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.

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.

Hybrid Dynamic Variables-Dependent Event-Triggered Fuzzy Model Predictive Control

This article focuses on dynamic event-triggered mechanism(DETM)-based model predictive control(MPC) for T-S fuzzy systems.A hybrid dynamic variables-dependent DETM is carefully devised,which includes a multiplicative dynamic variable and an additive dynamic variable.The addressed DETM-based fuzzy MPC issue is described as a “min-max” optimization problem(OP).To facilitate the co-design of the MPC controller and the weighting matrix of the DETM,an auxiliary OP is proposed based on a new Lyapunov function and a new robust positive invariant(RPI) set that contain the membership functions and the hybrid dynamic variables.A dynamic event-triggered fuzzy MPC algorithm is developed accordingly,whose recursive feasibility is analysed by employing the RPI set.With the designed controller,the involved fuzzy system is ensured to be asymptotically stable.Two examples show that the new DETM and DETM-based MPC algorithm have the advantages of reducing resource consumption while yielding the anticipated performance.

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.

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.

Linguistic Dynamic Modeling and Analysis of Psychological Health State Using Interval Type-2 Fuzzy Sets

The study of psychological health state is helpful to build appropriate models and take effective intervention strategies, and the results benefit the intervened released from psychological distress within the shortest possible time. In this paper, interval type-2 fuzzy sets and fuzzy comprehension evaluation are applied in the analysis of mental health status and crisis intervention. A closed-loop linguistic dynamic intervention model for psychological health state is built. Linguistic dynamic systems based on interval type-2 fuzzy sets are used to describe and analyze the evolutionary process of psychological health status. © 2014 Chinese Association of Automation.

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.

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.

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.

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.

Dynamic hesitant fuzzy linguistic group decision-making from a reliability perspective

A dynamic hesitant fuzzy linguistic group decisionmaking(DHFLGDM) problem is studied from the perspective of information reliability based on the theory of hesitant fuzzy linguistic term sets(HFLTSs). First, an approach is applied to transform the dynamic HFLTSs(DHFLTSs) into a set of proportional linguistic terms to eliminate the time dimension. Second, expert reliability is measured by considering both group similarity and degree of certainty, and an optimization method is employed to quantify the linguistic terms by maximizing the group similarity. Third, through computing the attribute stability as well as its reliability, a combination rule which considers both reliability and weight is proposed to aggregate the information, and then the aggregated grade values and degree of stability are used to make a selection. Finally,the application and feasibility of the proposed method are verified through a case study and method comparison.

Keystroke Dynamics Based Authentication Using Possibilistic Renyi Entropy Features and Composite Fuzzy Classifier

This paper presents the formulation of the possibilistic Renyi entropy function from the Renyi entropy function using the framework of Hanman-Anirban entropy function. The new entropy function is used to derive the information set features from keystroke dynamics for the authentication of users. A new composite fuzzy classifier is also proposed based on Mamta-Hanman entropy function and applied on the Information Set based features. A comparison of the results of the proposed approach with those of Support Vector Machine and Random Forest classifier shows that the new classifier outperforms the other two.

Dynamic assessment method of air target threat based on improved GIFSS

As the air combat environment becomes more complicated and changeable, accurate threat assessment of air target has a significant impact on air defense operations. This paper proposes an improved generalized intuitionistic fuzzy soft set (GIFSS) method for dynamic assessment of air target threat. Firstly, the threat assessment index is reasonably determined by analyzing the typical characteristics of air targets. Secondly, after the GIFSS at different time is obtained, the index weight is determined by the intuitionistic fuzzy set entropy and the relative entropy theory. Then, the inverse Poisson distribution method is used to determine the weight of time series, and then the time-weighted GIFSS is obtained. Finally, threat assessment of five air targets is carried out by using the improved GIFSS (I-GIFSS) and comparison methods. The validity and superiority of the proposed method are verified by calculation and comparison.

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.

