Interval-valued Intuitionistic Fuzzy Hybrid Research Articles

A novel multi-criteria decision making method to evaluate green innovation ecosystem resilience

Green innovation ecosystem resilience evaluation is crucial for ensuring sustainable development in dynamic environments. By comprehensively assessing resilience, it helps identify risks and facilitate effective responses, thus promoting sustainable development. To effectively evaluate the resilience of green innovation ecosystems, this paper proposes a model based on the interval-valued intuitionistic fuzzy multi-criteria decision-making (MCDM) method, designed to support decision-makers (DMs) in resilience evaluation. In this model, we improve the Criteria Importance Through Intercriteria Correlation (CRITIC) method by introducing Spearman's correlation coefficient to more accurately determine the objective weights of various indicators based on their interrelationships. Furthermore, we propose an Interval-Valued Intuitionistic Fuzzy Hybrid Average Aggregation (IVIFHAA) operator, which considers both the subjective and objective weight order for aggregating expert evaluation results. Additionally, a scoring function is introduced to generate ranked evaluation results. We also establish a resilience evaluation criteria system covering interconnectivity, sustainability, and diversity within green innovation ecosystems to assist DMs in resilience evaluation. Finally, to validate this method, we apply it to assess the resilience of regional green innovation ecosystems and compare it with other methods. The results demonstrate that the improved operator effectively reduces information loss and improves evaluation efficiency, while the improved CRITIC method handles outliers during the evaluation process.

A New Order Function for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Group Decision Making

Purpose: We introduce a multiple attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy (IVIF) domain. In these MAGDM problems, attribute values and attribute weights are represented in terms of IVIF sets (IVIFSs). Methodology: The present methodology is divided into two parts. Firstly, an appropriate order function has been developed for IVIFSs. Secondly, an algorithm has been proposed for solving the MAGDM problems with IVIF decision information. Findings: To show the effectiveness of the proposed method, a theoretical comparative study with respect to some existing literature is provided. A real-life based numerical example is given to demonstrate the proposed solution procedure. The advantage of this method is also described. Values: Using proposed order function, interval-valued intuitionistic fuzzy hybrid geometric and ordered weighted averaging operators, the present method provides a most preferred alternative in six steps. On the basis of a comparative study, it can be observed that the present method simple and easy to implement for solving the IVIF MAGDM model occurrence in real-life decision making problems.

Decision making based on linguistic interval-valued intuitionistic neutrosophic Dombi fuzzy hybrid weighted geometric operator

In this paper, we proposed the notion of a linguistic interval-valued intuitionistic neutrosophic fuzzy number. We define some score and accuracy functions of LIVINFNs are defined with a brief study of related properties. Moreover, we propose the geometric forms of LIVINDFWG, LIVINDFOWG, and LIVINDFHWG operator, which is called the geometric operators. Then, we present its characteristics and some special cases. Moreover, we put forward two new MADM approaches founded on the developed LIVINDFWG and LIVINDFOWG operators. Finally, a representative example is provided to verify the effectiveness and superiority of the proposed method by comparing it with other several existing representative MAGDM methods.

Corporate Governance-Based Strategic Approach to Sustainability in Energy Industry of Emerging Economies with a Novel Interval-Valued Intuitionistic Fuzzy Hybrid Decision Making Model

The sustainability in energy industry is one of the most prominent issues in emerging economies because of needs for the long-term growth of production and managerial capacity. Accordingly, corporate governance could lead to develop the sustainable production of energy industry. The purpose of this study is to define a set of criteria and dimensions for analyzing the corporate governance-based strategic approach to sustainability in the energy industry of emerging economies. For this purpose, this study provides several novelties by extending a hybrid decision making model with interval-valued intuitionistic fuzzy sets (IVIF) and defining the related criteria and dimensions of corporate governance-based strategic approach with the supported literature. IVIF decision making trial and evaluation laboratory (DEMATEL) is constructed for measuring the relative importance of criteria and dimensions. IVIF VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR) is applied for ranking the corporate governance-based performance of sustainable energy industries in emerging economies. Sensitivity analysis is also used for understanding the coherence of ranking results. Analysis results illustrate that the energy industry could provide more sustainable results than the conventional managerial policies by considering the social capital of board members. Additionally, mass-economies are closely related to the sustainable production capacities of energy industry and have the best performance results for the corporate governance-based sustainable energy production strategies. The results are discussed to provide the policy recommendations by comparing analysis results of emerging economies for further studies.

