Interval-valued Intuitionistic Fuzzy Information Research Articles

Some Generalized Dependent Aggregation Operators with Interval-Valued Intuitionistic Fuzzy Information and Their Application to Exploitation Investment Evaluation

We investigate multiple attribute group decision making (MAGDM) problems with arguments taking the form of interval-valued intuitionistic fuzzy numbers. In order to relieve influence of unfair arguments, a Gaussian distribution-based argument-dependent weighting method and a hybrid support-function-based argument-dependent weighting method are devised by, respectively, measuring support degrees of arguments indirectly and directly, based on which the Gaussian generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator (Gaussian-GIIFOWA) and geometric operator (Gaussian-GIIFOWG), the power generalized interval-valued intuitionistic fuzzy ordered weighted averaging (P-GIIFOWA) operator and geometric (P-GIIFOWA) operator are proposed to generalize a wide range of aggregation operators for decision makers to flexibly choose in decision modelling. And some desirable properties of the proposed operators are also analyzed. Further, application of an approach integrating proposed operators to exploitation investment evaluation of tourist spots has shown the effectiveness and practicality of developed methods; experimental results also verify the properties of proposed operators.

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.

New approach to MCDM under interval-valued intuitionistic fuzzy environment

It is well-known that how to determine the weights of criteria is an important problem of multicriteria decision making. To make further description of the aforementioned, in this paper we introduce an extended TOPSIS method for multicriteria decision making with interval-valued intuitionistic fuzzy information, where the weighted vector of each alternative is determined by rank- ing corresponding evaluation information. Meanwhile, we construct a new method to measure the distance between alternatives and positive ideal solution as well as negative ideal solution, which is score distance. Finally, the detailed decision making procedure is proposed and an illustrative example is applied to demonstrate its validity. It is worth while to point out that the weights determination for criteria will be helpful to future research on decision making analysis.

Methods for strategic decision-making problems with immediate probabilities in intuitionistic fuzzy setting

With respect to decision-making problems by using probabilities, immediate probabilities and information that can be represented with intuitionistic fuzzy information or interval-valued intuitionistic fuzzy information, some new decision analysis are proposed. Firstly, some operational laws, score function and accuracy function of intuitionistic fuzzy values or interval-valued intuitionistic fuzzy values are introduced. Then, we have developed some new probability aggregation operators with intuitionistic fuzzy information: Probability Intuitionistic Fuzzy Weighted Average (P-IFWA) operator, Immediate Probability Intuitionistic Fuzzy Ordered Weighted Average (IP-IFOWA) operator, Probability Intuitionistic Fuzzy Ordered Weighted Average (P-IFOWA) operator, Probability Intuitionistic Fuzzy Weighted Geometric (P-IFWG) operator, Immediate Probability Intuitionistic Fuzzy Ordered Weighted Geometric (IP-IFOWG) operator and Probability Intuitionistic Fuzzy Ordered Weighted Geometric (P-IFOWG) operator and applied these operators to decision-making problem about the selection of the optimal production strategy. Furthermore, we shall extend the developed models and procedures to solve probabilistic decision-making problems with interval-valued intuitionistic fuzzy information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.

Using a rough set model to extract rules in dominance-based interval-valued intuitionistic fuzzy information systems

Interval-valued intuitionistic fuzzy information systems are generalizations of conventional fuzzy-valued information systems. We introduce a dominance relation in the framework of interval-valued intuitionistic fuzzy information systems to come up with the concept we call a dominance-based interval-valued intuitionistic fuzzy information system (DIIFIS). This system is used to establish a dominance-based rough set model, which is grounded primarily on the substitution of the indiscernibility relation in the classic rough set theory with the aforementioned dominance-based relation. This relation is defined by the score and accuracy of interval-valued intuitionistic fuzzy value. To simplify knowledge representation and extract useful and simple dominance-based interval-valued intuitionistic fuzzy rules, we present two attribute reduction approaches to eliminating redundant information. To demonstrate the potential of these approaches, we apply them to computer auditing risk assessment, decision-making problems in wealth management, and pattern classification. Our findings confirm that the proposed rough set model is an effective means of extracting knowledge from dominance-based interval-valued intuitionistic fuzzy information systems.

A Class of New Interval-Valued Intuitionistic Fuzzy Distance Measures and their Applications in Discriminant Analysis

In this paper we develop a class of new distance measures for interval-valued intuitionistic fuzzy sets. Then we discuss some of the special cases of it by taking different parameters. Finally we apply them for discriminant analysis with interval-valued intuitionistic fuzzy information.

