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.

Aggregation Operators for Interval-Valued Pythagorean Fuzzy Hypersoft Set with Their Application to Solve MCDM Problem

Experts use Pythagorean fuzzy hypersoft sets(PFHSS)in their investigations to resolve the indeterminate and imprecise information in the decision-making process.Aggregation operators(AOs)perform a leading role in perceptivity among two circulations of prospect and pull out concerns from that perception.In this paper,we extend the concept of PFHSS to interval-valued PFHSS(IVPFHSS),which is the generalized form of intervalvalued intuitionistic fuzzy soft set.The IVPFHSS competently deals with uncertain and ambagious information compared to the existing interval-valued Pythagorean fuzzy soft set.It is the most potent method for amplifying fuzzy data in the decision-making(DM)practice.Some operational laws for IVPFHSS have been proposed.Based on offered operational laws,two inventive AOs have been established:interval-valued Pythagorean fuzzy hypersoft weighted average(IVPFHSWA)and interval-valued Pythagorean fuzzy hypersoft weighted geometric(IVPFHSWG)operators with their essential properties.Multi-criteria group decision-making(MCGDM)shows an active part in contracts with the difficulties in industrial enterprise for material selection.But,the prevalent MCGDM approaches consistently carry irreconcilable consequences.Based on the anticipated AOs,a robust MCGDMtechnique is deliberate formaterial selection in industrial enterprises to accommodate this shortcoming.A real-world application of the projectedMCGDMmethod for material selection(MS)of cryogenic storing vessels is presented.The impacts show that the intended model is more effective and reliable in handling imprecise data based on IVPFHSS.

On similarity measures of interval-valued intuitionistic fuzzy sets and their application to pattern recognitions

The concept of the degree of similarity between interval-valued intuitionistic fuzzy sets （IVIFSs） is introduced, and some distance measures between IVIFSs are defined based on the Hamming distance, the normalized Hamming distance, the weighted Hamming distance, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance, etc. Then, by combining the Hausdorff metric with the Hamming distance, the Euclidean distance and their weighted versions, two other similarity measures between IVIFSs, i. e., the weighted Hamming distance based on the Hausdorff metric and the weighted Euclidean distance based on the Hausdorff metric, are defined, and then some of their properties are studied. Finally, based on these distance measures, some similarity measures between IVIFSs are defined, and the similarity measures are applied to pattern recognitions with interval-valued intuitionistic fuzzy information.

Fully implicational methods for approximate reasoning based on interval-valued fuzzy sets

The aim of this paper is to discuss the approximate rea- soning problems with interval-valued fuzzy environments based on the fully implicational idea. First, this paper constructs a class of interval-valued fuzzy implications by means of a type of impli- cations and a parameter on the unit interval, then uses them to establish fully implicational reasoning methods for interval-valued fuzzy modus ponens （IFMP） and interval-valued fuzzy modus tel- lens （IFMT） problems. At the same time the reversibility properties of these methods are analyzed and the reversible conditions are given. It is shown that the existing unified forms of α-triple I （the abbreviation of triple implications） methods for FMP and FMT can be seen as the particular cases of our methods for IFMP and IFMT.

Interval-valued intuitionistic fuzzy aggregation operators

The notion of the interval-valued intuitionistic fuzzy set （IVIFS） is a generalization of that of the Atanassov＇s intuitionistic fuzzy set. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. There are various averaging operators defined for IVlFSs. These operators are not monotone with respect to the total order of IVIFS, which is undesirable. This paper shows how such averaging operators can be represented by using additive generators of the product triangular norm, which simplifies and extends the existing constructions. Moreover, two new aggregation operators based on the t.ukasiewicz triangular norm are proposed, which are monotone with respect to the total order of IVIFS. Finally, an application of the interval-valued intuitionistic fuzzy weighted averaging operator is given to multiple criteria decision making.

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.

Assessment of the Solid Waste Disposal Method during COVID-19 Period Using the ELECTRE Ⅲ Method in an Interval-Valued q-Rung Orthopair Fuzzy Approach

As the quantity of garbage created every day rises,solid waste management has become the world’s most important issue.As a result,improper solid waste disposal and major sanitary issues develop,which are only detected after they have become dangerous.Due to the system’s lockdown during the COVID-19 pandemic,this scenario became much more uncertain.We are at the stage to develop and execute effective waste management procedures,as well as long-term policies and forward-thinking programmes that can work even in the most adverse of scenarios.We incorporate major solid waste(organic and inorganic solid wastes)approaches that actually perform well in normal cases by reducing waste and environmental disasters;however,in such an uncertain scenario like the COVID-19 pandemic,the project automatically allows for a larger number of criteria,all of which are dealt with using fuzzy Multi-Criteria Group Decision Making(MCGDM)methods.The ELECTRE Ⅲ(ELimination Et Choice Translating REality-Ⅲ)approach,which is a novel decision-making strategy for determining the best way to dispose and reduce garbage by combining traditional ELECTRE Ⅲ with an interval-valued q-rung orthopair fuzzy set(IVq-ROFS),is described in detail in this article.To confirm the efficacy of the recommended model,a numerical explanation is provided,as well as sensitivity and comparative analyses.Obviously,the findings encourage decision-makers in authorities to deliberate about the proposals before creating solid waste management policies.

Interval-Valued Intuitionistic Fuzzy-Rough Sets

This paper combines interval-valued intuitionistic fuzzy sets and rough sets.It studies rougheness in interval-valued intuitionistic fuzzy sets and proposes one kind of interval-valued intuitionistic fuzzy-rough sets models under the equivalence relation in crisp sets.That extends the classical rough set defined by Pawlak.