A Hybrid Learning Method for the Data-Driven Design of Linguistic Dynamic Systems

In lots of data based prediction or modeling applications,uncertainties and/or noises in the observed data cannot be avoided.In such cases,it is more preferable and reasonable to provide linguistic(fuzzy)predicted results described by fuzzy memberships or fuzzy sets instead of the crisp estimates depicted by numbers.Linguistic dynamic system(LDS)provides a powerful tool for yielding linguistic(fuzzy)results.However,it is still difficult to construct LDS models from observed data.To solve this issue,this paper first presents a simplified LDS whose inputoutput mapping can be determined by closed-form formulas.Then,a hybrid learning method is proposed to construct the data-driven LDS model.The proposed hybrid learning method firstly generates fuzzy rules by the subtractive clustering method,then carries out further optimization of centers of the consequent triangular fuzzy sets in the fuzzy rules,and finally adopts multiobjective optimization algorithm to determine the left and right end-points of the consequent triangular fuzzy sets.The proposed approach is successfully applied to three real-world prediction applications which are:prediction of energy consumption of a building,forecasting of the traffic flow,and prediction of the wind speed.Simulation results show that the uncertainties in the data can be effectively captured by the linguistic(fuzzy)estimates.It can also be extended to some other prediction or modeling problems,in which observed data have high levels of uncertainties.

Risk Evaluation Based on Variable Fuzzy Sets and Information Diffusion Method

Risk evaluation is an effective way to reduce the impacts of natural hazards and it plays an increasingly important role in emergency management. Traditional methods of assessing risks mainly utilize Geographic Information System (GIS) to get risk map, and information diffusion method (IDM) to deal with incomplete data sets. However, there are few papers discuss the uncertainty of integrated hazards and consider dynamic risk under time dimension. The model proposed in this study combines the variable fuzzy set theory with information diffusion method (VFS-IDM) to solve the uncertainness of multiple hazards dynamic risk assessment when data sets are incomplete. This study employs fuzzy set theory (VFS) to calculate the relative membership degree and applies information entropy method (IEM) to obtain the weights of criteria indicators for multiple hazards evaluation. Then applies information diffusion method (IDM) to estimate condition probability distribution and vulnerability curve with the VFS-IEM model results, time data and multiple hazards losses. Then the expected value of multiple hazards dynamic risk can be calculated by using the normal information diffusion estimator so as to improve the accuracy of risk evaluation results.

应用Fuzzy集理论对地下水位动态分类

本文应用Fuzzy集理论,给出一个对地下水位动态进行分类的数学模型,并借助计算机对西安市部分地区地下水位进行了分类。

Intuitionistic fuzzy C-means clustering algorithms

Intuitionistic fuzzy sets(IFSs) are useful means to describe and deal with vague and uncertain data.An intuitionistic fuzzy C-means algorithm to cluster IFSs is developed.In each stage of the intuitionistic fuzzy C-means method the seeds are modified,and for each IFS a membership degree to each of the clusters is estimated.In the end of the algorithm,all the given IFSs are clustered according to the estimated membership degrees.Furthermore,the algorithm is extended for clustering interval-valued intuitionistic fuzzy sets(IVIFSs).Finally,the developed algorithms are illustrated through conducting experiments on both the real-world and simulated data sets.

Intuitionistic fuzzy hierarchical clustering algorithms

Intuitionistic fuzzy set （IFS） is a set of 2-tuple arguments, each of which is characterized by a membership degree and a nonmembership degree. The generalized form of IFS is interval-valued intuitionistic fuzzy set （IVIFS）, whose components are intervals rather than exact numbers. IFSs and IVIFSs have been found to be very useful to describe vagueness and uncertainty. However, it seems that little attention has been focused on the clustering analysis of IFSs and IVIFSs. An intuitionistic fuzzy hierarchical algorithm is introduced for clustering IFSs, which is based on the traditional hierarchical clustering procedure, the intuitionistic fuzzy aggregation operator, and the basic distance measures between IFSs： the Hamming distance, normalized Hamming, weighted Hamming, the Euclidean distance, the normalized Euclidean distance, and the weighted Euclidean distance. Subsequently, the algorithm is extended for clustering IVIFSs. Finally the algorithm and its extended form are applied to the classifications of building materials and enterprises respectively.

Knowledge modeling based on interval-valued fuzzy rough set and similarity inference: prediction of welding distortion

Knowledge-based modeling is a trend in complex system modeling technology. To extract the process knowledge from an information system, an approach of knowledge modeling based on interval-valued fuzzy rough set is presented in this paper, in which attribute reduction is a key to obtain the simplified knowledge model. Through defining dependency and inclusion functions, algorithms for attribute reduction and rule extraction are obtained. The approximation inference plays an important role in the development of the fuzzy system. To improve the inference mechanism, we provide a method of similaritybased inference in an interval-valued fuzzy environment. Combining the conventional compositional rule of inference with similarity based approximate reasoning, an inference result is deduced via rule translation, similarity matching, relation modification, and projection operation. This approach is applied to the problem of predicting welding distortion in marine structures, and the experimental results validate the effectiveness of the proposed methods of knowledge modeling and similarity-based inference.