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.

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.

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.

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.

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.

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.

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.

Evaluation of the maintenance window scheme using fuzzy soft set theory

The maintenance window scheme(MWS) is one of the most important railway transportation organizational plans and plays an important role in ensuring railway operational safety. However, MWS setting is a very complicated process, and most countries currently do so with the help of a computer-aided decision system. In general, a decision system can generate multiple alternatives for MWS within an acceptable time. Therefore, how to choose the best option from the alternatives is a vital decision. This paper presents a novel framework for MWS evaluation based on the Chinese railway system. Specifically, the requirements of each department related to MWS setting are analysed, and we construct an evaluation indicator system for MWS based on the preferences of different departments. Then, we apply the fuzzy soft set theory to MWS evaluation, a method that not only effectively deals with evaluation of uncertain information, but also gives flexibility for experts to input their subjective judgment.Additionally, using the ‘‘AND’’ operation of soft set theory allows combing evaluation information from multiple evaluators to give comprehensive results. Finally, a case study illustrates the proposed framework, showing that the proposed evaluation indicator system and evaluation method are effective and practical.

On Similarity Measures and Distance Measures of Fuzzy Soft Sets

In this paper we introduce several new similarity measures and distance measures between fuzzy soft sets, these measures are examined based on the set-theoretic approach and the matching function. Comparative studies of these measures are derived. By introducing two general formulas, we propose a new method to define the similarity measures and the distance measures between two fuzzy soft sets with different parameter sets.

The Multi-Interval-Valued Fuzzy Soft Set with Application in Decision Making

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. By combining the multi-fuzzy set and soft set models, Y. Yang, X. Tan and C. Meng introduced the concept of multi-fuzzy soft sets and studied some of its operations, such as complement, “AND”, “OR”, Union and Intersection. They also gave an algorithm to analyze a decision problem using multi-fuzzy soft set. In this paper, we introduce the concept of multi-interval-valued fuzzy soft set (M-IVFSS). We also define its basic operations, namely complement, union, intersection, AND and OR. Finally, we give an application of this concept in decision-making problem.

A Novel Multi-Attribute Decision-Making Method Based on Probabilistic Hesitant Fuzzy Soft Set and Its Application

The probabilistic hesitant fuzzy multi-attribute group decision-making method introduces probability and hesitation into decision-making problems at the same time,which can improve the reliability and accuracy of decision-making results,and has become a research hotspots in recent years.However,there are still many problems,such as overly complex calculations and difficulty in obtaining probability data.Based on these,the paper proposes a multi-attribute group decision-making model based on probability hesitant fuzzy soft sets.Firstly,the definition of probabilistic hesitant fuzzy soft set is given.Then,based on soft set theory and probabilistic hesitant fuzzy set,the similarity measure of probabilistic hesitant fuzzy soft set is proposed,and the two measures are further combined.Finally,it is applied to the construction of multi-attribute group decision-making model,and the effectiveness and rationality of the model are verified by an example.The example shows that the new similarity calculation formula and algorithm model in this paper have higher accuracy,and the calculation process is more simple,it provides a feasible method for multi-attribute group decision making problems.

Generalized Soft Expert Set and Its Applications

The expert set theory performs an important part in making decisions. It can successfully convey the opinions of every expert since it includes several experts. In this study, generalizations and soft expert sets are combined. First, the generalized soft expert set notion is presented, then follows the definition of operation approaches and characteristics as the complement, union, intersection, AND and OR. The application of the generalized soft expert set concept to decision issues is then presented with an example. The study also introduces the idea of a generalized soft expert matrix and demonstrates how it may be used to solve decision-making issues. The most striking aspect of this paper is to present the concepts of generalized soft expert sets and generalized soft expert matrices and to apply them to the same decision-making scenario.

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.

Einstein Weighted Geometric Operator for Pythagorean Fuzzy Hypersoft with Its Application in Material Selection

Hypersoft set theory is a most advanced form of soft set theory and an innovative mathematical tool for dealing with unclear complications.Pythagorean fuzzy hypersoft set(PFHSS)is the most influential and capable leeway of the hypersoft set(HSS)and Pythagorean fuzzy soft set(PFSS).It is also a general form of the intuitionistic fuzzy hypersoft set(IFHSS),which provides a better and more perfect assessment of the decision-making(DM)process.The fundamental objective of this work is to enrich the precision of decision-making.A novel mixed aggregation operator called Pythagorean fuzzy hypersoft Einstein weighted geometric(PFHSEWG)based on Einstein’s operational laws has been developed.Some necessary properties,such as idempotency,boundedness,and homogeneity,have been presented for the anticipated PFHSEWG operator.Multi-criteria decision-making(MCDM)plays an active role in dealing with the complications of manufacturing design for material selection.However,conventional methods of MCDM usually produce inconsistent results.Based on the proposed PFHSEWG operator,a robust MCDM procedure for material selection in manufacturing design is planned to address these inconveniences.The expected MCDM method for material selection(MS)of cryogenic storing vessels has been established in the real world.Significantly,the planned model for handling inaccurate data based on PFHSS is more operative and consistent.

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.

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.

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.

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.

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.