On Weighted Possibilistic Mean,Variance and Correlation of Interval-valued Fuzzy Numbers

In this paper, the concept of weighted possibilistic mean of interval- valued fuzzy number is first introduced. Further, the notions of weighted possibilistic variance, covariance and correlation of interval-valued fuzzy numbers are presented. Meantime, some important properties of them and relationships between them are studied.

On AP-Henstock Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In 2000, Wu and Gong [1] introduced the thought of the Henstock integrals of inter-valvalued functions and fuzzy-number-valued functions and obtained a number of their properties. The aim of this paper is to introduce the thought of the AP- Henstock integrals of interval-valued functions and fuzzy-number-valued functions which are extensions of [1] and investigate a number of their properties.

On Henstock-Stieltjes Integrals of Interval-Valued Functions and Fuzzy-Number-Valued Functions

In this paper we introduce the notion of the Henstock-Stieltjes (HS) integrals of interval-valued functions and fuzzy-number-valued functions and discuss some of their properties.

A KIND OF FUZZY LINEAR PROGRAMMING PROBLEMS BASED ON INTERVAL-VALUED FUZZY SETS

The objective of this paper is to deal with a kind of fuzzy linear programming problem based on interval\|valued fuzzy sets (IVFLP) through the medium of procedure that turns IVFLP into parametric linear programming via the mathematical programming.Some useful results for the benefit of solving IVFLP are expounded and proved,developed and discussed.Furthermore,that the proposed techniques in this paper allow the decision\|maker to assign a different degree of importance can provide a useful way to efficiently help the decision\|maker make their decisions.

基于Fuzzy-FMEA的AI绘画服务失效分析方法

目的AI绘画是艺术对技术的借力,存在技术挟持艺术引发艺术与技术双重异化的风险,并表征于AI绘画服务端。为规避人工智能技术在绘画领域的不当应用,从服务失效角度对其进行风险分析十分必要。方法针对传统FMEA存在忽视不确定性模糊评价等问题,提出一种引入模糊语言评价的Fuzzy-FMEA方法,用以识别AI绘画服务风险并确定整改优先级。首先设计体验实验,梳理AI绘画服务触点,记录受试者体验过程中的抱怨反应,计算抱怨指数,为后续Fuzzy-FMEA奠定基础;其次组建FMEA小组,建立模糊语言评价集合,对因人工智能技术应用不当影响智能体服务效能的服务触点进行失效分析,计算失效风险值,并对照第5版FMEA手册确定措施优先级。结论结合实验数据输出风险预警报告和服务重塑方向,以具体案例验证了该方法的可行性与有效性。

基于Fuzzy-PI的直驱永磁风力发电系统MPPT控制

通过对模糊PI控制算法、MPPT算法分析,并对变流器的控制策略进行推导,提出基于Fuzzy-PI控制策略,确定机侧以转速的偏差及其微分为输入,交轴电流为输出,风机达到最大功率跟踪效果;网侧变流器采用电压外环、电流内环双闭环控制策略。通过Simulink系统仿真,结果表明模糊PI控制系统能实现发电机的最大功率跟踪和单位功率因数运行,控制效果优于传统的PI控制策略。

Road Surface Modeling and Representation from Point Cloud Based on Fuzzy Clustering

A scheme for an automatic road surface modeling from a noisy point cloud is presented. The normal vectors of the point cloud are estimated by distance-weighted fitting of local plane. Then, an automatic recognition of the road surface from noise is performed based on the fuzzy clustering of normal vectors, with which the mean value is calculated and the projecting plane of point cloud is created to obtain the geometric model accordingly. Based on fuzzy clustering of the intensity attributed to each point, different objects on the road surface are assigned different colors for representing abundant appearances. This unsupervised method is demonstrated in the experiment and shows great effectiveness in reconstructing and rendering better road surface.

Fixed Point Results by Altering Distances in Fuzzy Metric Spaces

We establish fixed point theorems in complete fuzzy metric space by using notion of altering distance, initiated by Khan et al. [Bull. Austral. Math. Soc. 30 (1984), 1-9]. Also, we find an affirmative answer in fuzzy metric space to the problem of Sastry [TamkangJ. Math., 31(3) (2000), 243-250].

Common Fixed Points of Single and Multivalued Maps in Fuzzy Metric Spaces

In this paper we introduce the notion of common property (EA) in fuzzy metric spaces. Further we prove some common fixed points theorems for hybrid pair of single and multivalued maps under hybrid contractive conditions. Our results extend previous ones in fuzzy metric spaces.

The Pointwise Characterizations of Fuzzy Ideals and Fuzzy Prime Ideals

In this paper, the auther programs and discusses the fuzzy subrings, fuzzy ideals generated by fuzzy points.

A Fixed Point Approach to the Fuzzy Stability of a Mixed Type Functional Equation

Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.

Modified fuzzy point estimate method and its application to slope reliability analysis

A slope engineering system is a complex system, in which many uncertaintiesexist, including random uncertainties and fuzzy uncertainties. Traditionally, random uncertaintieswere often considered, while fuzzy uncertainties were ignored. Therefore, fuzzy-random methodsshould he proposed. A fuzzy point estimate method was proposed by Dodagoudar, that is, consideringthe effect of fuzzy-random factors, the fuzzy-random limit state function of slopes is changed torandom interval limit state function by the lambda level cutting, then the moments of the functioncan be obtained by the Rosenblueth's method, and the stability state of slopes can be evaluated bysynthesizing a group of moments. But in Dodagoudar's method, Rosenblueth's state function iscomposed of only two kinds of combinations of parameters rather than 2~n kinds of combinations. So amodified fuzzy point estimate method is proposed by the authors, and it is used in a slopereliability analysis.