A Method for Group Decision Making Based on Interval-Valued Intuitionistic Fuzzy Geometric Distance Measures

In this paper, at first, we develop some new geometric distance measures for interval-valued intuitionistic fuzzy information, including the interval-valued intuitionistic fuzzy weighted geometric distance (IVIFWGD) measure, the interval-valued intuitionistic fuzzy ordered weighted geometric distance (IVIFOWGD) measure and the interval-valued intuitionistic fuzzy hybrid weighted geometric distance (IVIFHWGD) measure. Also, several desirable properties of these new distance measures are studied and a numerical example is given to show application of the distance measure to pattern recognition problems. And then, based on the developed distance measures a consensus reaching process with interval-valued intuitionistic fuzzy preference information for group decision making is proposed. Finally, an illustrative example with interval-valued intuitionistic fuzzy information is given.

Multiple attribute decision making based on novel interval-valued intuitionistic fuzzy geometric averaging operators

In this paper, we propose a new multiple attribute decision making method based on the proposed interval-valued intuitionistic fuzzy weighted geometric averaging (IVIFWGA) operator, the proposed interval-valued intuitionistic fuzzy ordered weighted geometric averaging (IVIFOWGA) operator and the proposed interval-valued intuitionistic fuzzy hybrid geometric averaging (IVIFHGA) operator. First, we propose a new multiplication operator and propose a new power operator of interval-valued intuitionistic fuzzy values (IVIFVs). We also prove some properties of the proposed multiplication operator between IVIFVs. Then, we propose the IVIFWGA operator, the IVIFOWGA operator and the IVIFHGA operator for aggregating IVIFVs. Finally, we propose a new multiple attribute decision making method based on the proposed interval-valued intuitionistic fuzzy geometric averaging operators. The experimental results show that the proposed multiple attribute decision making method can overcome the drawbacks of the existing methods.

Multiple attribute group decision making based on interval-valued intuitionistic fuzzy aggregation operators and transformation techniques of interval-valued intuitionistic fuzzy values

In this paper, we propose a new method for multiple attribute group decision making (MAGDM) based on the proposed interval-valued intuitionistic fuzzy aggregation (IVIFA) operators (including the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator, the interval-valued intuitionistic fuzzy ordered weighted averaging (IVIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid weighted averaging (IVIFHWA) operator) of interval-valued intuitionistic fuzzy values (IVIFVs). First, we propose transformation techniques between IVIFVs and right-angled triangular fuzzy numbers based on the proposed addition operator of IVIFVs. We also prove some properties of the proposed addition operator of IVIFVs. Then, we propose the IVIFWA operator, the IVIFOWA operator and the IVIFHWA operator for aggregating IVIFVs. Finally, we propose a new MAGDM method based on the proposed IVIFA operators. The experimental results show that the proposed MAGDM method can overcome the drawbacks of the existing methods. It provides us with a useful way for MAGDM in interval-valued intuitionistic fuzzy environments.

English

In this paper, the Multiple Attribute Group Decision Making (MAGDM) problems is based on the Renyi's, Daroczy's and R-norm entropy weights especially when the attribute weights are completely unknown. The interval-valued intuitionistic fuzzy ordered weighted averaging (IIFOWA) operator and the interval-valued intuitionistic fuzzy hybrid averaging (IIFHA) operator are utilized to aggregate the interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers. Correlation coefficient of Interval Valued Intuitionistic Fuzzy Sets (IVIFS) is utilized to rank the alternatives and select the most desirable one. A numerical illustration is presented to demonstrate the proposed approach.

Extension of VIKOR Method for Multi-Attribute Group Decision Making with Incomplete Weights

In this paper, we First utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Extension of VIKOR Method for Multi-Attribute Group Decision Making with Interval-Valued Intuitionistic Fuzzy Assessments and Incomplete Weights

In this paper, we investigate the multi-attribute group decision making (MAGDM) problems in which all the information provided by the decision makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFN), and the information about attribute weights is partially known. First, we utilize the induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision makers into a collective interval-valued intuitionistic fuzzy decision matrix. Based on the basic ideal of traditional VIKOR method, we establish an optimization model to determine the weights of attributes. Then, calculation steps based on the collective interval-valued intuitionistic fuzzy decision matrix and traditional VIKOR method for solving the MAGDM problems with interval-valued intuitionistic fuzzy assessments and partially known weight information are given. Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Induced Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet integral operators and their application in decision making

AbstractBased on the Choquet integral and the generalized Shapley function, two new induced Atanassov's interval-valued intuitionistic fuzzy hybrid aggregation operators are defined, which are named as the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet arithmetical averaging (IGS-IVIFHCAA) operator and the induced generalized Shapley Atanassov's interval-valued intuitionistic fuzzy hybrid Choquet geometric mean (IGS-IVIFHCGM) operator. These operators do not only globally consider the importance of elements and their ordered positions, but also overall reflect the correlations among them and their ordered positions. Meantime, some important cases are examined, and some desirable properties are studied. Furthermore, if the information about the weighting vectors is incompletely known, the models for the optimal λ–fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under Atanassov...

