An Integrated Algorithmic MADM Approach for Heart Diseases' Diagnosis Based on Neutrosophic Hypersoft Set with Possibility Degree-Based Setting.

The possibility neutrosophic hypersoft set (pNHs-set) is a generalized version of the possibility neutrosophic soft set (pNs-set). It tackles the limitations of the pNs-set regarding the use of the multi-argument approximate function. This function maps sub-parametric tuples to a power set of the universe. It emphasizes the partitioning of each attribute into its respective attribute-valued set. These features make it a completely new mathematical tool for solving problems dealing with uncertainties. This makes the decision-making process more flexible and reliable. In this study, after characterizing some elementary notions and algebraic operations of the pNHs-set, Sanchez's method (a classical approach for medical diagnosis) is modified under the pNHs-set environment. A modified algorithm is proposed for the medical diagnosis of heart diseases by integrating the concept of the pNHs-set and the modified Sanchez's method. The authenticity of the proposed algorithm is evaluated through its implementation in a real-world scenario with real data from the Cleveland data set for heart diseases. The beneficial aspects of the proposed approach are evaluated through a structural comparison with some pertinent existing approaches.

A Novel Fuzzy Parameterized Fuzzy Hypersoft Set and Riesz Summability Approach Based Decision Support System for Diagnosis of Heart Diseases.

Fuzzy parameterized fuzzy hypersoft set (Δ-set) is more flexible and reliable model as it is capable of tackling features such as the assortment of attributes into their relevant subattributes and the determination of vague nature of parameters and their subparametric-valued tuples by employing the concept of fuzzy parameterization and multiargument approximations, respectively. The existing literature on medical diagnosis paid no attention to such features. Riesz Summability (a classical concept of mathematical analysis) is meant to cope with the sequential nature of data. This study aims to integrate these features collectively by using the concepts of fuzzy parameterized fuzzy hypersoft set (Δ-set) and Riesz Summability. After investigating some properties and aggregations of Δ-set, two novel decision-support algorithms are proposed for medical diagnostic decision-making by using the aggregations of Δ-set and Riesz mean technique. These algorithms are then validated using a case study based on real attributes and subattributes of the Cleveland dataset for heart-ailments-based diagnosis. The real values of attributes and subattributes are transformed into fuzzy values by using appropriate transformation criteria. It is proved that both algorithms yield the same and reliable results while considering hypersoft settings. In order to judge flexibility and reliability, the preferential aspects of the proposed study are assessed by its structural comparison with some related pre-developed structures. The proposed approach ensures that reliable results can be obtained by taking a smaller number of evaluating traits and their related subvalues-based tuples for the diagnosis of heart-related ailments.

An Intelligent Multiattribute Decision-Support Framework Based on Parameterization of Neutrosophic Hypersoft Set.

Hypersoft set is a novel area of interest which is able to tackle the real-world scenarios where classification of parameters into their respective sub-parametric values in the form of overlapping sets is mandatory. It employs a new approximate mapping which considers such sets in the form of sub-parametric tuples as its domain. The existing soft set-like structures are insufficient to tackle such kind of situations. This research intends to establish a novel concept of parameterization of fuzzy set under hypersoft set environment with uncertain components of intuitionistic fuzzy set and neutrosophic set. Two novel structures, i.e., fuzzy parameterized intuitionistic fuzzy hypersoft set (fpifhs-set) and fuzzy parameterized neutrosophic hypersoft set (fpnhs-set), are developed by employing algebraic techniques like theoretic, analytical, pictorial, and algorithmic techniques. After characterizing the elementary properties and set-theoretic operations of fpifhs-set and fpnhs-set, two novel algorithms are proposed to solve real-life decision-making COVID-19 problem. The results of both algorithms are compared with related already established models through certain evaluating features to judge the advantageous aspects of the proposed study. The generalization of the proposed models is discussed by describing some of their particular cases.

The Assessment of Medication Effects in Omicron Patients through MADM Approach Based on Distance Measures of Interval-Valued Fuzzy Hypersoft Set.

Omicron, so-called COVID-2, is an emerging variant of COVID-19 which is proved to be the most fatal amongst the other variants such as alpha, beta and gamma variants (α, ß, γ variants) due to its stern and perilous nature. It has caused hazardous effects globally in a very short span of time. The diagnosis and medication of Omicron patients are both challenging undertakings for researchers (medical experts) due to the involvement of various uncertainties and the vagueness of its altering behavior. In this study, an algebraic approach, interval-valued fuzzy hypersoft set (iv-FHSS), is employed to assess the conditions of patients after the application of suitable medication. Firstly, the distance measures between two iv-FHSSs are formulated with a brief description some of its properties, then a multi-attribute decision-making framework is designed through the proposal of an algorithm. This framework consists of three phases of medication. In the first phase, the Omicron-diagnosed patients are shortlisted and an iv-FHSS is constructed for such patients and then they are medicated. Another iv-FHSS is constructed after their first medication. Similarly, the relevant iv-FHSSs are constructed after second and third medications in other phases. The distance measures of these post-medication-based iv-FHSSs are computed with pre-medication-based iv-FHSS and the monotone pattern of distance measures are analyzed. It is observed that a decreasing pattern of computed distance measures assures that the medication is working well and the patients are recovering. In case of an increasing pattern, the medication is changed and the same procedure is repeated for the assessment of its effects. This approach is reliable due to the consideration of parameters (symptoms) and sub parameters (sub symptoms) jointly as multi-argument approximations.