The multi-fuzzy N-soft set and its applications to decision-making

A progressive approach to multi-criteria group decision-making: N-bipolar hypersoft topology perspective

This paper investigates N-bipolar hypersoft topology (N-BHST), a novel extension of both the well-established N-hypersoft topology (N-HST) and hypersoft topology (HST). Deviating significantly from its precursor, the N-bipolar hypersoft (N-BHS) set, N-BHST introduces a multi-opinion approach to decision-making, augmenting robustness and adaptability. This innovative framework addresses identified limitations in N-bipolar soft topology (N-BST), especially in managing multi-argument approximate functions. The study analyzes various operators (closure, interior, exterior, and boundary) within the N-BHST framework, elucidating their interrelationships. Additionally, an examination is carried out on the enhancement of multi-criteria group decision-making (MCGDM) using N-BHST, setting it apart from existing models. A numerical example is presented to illustrate its application in real-world decision scenarios.

Prioritized Aggregation Operators for Complex Intuitionistic Fuzzy Sets Based on Aczel-Alsina T-norm and T-conorm and Their Applications in Decision-Making

The Aczel-Alsina t-norms ware proposed by Aczel and Alsina in 1982, which are a very effective and dominant technique used in the construction of any kind of aggregation operators. Moreover, the Algebraic t-norms are a special case of the Aczel-Alsina t-norms because of the parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0 Collapse

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.

An integrated ELECTRE method for selection of rehabilitation center with m-polar fuzzy N-soft information

The primary goal of this research article is to apply ELECTRE I, a fundamental multi-criteria group decision-making technique, in an m-polar fuzzy N-soft environment. This new methodology helps us to pinpoint the best alternative(s) in the presence of multi-polar options with N-graded qualities. Its basic operational idea entails the comparison between any two alternatives by the assessment of score degrees. Concordance and discordance indices are then calculated to evaluate the alternatives' superiority and inferiority. We may disqualify the incompetent alternatives using concordance and discordance levels. An m-polar fuzzy N-soft dominance matrix can represent the combined effect of concordance and discordance dominance matrices. The steps of this new multi-criteria group decision making technique are summarized in a flowchart. In order to demonstrate its authenticity and applicability, we employ a case study involving the establishment of a rehabilitation facility for drug abusers. A comparison with the m-polar fuzzy PROMETHEE and m-polar fuzzy ELECTRE I methodologies establishes its validity. Finally, we conclude our study of the methodology proposed in this paper with a critical analysis of its benefits and drawbacks.

Extended fuzzy N-Soft PROMETHEE method and its application in robot butler selection

This paper extends the literature on fuzzy PROMETHEE, a well-known multi-criteria group decision-making technique. The PROMETHEE technique ranks alternatives by specifying an allowable preference function that measures their deviations from other alternatives in the presence of conflicting criteria. Its ambiguous variation helps to make an appropriate decision or choose the best option in the presence of some ambiguity. Here, we focus on the more general uncertainty in human decision-making, as we allow N-grading in fuzzy parametric descriptions. In this setting, we propose a suitable fuzzy N-soft PROMETHEE technique. We recommend using an Analytic Hierarchy Process to test the feasibility of standard weights before application. Then the fuzzy N-soft PROMETHEE method is explained. It ranks the alternatives after some steps summarized in a detailed flowchart. Furthermore, its practicality and feasibility are demonstrated through an application that selects the best robot housekeepers. The comparison between the fuzzy PROMETHEE method and the technique proposed in this work demonstrates the confidence and accuracy of the latter method.

An approach in medical diagnosis based on Z-numbers soft set

Background

In the process of medical diagnosis, a large amount of uncertain and inconsistent information is inevitably involved. There have been many fruitful results were investigated for medical diagnosis by utilizing different traditional uncertainty mathematical tools. It is found that there is limited study on measuring reliability of the information involved are rare, moreover, the existed methods cannot give the measuring reliability of every judgment to all symptoms in details.

Objectives

It is quite essential to recognize the impact on the reliability of the fuzzy information provided under inadequate experience, lack of knowledge and so on. In this paper, the notion of the Z-numbers soft set is proposed to handle the reliability of every judgment to all symptoms in details. The study in this paper is an interdisciplinary approach towards rapid and efficient medical diagnosis.

