An Intelligent MCGDM Model in Green Suppliers Selection Using Interactional Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Sets

Green supplier selection is an important debate in green supply chain management(GSCM),attracting global attention from scholars,especially companies and policymakers.Companies frequently search for new ideas and strategies to assist them in realizing sustainable development.Because of the speculative character of human opinions,supplier selection frequently includes unreliable data,and the interval-valued Pythagorean fuzzy soft set(IVPFSS)provides an exceptional capacity to cope with excessive fuzziness,inconsistency,and inexactness through the decision-making procedure.The main goal of this study is to come up with new operational laws for interval-valued Pythagorean fuzzy soft numbers(IVPFSNs)and create two interaction operators-the intervalvalued Pythagorean fuzzy soft interaction weighted average(IVPFSIWA)and the interval-valued Pythagorean fuzzy soft interaction weighted geometric(IVPFSIWG)operators,and analyze their properties.These operators are highly advantageous in addressing uncertain problems by considering membership and non-membership values within intervals,providing a superior solution to other methods.Moreover,specialist judgments were calculated by the MCGDM technique,supporting the use of interaction AOs to regulate the interdependence and fundamental partiality of green supplier assessment aspects.Lastly,a statistical clarification of the planned method for green supplier selection is presented.

The Applications of Vague Soft Sets and Generalized Vague Soft Sets

The problem of decision making in an imprecise environment has found paramount importance in recent years. In this paper, we define vague soft relation and similarity measure of vague soft sets. Using these definitions, some novel methods of object recognition from an imprecise multiobserver data has been presented. Moreover, we introduce the notion of generalized vague soft sets and study some of its properties. The similarity measure of generalized vague soft sets is also presented and an application of this measure in decision making problems has been shown.

Vulnerability analysis for airport networks based on fuzzy soft sets: From the structural and functional perspective

Abstract Recently, much attention has been paid to the reliability and vulnerability of critical infrastructure. In air traffic systems, the vulnerability analysis for airport networks can be used to guide air traffic administrations in their prioritization of the maintenance and repair of airports, as well as to avoid unnecessary disturbances in the planning of flight schedules. In this paper, the evaluation methods of airport importance and network efficiency arc established. Firstly, the evaluation indices of airport importance are proposed from both the topological and functional perspectives. The topological characteristics come from the structure of airport network and the functional features stem from the traffic flow distribution taking place inside the network. Secondly, an integrated evaluation method based on fuzzy soft set theory is proposed to identify the key airports, which can fuse together importance indices over different time intervals. Thirdly, an airport network efficiency method is established for the purpose of assessing the accuracy of the evaluation method. Finally, empirical studies using real traffic data of US and China＇s airport networks show that the evaluation method proposed in this papcr is the most accuratc. Thc vulucrability of US and China＇s airport networks is compared. The similarities and differences between airport geography distribution and airport importance distribution are discussed here and the dynamics of airport importance is studied as well.

An Advanced Uncertainty Measure Using Fuzzy Soft Sets:Application to Decision-Making Problems

In this paper, uncertainty has been measured in the form of fuzziness which arises due to imprecise boundaries of fuzzy sets. Uncertainty caused due to human’s cognition can be decreased by the use of fuzzy soft sets. There are different approaches to deal with the measurement of uncertainty. The method we proposed uses fuzzified evidence theory to calculate total degree of fuzziness of the parameters. It consists of mainly four parts.The first part is to measure uncertainties of parameters using fuzzy soft sets and then to modulate the uncertainties calculated. Afterward, the appropriate basic probability assignments with respect to each parameter are produced. In the last, we use Dempster’s rule of combination to fuse independent parameters into integrated one. To validate the proposed method, we perform an experiment and compare our outputs with grey relational analysis method. Also,a medical diagnosis application in reference to COVID-19 has been given to show the effectiveness of advanced method by comparing with other method.

