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.

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.

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.

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.

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.

A Multi-Attribute Decision-Making Method Using Belief-Based Probabilistic Linguistic Term Sets and Its Application in Emergency Decision-Making

Probabilistic linguistic term sets(PLTSs)are an effective tool for expressing subjective human cognition that offer advantages in the field ofmulti-attribute decision-making(MADM).However,studies have found that PLTSs have lost their ability to accurately capture the views of decision-makers(DMs)in certain circumstances,such as when the DM hesitates between multiple linguistic terms or the decision information is incomplete,thus affecting their role in the decision-making process.Belief function theory is a leading streamof thought in uncertainty processing that is suitable for dealing with the limitations of PLTS.Therefore,the purpose of this study is to extend PLTS to incorporate belief function theory.First,we provide the basic concepts of the extended PLTS(i.e.,belief-based PLTS)through case analyses.Second,the aggregation operator of belief-based PLTS is defined with the ordered weighted average(OWA)-based soft likelihood function,which is improved by considering the reliability of the information source.Third,to measure the magnitude of different belief-based PLTSs,the belief interval of singleton is calculated,and the comparison method of belief-based PLTS is constructed based on probabilities.On the basis of the preceding discussion,we further develop an emergency decision framework that includes several novel techniques,such as attribute weight determination and decision information aggregation.Finally,the usefulness of the framework is demonstrated through a case study,and its effectiveness is illustrated through a series of comparisons.

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.

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.

Fuzzy Soft Expert Set and Its Application

In 1999, Molodtsov introduced the concept of soft set theory as a general mathematical tool for dealing with uncertainty. Alkhazaleh and Salleh (2011) define the concept of soft expert sets where the user can know the opinion of all experts in one model and give an application of this concept in decision making problem. So in this paper, we generalize the concept of a soft expert set to fuzzy soft expert set, which will be more effective and useful. We also define its basic operations, namely complement, union, intersection, AND and OR. We give an application of this concept in decision making problem. Finally, we study a mapping on fuzzy soft expert classes and its properties.

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.

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.

Interval-Valued Neutrosophic Soft Expert Set from Real Space to Complex Space

A fuzzy system is a novel computing technique that accesses uncertain information by fuzzy representation.In the decision-making process,fuzzy system and soft computing are effective tools that are tolerant to imprecision,uncertainty,and partial truths.Evolutionary fuzzy systems have been developed with the appearance of interval fuzzy,dual fuzzy,hesitant fuzzy,neutrosophic,plithogenic representations,etc.Moreover,by capturing compound features and convey multi-dimensional data,complex numbers are utilized to generalize fuzzy and neutrosophic fuzzy sets.In this paper,a representation of neutrosophic soft expert systems based on the real and complex numbers in the interval form is proposed.The interval-valued neutrosophic soft expert set(I-VNSES)is defined,and the interval-valued complex neutrosophic soft expert set(I-VCNSES)is formally generalized from the concept of IVNSES.For both I-VNSES and I-VCNSES,we introduce the relevant basic theoretical operations and study their properties.Based on these new concepts,a generalized algorithm is proposed and applied to handle the imbedded indeterminacy in the two-dimensional interval data.The proposed algorithm is tested on the economic factors that affected the Malaysian economy in 2020 to see which ones are the most influential.Eventually,a comparison of three current approaches is used to back up this study.

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.

Commonsense Reasoning and Nonmonotonic Aggregation Connectives on Fuzzy Sets

Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. In this paper, we introduce a pair of nonmonotonic aggregation connectives on fuzzy sets-soft intersection and soft union, in the light of Zadeh’s fuzzy set theory. Some important features of the nonmonotonic connectives are also discussed.

Possibility Fuzzy Soft Expert Set

In this paper we introduce the concept of possibility fuzzy soft expert set .We also define its basic operations, namely complement, union, intersection, AND and OR, and study some of their properties. Finally, we give an application of this theory in solving a decision making problem.

A Survey of Software Packages Used for Rough Set Analysis

Soft computing is a combination of methods that complement each other when dealing with ambiguous real life decision systems. Rough Set Theory (RST) is a technique used in soft computing that enhances the idea of classical sets to deal with incomplete knowledge and provides a mechanism for concept approximation. It uses reducts to isolate key attributes affecting outcomes in decision systems. The paper summarizes two algorithms for reduct calculation. Moreover, to automate the application of RST, different software packages are available. The paper provides a survey of packages that are most frequently used to perform data analysis based on Rough Sets. For benefit of researchers, a comparison of based on functionalities of those software is also provided.

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.