An approach for multiple attribute group decision making problems with interval-valued intuitionistic trapezoidal fuzzy numbers

This article proposes an approach to resolve multiple attribute group decision making (MAGDM) problems with interval-valued intuitionistic trapezoidal fuzzy numbers (IVITFNs). We first introduce the cut set of IVITFNs and investigate the attitudinal score and accuracy expected functions for IVITFNs. Their novelty is that they allow the comparison of IVITFNs by taking into accounting of the experts’ risk attitude. Based on these expected functions, a ranking method for IVITFNs is proposed and a ranking sensitivity analysis method with respect to the risk attitude is developed. To aggregate the information with IVITFNs, we study the desirable properties of the interval-valued intuitionistic trapezoidal fuzzy weighted geometric (IVITFWG) operator, the interval-valued intuitionistic trapezoidal fuzzy ordered weighted geometric (IVITFOWG) operator, and the interval-valued intuitionistic trapezoidal fuzzy hybrid geometric (IVITFHG) operator. It is worth noting that the aggregated value by using these operators is also an interval-valued intuitionistic trapezoidal fuzzy value. Then, based on these expected functions and aggregating operators, an approach is proposed to solve MAGDM problems in which the attribute values take the form of interval-valued intuitionistic fuzzy numbers and the expert weights take the form of real numbers. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

The induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging operator and its application in decision making

The Shapley function is a very effective tool to measure the importance of elements, which can reflect the interactive characteristics among them. In this study we use the Shapley function to propose an induced generalized interval-valued intuitionistic fuzzy hybrid Shapley averaging (IG-IVIFHSA) operator. This operator does not only globally consider the importance of elements and their ordered positions, but also overall reflect the interaction among them and among their ordered positions. It is worth pointing out that most of the existing hybrid aggregation operators are special cases of our operator. Meantime, some important cases are considered, and some desirable properties are studied. Furthermore, the models for the optimal fuzzy measures on attribute set and ordered set are established, respectively. Moreover, an approach to multi-attribute decision making under interval-valued intuitionistic fuzzy environment is developed. Finally, two numerical examples are given to verify the developed method and demonstrate its practicality and feasibility.

Interval-valued intuitionistic fuzzy hybrid weighted averaging operator based on Einstein operation and its application to decision making

The notion of interval-valued intuitionistic fuzzy set IVIFS is a generalization of that of Atanassov's intuitionistic fuzzy set AIFS. The fundamental characteristic of IVIFS is that the values of its membership function and non-membership function are intervals rather than exact numbers. In this paper, we define some Einstein operations on IVIFS and develop three arithmetic averaging operators, such as the interval-valued intuitionistic fuzzy Einstein weighted averaging IVIFWAe operator, interval-valued intuitionistic fuzzy Einstein ordered weighted averaging IVIFOWAe operator, and interval-valued intuitionistic fuzzy Einstein hybrid weighted averaging IVIFHWAe operator, for aggregating interval-valued intuitionistic fuzzy information. The IVIFHWAe operator generalizes both the IVIFWAe and IVIFOWAe operators. Moreover, we establish various properties of these operators and derive the relationship between the proposed operators and the exiting aggregation operators. Finally, we apply the IVIFHWAe operator to multiple attribute decision making with interval-valued intuitionistic fuzzy information.

Model for Evaluating the Security of Wireless Sensor Network in Interval-Valued Intuitionistic Fuzzy Environment

In this paper, we investigate the multiple attribute decision making(MADM) problems for evaluating the security of wireless sensor networks with interval-valued intuitionistic fuzzy information. We utilize the interval-valued intuitionistic fuzzy hybrid geometric (IVIFHG) operator to aggregate the interval-valued intuitionistic fuzzy numbers corresponding to each alternative and derive the overall value of the alternatives, then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally an illustrative example has been given to show the developed approach and demonstrate its practicality and effectiveness.