Covering-Based Soft Rough Sets

Covering-based rough sets process data organized by a covering of the universe. A soft set is a parameterized family of subsets of the universe. Both theories can deal with the uncertainties of data. Soft sets have not any restrictions on the approximate description of the object,and they might form a covering of the universe. From this viewpoint,we establish a connection between these two theories. Specifically,we propose a complementary parameter for this purpose. With this parameter,the soft covering approximation space is established and the two theories are bridged. Furthermore,we study some relations between the covering and the soft covering approximation space and obtain some significant results. Finally,we define a notion of combine parameter which can help us to simplify the set of parameters and reduce the storage requirement of a soft covering approximation space.

Neutrosophic Soft Expert Sets

In this paper we introduce the concept of neutrosophic soft expert set (NSES). We also define its basic operations, namely complement, union, intersection, AND and OR, and study some of their properties. We give examples for these concepts. We give an application of this concept in a decision-making problem.

Notes on “Generalised Fuzzy Soft Sets”

In this paper,we point out that several assertions（Propositions 3.15 and 5.2（v）） in a previous paper by Majumdar and Samanta are not true in general,by counterexamples.

Einstein Hybrid Structure of q-Rung Orthopair Fuzzy Soft Set and Its Application for Diagnosis of Waterborne Infectious Disease

This research is devoted to diagnosing water-borne infectious diseases caused by floods employing a novel diagnosis approach,the Einstein hybrid structure of q-rung orthopair fuzzy soft set.This approach integrates parts of fuzzy logic and soft set theory to develop a robust alternative for disease detection in stressful situations,especially in areas affected by floods.Compared to the traditional intuitionistic fuzzy soft set and Pythagorean fuzzy soft set,the q-rung orthopair fuzzy soft set(q-ROFSS)adequately incorporates unclear and indeterminate facts.The major objective of this investigation is to formulate the q-rung orthopair fuzzy soft Einstein hybrid weighted average(q-ROFSEHWA)operator and its specific characteristics.Moreover,our stated operator is implementing intelligentmulti-criteria group decision-making(MCGDM)methodology.Floods are severe natural catastrophes that raise the risk of diseases and epidemics,particularly those caused by contaminants in the water,such as gastrointestinal diseases,respiratory infections,vector-borne diseases,skin infections,and water-borne parasites.The designed MCGDM strategy tackles the prevalence of certain conditions in flood-affected patients.A comparative investigation determined that the suggested method for detecting water-borne infectious disease due to floods is more effective and productive than conventional methods because of its logical structure.

（∈γ, ∈γ Vqδ）-intuitionistic Fuzzy（Soft） Filter of BL-algebras

In the paper, in order to further study the properties of filters of BL-algebras, we propose the concepts of the （∈γ, ∈γ Vqδ）-intuitionistic fuzzy filters and （∈γ, ∈γ Vqδ）- intuitionistic fuzzy soft filters of BL-algebras and derive some related results. Finally, we discuss the properties of images and inverse images of （∈γ, ∈γ Vqδ）-intuitionistic fuzzy soft filters of BL-algebras.

Decision Making Algorithmic Approaches Based on Parameterization of Neutrosophic Set under Hypersoft Set Environment with Fuzzy, Intuitionistic Fuzzy and Neutrosophic Settings

Hypersoft set is an extension of soft set as it further partitions each attribute into its corresponding attribute-valued set.This structure is more flexible and useful as it addresses the limitation of soft set for dealing with the scenarios having disjoint attribute-valued sets corresponding to distinct attributes.The main purpose of this study is to make the existing literature regarding neutrosophic parameterized soft set in line with the need of multi-attribute approximate function.Firstly,we conceptualize the neutrosophic parameterized hypersoft sets under the settings of fuzzy set,intuitionistic fuzzy set and neutrosophic set along with some of their elementary properties and set theoretic operations.Secondly,we propose decision-making-based algorithms with the help of these theories.Moreover,illustrative examples are presented which depict the structural validity for successful application to the problems involving vagueness and uncertainties.Lastly,the generalization of the proposed structure is discussed.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Soft Set with Their Application to Solve Multi-Attribute Group Decision Making Problem

