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.

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.

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.

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.

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.

Some interval-valued intuitionistic uncertain linguistic hybrid Shapley operators

Two interval-valued intuitionistic uncertain linguistic hybrid operators cal ed the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley averaging （I-IIULHSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid Shapley geometric （I-IIULHSG） operator are defined. These operators not only reflect the importance of elements and their ordered positions, but also consider the correlations among elements and their ordered positions. Since the fuzzy measures are defined on the power set, it makes the problem exponentially complex. In order to simplify the complexity of solving a fuzzy measure, we further define the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley averaging （I-IIULHλSA） operator and the induced interval-valued intuitionistic uncertain linguistic hybrid λ-Shapley geometric （I-IIULHλSG） operator. Moreover, an approach for multi-attribute group decision making under the interval-valued intuitionistic uncertain linguistic environment is developed. Finally, a numerical example is provided to verify the developed procedure and demonstrate its practicality and feasibility.

Synthetic security assessment for incomplete interval-valued information system

In order to understand the security conditions of the incomplete interval-valued information system （IllS） and acquire the corresponding solution of security problems, this paper proposes a multi-attribute group decision- making （MAGDM） security assessment method based on the technique for order performance by similarity to ideal solution （TOPSIS）. For IllS with preference information, combining with dominance-based rough set approach （DRSA）, the effect of incomplete interval-valued information on decision results is discussed. For the imprecise judgment matrices, the security attribute weight can be obtained using Gibbs sampling. A numerical example shows that the proposed method can acquire some valuable knowledge hidden in the incomplete interval-valued information. The effectiveness of the proposed method in the synthetic security assessment for IIIS is verified.

Solving the Interval-Valued Linear Fractional Programming Problem

This paper introduces an interval valued linear fractional programming problem (IVLFP). An IVLFP is a linear frac-tional programming problem with interval coefficients in the objective function. It is proved that we can convert an IVLFP to an optimization problem with interval valued objective function which its bounds are linear fractional functions. Also there is a discussion for the solutions of this kind of optimization problem.

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.

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.

Improved Discrete Interval-Valued Stress-Strength Interference Model Based on Extended Universal Generating Function

In practical engineering,sometimes the probability density functions( PDFs) of stress and strength can not be exactly determined,or only limited experiment data are available. In these cases,the traditional stress-strength interference( SSI) model based on classical probabilistic approach can not be used to evaluate reliabilities of components. To solve this issue, the traditional universal generating function( UGF) is introduced and then it is extended to represent the discrete interval-valued random variable.Based on the extended UGF,an improved discrete interval-valued SSI model is proposed, which has higher calculation precision compared with the existing methods. Finally,an illustrative case is given to demonstrate the validity of the proposed model.

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.

Exploring Long-Memory Process in the Prediction of Interval-Valued Financial Time Series and Its Application

Long-memory process has been widely studied in classical financial time series analysis,which has merely been reported in the field of interval-valued financial time series.The aim of this paper is to explore long-memory process in the prediction of interval-valued time series(IvTS).To model the long-memory process,two novel interval-valued time series prediction models named as interval-valued vector autoregressive fractionally integrated moving average(IV-VARFIMA)and ARFIMAX-FIGARCH were established.In the developed long-memory pattern,both of the short term and long-term influences contained in IvTS can be included.As an application of the proposed models,interval-valued form of WTI crude oil futures price series is predicted.Compared to current IvTS prediction models,IV-VARFIMA and ARFIMAX-FIGARCH can provide better in-sample and out-of-sample forecasts.

Sufficiency and Duality for Nonsmooth Interval-Valued Optimization Problems via Generalized Invex-Infine Functions

In this paper,a new concept of generalized-affineness type of functions is introduced.This class of functions is more general than some of the corresponding ones discussed in Chuong(Nonlinear Anal Theory Methods Appl 75:5044–5052,2018),Sach et al.(J Global Optim 27:51–81,2003)and Nobakhtian(Comput Math Appl 51:1385–1394,2006).These concepts are used to discuss the sufficient optimality conditions for the interval-valued programming problem in terms of the limiting/Mordukhovich subdifferential of locally Lipschitz functions.Furthermore,two types of dual problems,namely Mond–Weir type and mixed type duals are formulated for an interval-valued programming problem and usual duality theorems are derived.Our results improve and generalize the results appeared in Kummari and Ahmad(UPB Sci Bull Ser A 82(1):45–54,2020).