Some induced intuitionistic fuzzy aggregation operators applied to multi-attribute group decision making

In this paper, we define various induced intuitionistic fuzzy aggregation operators, including induced intuitionistic fuzzy ordered weighted averaging (OWA) operator, induced intuitionistic fuzzy hybrid averaging (I-IFHA) operator, induced interval-valued intuitionistic fuzzy OWA operator, and induced interval-valued intuitionistic fuzzy hybrid averaging (I-IIFHA) operator. We also establish various properties of these operators. And then, an approach based on I-IFHA operator and intuitionistic fuzzy weighted averaging (WA) operator is developed to solve multi-attribute group decision-making (MAGDM) problems. In such problems, attribute weights and the decision makers' (DMs') weights are real numbers and attribute values provided by the DMs are intuitionistic fuzzy numbers (IFNs), and an approach based on I-IIFHA operator and interval-valued intuitionistic fuzzy WA operator is developed to solve MAGDM problems where the attribute values provided by the DMs are interval-valued IFNs. Furthermore, induced intuitionistic fuzzy hybrid geometric operator and induced interval-valued intuitionistic fuzzy hybrid geometric operator are proposed. Finally, a numerical example is presented to illustrate the developed approaches.

Some Intuitionistic Fuzzy Weighted Distance Measures and Their Application to Group Decision Making

Xu and Chen (J Syst Sci Syst Eng 17:432–445, 2008) introduced a new decision-making technique called the ordered weighted distance (OWD) measure, having been proved useful for the treatment of situation where the available information is represented in exact numerical values. In this paper, we consider the situations with intuitionistic fuzzy and interval-valued intuitionistic information, and develop some intuitionistic fuzzy weighted distance measures such as intuitionistic fuzzy ordered weighted distance (IFOWD) measure, interval-valued intuitionistic fuzzy ordered weighted distance (IVIFOWD) measure, intuitionistic fuzzy hybrid weighted distance (IFHWD) measure and interval-valued intuitionistic fuzzy hybrid weighted distance (IVIFHWD) measure. These developed weighted distance measures are very suitable to deal with the situation where the input data are represented in intuitionistic fuzzy numbers or interval-lvalued intuitionistic fuzzy numbers. Then we present a consensus reaching process for group decision making with intuitionistic fuzzy preference information based on the developed distance measures. Finally, a practical application of he developed approach to the problem of evaluating university faculty for tenure and promotion is given.

Extension of the VIKOR method for group decision making with interval-valued intuitionistic fuzzy information

The aim of this paper is to extend the VIKOR method for multiple attribute group decision making in interval-valued intuitionistic fuzzy environment, in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number, and the information about attribute weights is partially known, which is an important research field in decision science and operation research. First, we use the interval-valued intuitionistic fuzzy hybrid geometric operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. We use the different distances to calculate the particular measure of closeness of each alternative to the interval-valued intuitionistic positive-ideal solution. According to values of the particular measure, we rank the alternatives and then select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.

Extension of the TOPSIS method for decision making problems under interval-valued intuitionistic fuzzy environment

TOPSIS is one of the well-known methods for multiple attribute decision making (MADM). In this paper, we extend the TOPSIS method to solve multiple attribute group decision making (MAGDM) problems in interval-valued intuitionistic fuzzy environment in which all the preference information provided by the decision-makers is presented as interval-valued intuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy number (IVIFNs), and the information about attribute weights is partially known. First, we use the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator to aggregate all individual interval-valued intuitionistic fuzzy decision matrices provided by the decision-makers into the collective interval-valued intuitionistic fuzzy decision matrix, and then we use the score function to calculate the score of each attribute value and construct the score matrix of the collective interval-valued intuitionistic fuzzy decision matrix. From the score matrix and the given attribute weight information, we establish an optimization model to determine the weights of attributes, and construct the weighted collective interval-valued intuitionistic fuzzy decision matrix, and then determine the interval-valued intuitionistic positive-ideal solution and interval-valued intuitionistic negative-ideal solution. Based on different distance definitions, we calculate the relative closeness of each alternative to the interval-valued intuitionistic positive-ideal solution and rank the alternatives according to the relative closeness to the interval-valued intuitionistic positive-ideal solution and select the most desirable one(s). Finally, an example is used to illustrate the applicability of the proposed approach.

Multi-person Multi-attribute Decision Making Problems Based on Interval-valued Intuitionistic Fuzzy Information

Based on the interval-valued intuitionistic fuzzy hybrid geometric (IIFHG) operator and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator, we investigate the group decision making problems in which all the information provided by the decision-makers is presented as interval-valued in tuitionistic fuzzy decision matrices where each of the elements is characterized by interval-valued intuitionistic fuzzy numbers, and the information about attribute weights is partially known. Anumerical example is used to illustrate the applicability of the proposed approach.