Interval-valued Pythagorean fuzzy soft set(IVPFSS)is a generalization of the interval-valued intuitionistic fuzzy soft set(IVIFSS)and interval-valued Pythagorean fuzzy set(IVPFS).The IVPFSS handled more uncertainty comparative to IVIFSS;it is the most significant technique for explaining fuzzy information in the decision-making process.In this work,some novel operational laws for IVPFSS have been proposed.Based on presented operational laws,two innovative aggregation operators(AOs)have been developed such as interval-valued Pythagorean fuzzy soft weighted average(IVPFSWA)and interval-valued Pythagorean fuzzy soft weighted geometric(IVPFSWG)operators with their fundamental properties.A multi-attribute group decision-making(MAGDM)approach has been established utilizing our developed operators.A numerical example has been presented to ensure the validity of the proposed MAGDM technique.Finally,comparative studies have been given between the proposed approach and some existing studies.The obtained results through comparative studies show that the proposed technique is more credible and reliable than existing approaches.

Softζ-Rough Set and Its Applications in Decision Making of Coronavirus

In this paper,we present a proposed method for generating a soft rough approximation as a modification and generalization of Zhaowen et al.approach.Comparisons were obtained between our approach and the previous study and also.Eventually,an application on Coronavirus(COVID-19)has been presented,illustrated using our proposed concept,and some influencing results for symptoms of Coronavirus patients have been deduced.Moreover,following these concepts,we construct an algorithm and apply it to a decision-making problem to demonstrate the applicability of our proposed approach.Finally,a proposed approach that competes with others has been obtained,as well as realistic results for patients with Coronavirus.Moreover,we used MATLAB programming to obtain the results;these results are consistent with those of theWorld Health Organization and an accurate proposal competing with the method of Zhaowen et al.has been studied.Therefore,it is recommended that our proposed concept be used in future decision making.

Generalized Normalized Euclidean Distance Based Fuzzy Soft Set Similarity for Data Classification

Classification is one of the data mining processes used to predict predetermined target classes with data learning accurately.This study discusses data classification using a fuzzy soft set method to predict target classes accurately.This study aims to form a data classification algorithm using the fuzzy soft set method.In this study,the fuzzy soft set was calculated based on the normalized Hamming distance.Each parameter in this method is mapped to a power set from a subset of the fuzzy set using a fuzzy approximation function.In the classification step,a generalized normalized Euclidean distance is used to determine the similarity between two sets of fuzzy soft sets.The experiments used the University of California(UCI)Machine Learning dataset to assess the accuracy of the proposed data classification method.The dataset samples were divided into training(75%of samples)and test(25%of samples)sets.Experiments were performed in MATLAB R2010a software.The experiments showed that:(1)The fastest sequence is matching function,distance measure,similarity,normalized Euclidean distance,(2)the proposed approach can improve accuracy and recall by up to 10.3436%and 6.9723%,respectively,compared with baseline techniques.Hence,the fuzzy soft set method is appropriate for classifying data.

The characterization of Γ-modules in terms of fuzzy soft Γ-submodules

In this paper,we focus on combining the theories of fuzzy soft sets with Γ-modules,and establishing a new framework for fuzzy soft Γ-submodules.The main contributions of the paper are 3-fold.First,we present the concepts of（R,S）-bi-Γ-submodules,quasi-Γ-submodules and regular Γ-modules.Meanwhile,some illustrative examples are given to show the rationality of the definitions introduced in this paper.Second,several new kinds of generalized fuzzy soft Γ-submodules are proposed,and related properties and mutual relationships are also investigated.Third,we discover some intrinsic connections between the generalized fuzzy soft Γ-submodules presented in this paper and crisp Γ-submodules,and describe the relationships between regular Γ-modules and the generalized fuzzy soft Γ-submodules presented in this paper.