Methods

An approach based on Z-numbers soft set (ZnSS)to medical diagnosis has been developed and is used to estimate whether two patterns or images are identical or approximately. The notion of Z-numbers soft set is proposed by combing the theory of soft set and Z-numbers theory. The basic properties of subset, equal, intersection, union and complement operations on the Z-numbers soft sets are defined and the similarity measure of two Z-numbers soft sets are also discussed in this paper.

Results

An illustrative example similar to existing studies is showed to verify the effectiveness and feasibility, which can highlight the proposed method and demonstrate the solution characteristics.

Conclusion

Diagnosing diseases by uncertainty symptoms is not a direct and simple task at all. The approach based on ZnSS presented in this paper can not only measure reliability of the information involved, but also give the measuring reliability of every judgment to all symptoms in details.

Complex fermatean fuzzy N-soft sets: a new hybrid model with applications

Decision-making methods play an important role in the real-life of human beings and consist of choosing the best options from a set of possible choices. This paper proposes the notion of complex Fermatean fuzzy N-soft set (CFFNS f S) which, by means of ranking parameters, is capable of handling two-dimensional information related to the degree of satisfaction and dissatisfaction implicit in the nature of human decisions. We define the fundamental set-theoretic operations of CFFNS f S and elaborate the CFFS f S associated with threshold. The algebraic and Yager operations on CFFNS f numbers are also defined. Several algorithms are proposed to demonstrate the applicability of CFFNS f S to multi-attribute decision making. The advanced algorithms are described and accomplished by several numerical examples. Then, a comparative study manifests the validity, feasibility, and reliability of the proposed model. This method is compared with the Fermatean fuzzy Yager weighted geometric (FFY w G) and the Fermatean fuzzy Yager weighted average (FFY w A) operators. Further, we developed a remarkable CFFNS f -TOPSIS approach by applying innovative CFFNS f weighted average operator and distance measure. The presented technique is fantastically designed for the classification of the most favorable alternative by examining the closeness of all available choices from particular ideal solutions. Afterward, we demonstrate the amenability of the initiated approach by analyzing its tremendous potential to select the best city in the USA for farming. An integrated comparative analysis with existing Fermatean fuzzy TOPSIS technique is rendered to certify the terrific capability of the established approach. Further, we decisively investigate the rationality and reliability of the presented CFFNS f S and CFFNS f -TOPSIS approach by highlighting its advantages over the existent models and TOPSIS approaches. Finally, we holistically describe the conclusion of the whole work.

Multi-criteria Optimization Technique with Complex Pythagorean Fuzzy N-soft Information

The main objective of this article is to lay the foundations of a novel multi-criteria optimization technique, namely, the complex Pythagorean fuzzy N-soft VIKOR (CPFNS-VIKOR) method that is highly proficient to express a great deal of linguistic imprecision and vagueness inherent in human assessments. This strategy provides a versatile decision-making tool for the ranking-based fuzzy modeling of two-dimensional parameterized data. The CPFNS-VIKOR method integrates the ground-breaking specialities of the VIKOR method with the outstanding parametric structure of the complex Pythagorean fuzzy N-soft model. It is exclusively designed for the specification of a compromise optimal solution having maximum group utility and minimum individual regret of the opponent by analyzing their weighted proximity from ideal solutions. The developed strategy factually permits specific linguistic terms to demystify the individual perspectives of the decision-making experts regarding the efficacy of the alternatives and the priorities of the applicable criteria. We comprehensively assemble these independent appraisals of all the experts using the complex Pythagorean fuzzy N-soft weighted averaging operator. Moreover, we calibrate the ranking measure by utilizing group utility measure and regret measure in order to specify the hierarchical outranking of the feasible alternatives. We demonstrate the systematic methodology and framework of the proposed method with the assistance of an explicative flow chart. We skilfully investigate an empirical analysis related to selection of constructive industrial robots for the modernization of a manufacturing industry which really justifies the remarkable accountability of the proposed strategy. Furthermore, we validate this technique by a comparative study with the existing complex Pythagorean fuzzy TOPSIS (CPF-TOPSIS) method, complex Pythagorean fuzzy VIKOR (CPF-VIKOR) method and Pythagorean fuzzy TOPSIS (PF-TOPSIS) method. The comparative study is exemplified with an illustrative bar chart that visually endorses the rationality of the proposed methodology by interpreting highly compatible and accurate final outcomes. Finally, we holistically analyze the functionality of the developed strategy to enlighten its merits and prominence over other available competent approaches.