2020 for its devastating impact on humans. With the advancements in computer science algorithms, the detection of this type of virus in the early stages is urgently needed for the fast recovery of patients. In this paper, a study of neutrosophic set significance on deep transfer learning models will be presented. The study will be conducted over a limited COVID-19 x-ray. The study relies on neutrosophic set and theory to convert the medical images from the grayscale spatial domain to the neutrosophic domain. The neutrosophic domain consists of three types of images, and they are the True (T) images, the Indeterminacy (I) images, and the Falsity (F) images. The dataset used in this research has been collected from different sources. The dataset is classified into four classes {COVID-19, normal, pneumonia bacterial, and pneumonia virus}. This study aims to review the effect of neutrosophic sets on deep transfer learning models. The selected deep learning models in this study are Alexnet, Googlenet, and Restnet18. Those models are selected as they have a small number of layers on their architectures. To test the performance of the conversion to the neutrosophic domain, more than 36 trials have been conducted and recorded. A combination of training and testing strategies by splitting the dataset into (90-10%, 80-20%, 70-30) is included in the experiments. Four domains of images are tested, and they are, the original domain, the True (T) domain, the Indeterminacy (I) domain, and the Falsity (F) domain. The four domains with the different training and testing strategies were tested using the selected deep transfer models. According to the experimental results, the Indeterminacy (I) neutrosophic domain achieves the highest accuracy possible with 87.1% in the testing accuracy and performance metrics such as Precision, Recall, and F1 Score. The study concludes that using the neutrosophic set with deep learning models may be an encouraging transition to achieve better testing accuracy, especially with limited COVID-19 datasets.

A Survey on Deep Transfer Learning to Edge Computing for Mitigating the COVID-19 Pandemic: DTL-EC

Global Health sometimes faces pandemics as are currently facing COVID-19 disease. The spreading and infection factors of this disease are very high. A huge number of people from most of the countries are infected within six months from its first report of appearance and it keeps spreading. The required systems are not ready up to some stages for any pandemic;therefore, mitigation with existing capacity becomes necessary. On the other hand, modern-era largely depends on Artificial Intelligence(AI) including Data Science;and Deep Learning(DL) is one of the current flag-bearer of these techniques. It could use to mitigate COVID-19 like pandemics in terms of stop spread, diagnosis of the disease, drug & vaccine discovery, treatment, patient care, and many more. But this DL requires large datasets as well as powerful computing resources. A shortage of reliable datasets of a running pandemic is a common phenomenon. So, Deep Transfer Learning(DTL) would be effective as it learns from one task and could work on another task. In addition, Edge Devices(ED) such as IoT, Webcam, Drone, Intelligent Medical Equipment, Robot, etc. are very useful in a pandemic situation. These types of equipment make the infrastructures sophisticated and automated which helps to cope with an outbreak. But these are equipped with low computing resources, so, applying DL is also a bit challenging;therefore, DTL also would be effective there. This article scholarly studies the potentiality and challenges of these issues. It has described relevant technical backgrounds and reviews of the related recent state-of-the-art. This article also draws a pipeline of DTL over Edge Computing as a future scope to assist the mitigation of any pandemic.