Soft Locally Compact Spaces and Soft Paracompact Spaces

The concept of soft topological space was introduced by some authors. In the present paper, we investigate some basic notions of soft topological spaces by using new soft point concept. Later we give soft locally compact space and the relationships between them are discussed in detail. Finally, we define soft paracompactness and explore some of its basic properties.

Emerging Trends in Social Networking Systems and Generation Gap with Neutrosophic Crisp Soft Mapping

This paper aims to introduce the novel concept of neutrosophic crisp soft set(NCSS),including various types of neutrosophic crisp soft sets(NCSSs)and their fundamental operations.We define NCS-mapping and its inverse NCS-mapping between two NCS-classes.We develop a robust mathematical modeling with the help of NCS-mapping to analyze the emerging trends in social networking systems(SNSs)for our various generations.We investigate the advantages,disadvantages,and natural aspects of SNSs for five generations.With the changing of the generations,it is analyzed that emerging trends and the benefits of SNSs are increasing day by day.The suggested modeling with NCS-mapping is applicable in solving various decision-making problems.

Decision-Making Problems under the Environment of m-Polar Diophantine Neutrosophic N-Soft Set

Fuzzy models are present everywhere from natural to artificial structures,embodying the dynamic processes in physical,biological,and social systems.As real-life problems are often uncertain on account of inconsistent and indeterminate information,it seems very demanding for an expert to solve those problems using a fuzzy model.In this regard,we develop a hybrid new model m-polar Diophantine neutrosophic N-soft set which is based on neutrosophic set and soft set.Additionally,we define several different sorts of compliments on the proposed set.A proposed set is a generalized form of fuzzy,soft,Pythagorean fuzzy,Pythagorean fuzzy soft,and Pythagorean fuzzy N-soft sets.In thismanner,m-polar Diophantine neutrosophic N-soft set is more proficient,a versatile model to oversee vulnerabilities as it likewise survives the downsides of existing models which are to be summed up.Furthermore,we give the application of the proposed set in multi-attribute decision-making problems by defining a new choice-value function.

On Soft Pre-Rough Approximation Space with Applications in Decision Making

A soft,rough set model is a distinctive mathematical model that can be used to relate a variety of real-life data.In the present work,we introduce new concepts of rough set based on soft pre-lower and soft pre-upper approximation space.These concepts are soft pre-rough equality,soft pre-rough inclusion,soft pre-rough belonging,soft predefinability,soft pre-internal lower,and soft pre-external lower.We study the properties of these concepts.Finally,we use the soft pre-rough approximation to illustrate the importance of our method in decision-making for Chikungunya medical illnesses.In reality,the impact factors of Chikungunya’s medical infection were determined.Moreover,we develop two new algorithms to address Chikungunya virus issues.Our proposed approach is sensible and effective.

A study on distributive and modular lattice ordered fuzzy soft group and its duality

Soft set theory has a rich potential application in several fields. A soft group is a parameterized family of subgroups and a fuzzy soft group is a parameterized family of fuzzy subgroups. The concept of fuzzy soft group is the generalization of soft group. Abdulkadir Aygunoglu and Halis Aygun introduced the notion of fuzzy soft groups in 2009[1]. In this paper, the concept of lattice ordered fuzzy soft groups and its duality has been introduced. Then distributive and modular lattice ordered fuzzy soft groups are analysed. The objective of this paper is to study the lattice theory over the collection of fuzzy soft group in a parametric manner. Some pertinent properties have been analysed and hence established duality principle.

A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making

The aim of this paper is to introduce the concept of a generalized Pythagorean fuzzy soft set(GPFSS),which is a combination of the generalized fuzzy soft sets and Pythagorean fuzzy sets.Several of important operations of GPFSS including complement,restricted union,and extended intersection are discussed.The basic properties of GPFSS are presented.Further,an algorithm of GPFSSs is given to solve the fuzzy soft decision-making.Finally,a comparative analysis between the GPFSS approach and some existing approaches is provided to show their reliability over them.