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.

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.

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.

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 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.

Bipolar Interval-Valued Neutrosophic Optimization Model of Integrated Healthcare System

Bipolar Interval-valued neutrosophic set is another generalization of fuzzy set,neutrosophic set,bipolar fuzzy set and bipolar neutrosophic set and thus when applied to the optimization problem handles uncertain data more efficiently and flexibly.Current work is an effort to design a flexible optimization model in the backdrop of interval-valued bipolar neutrosophic sets.Bipolar interval-valued neutrosophic membership grades are picked so that they indicate the restriction of the plausible infringement of the inequalities given in the problem.To prove the adequacy and effectiveness of the method a unified system of sustainable medical healthcare supply chain model with an uncertain figure of product complaints is used.Time,quality and cost are considered as satisfaction level to choose best supplier for medicine procurement.The proposed model ensures 99%satisfaction for cost reduction,63%satisfaction for the quality of product and 64%satisfaction for total time taken in medicine supply chain.

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.

A New Attempt to Neutrosophic Soft Bi-Topological Spaces

In this article,new generalized neutrosophic soft∗b open set is introduced in neutrosophic soft bi-topological structurers(NSBTS)concerning soft points of the space.This new set is produced by making the marriage of soft semi-open set with soft pre-open set in neutrosophic soft topological structure.An ample of results are investigated in NSBTS on the basis of this new neutrosophic soft∗b open set.Proper examples are settled for justification of these results.The non-validity of some results is vindicated with examples.

Diagnosis of lumbar degenerative disc disease by using L^(p)-spaces related to generalized interval-valued m-polar neutrosophic choquet integral Operator

Innovative and astonishing developments in the field of spine analysis can commence with this manuscript.The lumbar disks(L1−L2 to L5−S1)are most commonly impaired by degeneration due to their long-standing degeneration and associated strain.We investigate the indications,purposes,risk factors,and therapies of lumbar degenerated disc disease(L-DDD).We assume that the degeneration of five discs creates many effects,making it difficult to differentiate between the different types of degenerated discs and their seriousness.Since the indeterminacy and falsity portions of science or clinical diagnosis are often ignored.Due to this complexity,the reliability of the patient’s progress report cannot be calculated,nor can the period of therapy be measured.The revolutionary concept of interval-valued m-polar neutrosophic Choquet integral aggregation operator(IVmPNCIAO)is proposed to eliminate these problems.We associate generalized interval-valued m-polar neutrosophic Choquet integral aggregation operator(GIVmPNCIAO)with the statistical formulation of L^(p)-spaces and use it to identify the actual kind of degenerative disc in the lumbar spine.For the classification of interval-valued m-polar neutrosophic numbers(IVMPNNs),we set the ranking index and score function.These concepts are appropriate and necessary in order to better diagnose degeneration by associating it with mathematical modeling.We construct a pre-diagnosis map based on the fuzzy interval[0,1]to classify the types of degenerative discs.We develop an algorithm by using GIVmPNCIAO based on interval-valued m-polar neutrosophic sets(IVMPNNs)to identify the degenerative disc appropriately and to choose the most exquisite treatment for the corresponding degeneration of every patient.Furthermore,we discuss the sensitivity analysis with parameter p in GIVmPNCIAO to investigate the patient’s improvement record.

单值中智软集及其相关性质

为进一步丰富软集理论并扩展其适用范围,将软集和中智集有效结合,提出了单值中智软集的概念,给出了相关运算及性质,并证明了基于上述运算定义所得到的结合律、对偶律、分配律等定理。该研究不仅完善了中智集理论,也为软集在决策领域上的应用提供了新工具。

基于区间值中智软集合的突发事件下弹性供应商选择方法研究

针对突发事件下存在的诸多不确定性,进一步解决弹性供应商的选择问题,提出一种基于前景理论的区间值中智软集合的群决策方法。首先,采用区间值中智软集合表示突发事件下存在复杂不确定和冲突信息的供应商弹性评价;其次,提出区间值中智软集合的确定程度、冲突程度以及邻近度测度方法,并基于此运用熵权法分别得到专家权重,参数客观权重和参数综合权重;最后,结合考虑专家心理偏好的前景理论,构建弹性供应商选择的群决策方法。通过实例验证了所提方法的可行性和优越性。