Pythagorean fuzzy soft set (PFSS) is one of the useful extension of the Pythagorean fuzzy set (PFS) to deal with the vagueness and uncertainties in the data. The major advantages of PFSS over the ...other existing sets are to consider the parameterized tool of the family of PFS. Keeping this advantage, in this paper we define some new entropy measures for PFSS to compute the degree of fuzziness of the set. The axiomatic definition and their validity are stated. The larger the entropy, the lesser the vagueness and so, the decision making based on entropy is a useful one. Further, a decisionmaking algorithm is explored to solve the decision-making problem under the PFSS environment. A numerical example is given to validate the method and compare their performance with the existing intuitionistic fuzzy soft set entropy measures.
A Pythagorean fuzzy soft set is a parameterized family of Pythagorean fuzzy sets and a generalization of intuitionistic fuzzy soft sets. In this paper, the notions of entropy and distance measures ...are defined for the Pythagorean fuzzy soft sets (PFSSs). Since, the already existing techniques for finding entropy and distance measures are not working for PFSSs, it is necessary to introduce these techniques in the contest of PFSSs. This work proposes a characterization of the Pythagorean fuzzy soft entropy. Also, the expressions for the standard distance measures like Hamming distance and Euclidean distance are obtained. Further, the applications of PFSSs in decision making problem and pattern recognition problem are discussed. Finally, comparative studies with other existing equations are also carried out.
In this paper, we extended the technique of measuring similarity between topological spaces using bottle neck distance between persistence diagrams to hypergraph networks. Finding a relationship ...between the bottleneck distance of the Cartesian product of topological spaces and the bottleneck distance of individual spaces, we are trying to ease the comparative study of the Cartesian product of topological spaces. The Cartesian product and the strong product of weighted hypergraphs are defined, and the relationship between the bottleneck distance between hypergraph products and the bottleneck distance between individual hypergraphs is determined. For this, clique complex filtration and the Vietoris–Rips filtration in unweighted and weighted hypergraphs are defined and used.
This paper aims to develop distance and similarity measures for (
p
,
q
)-fuzzy sets from t-norms and t-conorms. It showcases a way to generate these measures from a given t-norm or a t-conorm ...operator. These newly developed distance and similarity measures have applications in various domains, including problems in pattern recognition. The article provides a comparison between the proposed measures and the existing measures for Fermatean fuzzy sets. Additionally, it illustrates a numerical example to showcase the practical application of the proposed distance measures in diagnosing common lung diseases.
Article Highlights
It suggests various similarity and distance measures for (
p
,
q
)-fuzzy sets using t-norms and t-conorms, respectively.
It employs the suggested similarity and distance measures in a pattern recognition problem related to medical diagnosis.
It compares the proposed measures with those defined in the literature for Fermatean fuzzy sets.
This study introduces the concepts of complements, t-norms, t-conorms, and cut sets in the context of multi-dimensional fuzzy sets. Some fundamental results including DeMorgan-type identities, ...concerning these, are obtained. The advantage of using multidimensional fuzzy sets for analyzing data is that each element in the universe can be given individual attention as per the requirement. By utilizing this scope, as an application of the introduced concepts, stage identification of certain diseases based on Multidimensional fuzzy sets and intuitionistic fuzzy sets is provided together with a comparative study on typical biomedical data.
Highlights
Restriction of standard multidimensional complement, t-norm, and t-conorm to the one-dimensional fuzzy sets coincides respectively with standard operators defined there.
The upper bound and lower bound for multidimensional t-norm and t-conorm are obtained.
The important examples of multidimensional t-norm and t-conorm are used to obtain solutions for some decision-making problems in the bio-medical sector as illustrated in the last section.
In this paper, the definition of spherical fuzzy soft sets and some of its properties are introduced. Spherical fuzzy soft sets are a generalization of soft sets. Notably, we showed DeMorgan’s laws ...that are valid in spherical fuzzy soft set theory. Also, we propose an algorithm to solve the decision-making problem based on adjustable soft discernibility matrix. It gives an order relation between all the objects of our universe. Finally, an illustrative example is discussed to prove that they can be effectively used to solve problems with uncertainties.
Aboriginal women experience disproportionately higher rates of cervical cancer mortality yet are less likely to participate in screening for early detection. This study sought to determine whether a ...community-based HPV self-sampling service model can effectively recruit never-screened and under-screened Aboriginal women to participate in cervical cancer screening; assess the clinical outcomes; and explore the acceptability of the model from the perspective of the participants.
Aboriginal women aged 25-69 years of age were recruited from eight rural and remote communities in New South Wales, Australia to participate in HPV self-sampling via a community-based service model. Outcome measures were: number of women screened by HPV self-sampling, their prior cervical screening status (under-screened or never-screened), clinical outcomes and participation in follow-up pathways of care, and satisfaction with the service model.
In total, 215 women conducted a HPV self-sampling test and 200 evaluation surveys were completed. One-fifth of participants (n = 46) were never-screened and one-third (n = 69) were under-screened. Many were unsure of their screening status. Nine women were HPV 16/18 positive and eight had completed all follow up by the conclusion of the study. A further 30 women tested positive for a high risk type other than HPV 16/18 (HPV other), of which 14 had completed follow up at the conclusion of the study. Satisfaction with the HPV self-sampling kit, the process of self-sampling and the service model was high (> 92% satisfied on all items). Many women had difficulty understanding their official HPV results and placed high importance on the nurse explaining it to them.
A community-based service model that respects Aboriginal Women's Business can effectively recruit under-screened and never-screened Aboriginal women to complete cervical cancer screening. Furthermore, this service model supports them to complete recommended follow-up care and engage with their local existing health services.
This paper addresses an extension of the concept of topological spaces to that of hesitant fuzzy spaces. The topology is established using a conjunction and disjunction operator on hesitant fuzzy ...sets whose properties are discussed in the beginning. Some examples are discussed before introducing the concepts of interior and closure of a hesitant fuzzy set. The properties of these operators are verified to justify the definitions. The concepts of a hesitant fuzzy subspace topology and continuous mappings on hesitant fuzzy sets are studied. The concepts of connectedness and compactness of hesitant fuzzy topological spaces are studied and various results regarding them are proved.
Stroke is a standout amongst the most imperative reasons of incapacity on the planet. Due to partial or full paralysis, the majority of patients are compelled to rely upon parental figures and ...caregivers in residual life. With post-stroke rehabilitation, different types of assistive technologies have been proposed to offer developments to the influenced body parts of the incapacitated. In a large portion of these devices, the clients neither have control over the tasks nor can get feedback concerning the status of the exoskeleton. Additionally, there is no arrangement to detect user movements or accidental fall. The proposed framework tackles these issues utilizing a brain-controlled lower limb exoskeleton (BCLLE) in which the exoskeleton movements are controlled based on user intentions. An adaptive mechanism based on sensory feedback is integrated to reduce the system false rate. The BCLLE uses a flexible design which can be customized according to the degree of disability. The exoskeleton is modeled according to the human body anatomy, which makes it a perfect fit for the affected body part. The BCLLE system also automatically identifies the status of the paralyzed person and transmits information securely using Novel-T Symmetric Encryption Algorithm (NTSA) to caregivers in case of emergencies. The exoskeleton is fitted with motors which are controlled by the brain waves of the user with an electroencephalogram (EEG) headset. The EEG headset captures the human intentions based on the signals acquired from the brain. The brain-computer interface converts these signals into digital data and is interfaced with the motors via a microcontroller. The microcontroller controls the high torque motors connected to the exoskeleton's joints based on user intentions. Classification accuracy of more than 80% is obtained with our proposed method which is much higher compared with all existing solutions.
The spherical fuzzy soft set is a generalized soft set model, which is more realistic, practical, and accurate. It is an extended version of existing fuzzy soft set models that can be used to ...describe imprecise data in real-world scenarios. The paper seeks to introduce the new concept of spherical fuzzy soft topology defined on spherical fuzzy soft sets. In this work, we define some basic concepts including spherical fuzzy soft basis, spherical fuzzy soft subspace, spherical fuzzy soft interior, spherical fuzzy soft closure, and spherical fuzzy soft boundary. The properties of these defined set are also discussed and explained with an appropriate examples. Also, we establish certain important results and introduce spherical fuzzy soft separation axioms, spherical fuzzy soft regular space, and spherical fuzzy soft normal space. Furthermore, as an application, a group decision-making algorithm is presented based on the TOPSIS (Technique of Order Preference by Similarity to an Ideal Solution) method for solving the decision-making problems. The applicability of the proposed method is demonstrated through a numerical example. The comprehensive advantages of the proposed work have been stated over the existing methods.
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