Model for Evaluating the Computer Network Security with Interval-Valued Intuitionistic Fuzzy Information

In this paper, we investigate the multiple attribute decision making (MADM) problems for for evaluating the computer network security with interval-valued intuitionistic fuzzy information. To determine the attribute weights, a model based on the information entropy, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted averaging (IVIFWA) operator to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then rank the alternatives and select the most desirable one(s) according to the score function and accuracy function. Finally, an illustrative example is given.

A Novel Efficient Approach to Evaluating the Security of Wireless Sensor Network with Interval-Valued Intuitionistic Fuzzy Information

A Novel Efficient Approach to Evaluating the Security of Wireless Sensor Network with Interval-Valued Intuitionistic Fuzzy Information

Research on the Comprehensive Evaluation of Sports Management System with Interval-valued Intuitionistic Fuzzy Information

Research on the Comprehensive Evaluation of Sports Management System with Interval-valued Intuitionistic Fuzzy Information

SOME CONTINUOUS AGGREGATION OPERATORS WITH INTERVAL-VALUED INTUITIONISTIC FUZZY INFORMATION AND THEIR APPLICATION TO DECISION MAKING

In this paper, some new operators for aggregating interval-valued intuitionistic fuzzy information are proposed to deal with multiple attribute decision making problems. Firstly, the C-IFOWA operator and C-IFOWG operator are developed to aggregate all the values in the interval-valued intuitionistic fuzzy numbers. Some of their desirable properties are also studied. Secondly, in order to aggregate a set of interval-valued intuitionistic fuzzy numbers, some new aggregation operators are proposed based on the C-IFOWA operator and C-IFOWG operator. Thirdly, two methods for multiple attribute decision making, in which the attribute values are given in the forms of interval-valued intuitionistic fuzzy numbers are presented. Finally, two numerical examples are provided to illustrate the practicality and validity of the proposed methods.

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.

Model for Supplier Selection in Interval-Valued Intuitionistic Fuzzy Setting

The aim of this paper is to investigate the multiple attribute decision making problems to deal with the supplier selection in supply chain management with interval-valued intuitionistic fuzzy information. Based on the traditional project method, calculation steps for solving interval-valued intuitionistic fuzzy multiple attribute decision-making problems with known weight information are given. The project values between every alternative and negative ideal solution are calculated. Then, the project values are utilized defined to determine the ranking order of all alternatives. Finally, an illustrative example with supplier selection is given.

The induced generalized aggregation operators for intuitionistic fuzzy sets and their application in group decision making

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (I-GIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for intuitionistic fuzzy information, including all the particular cases of the I-IFOWA operator, GIFOWA operator and the induced intuitionistic fuzzy ordered geometric (I-IFOWG) operator. We also present the induced generalized interval-valued intuitionistic fuzzy ordered weighted averaging (I-GIIFOWA) operator to accommodate the environment in which the given arguments are interval-valued intuitionistic fuzzy sets. Further, we develop procedures to apply them to solve group multiple attribute decision making problems with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. Finally, we present their application to show the effectiveness of the developed methods.

A new multiple criteria decision making method based on intuitionistic fuzzy information

The risk attitude of a decision maker is considered in the decision process. Inspired by mean–variance type utility functions in the financial risk management, a new class of decision functions are defined based on the weighted score function and the weighted accuracy function in the intuitionistic fuzzy setting. By choosing a suitable parameter value, the decision maker’s risk attitude can be flexibly reflected by our decision function. The new method can be applied for both the exactly known and partly known criteria weight situations. For the latter case, it is only necessary to solve one linear programming problem. The developed models and algorithms are then extended to multiple criteria decision making problems with the interval-valued intuitionistic fuzzy information. Numerical examples are provided to illustrate the practicality, flexibility and efficiency of our new algorithms.

Method for Selecting the Suitable Bridge Construction Projects with Interval-Valued Intuitionistic Fuzzy Information

The aim of this paper is to investigate the multiple attribute decision making problems to select the bridge construction projects with interval-valued intuitionistic fuzzy information, in which the information about attribute weights is completely known, and the attribute values take the form of interval-valued intuitionistic fuzzy numbers. A modified TOPSIS analysis method is proposed. Then, based on the traditional TOPSIS method, calculation steps for solving interval-valued intuitionistic fuzzy multiple attribute decision-making problems with known weight information are given. Finally, an illustrative example involving a bridge construction project selection is given to verify the developed approach and to demonstrate its practicality and effectiveness.

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.

A multi-criteria decision making procedure based on interval-valued intuitionistic fuzzy bonferroni means

Inspired by the idea of Bonferroni mean, in this paper we develop an aggregation technique called the interval-valued intuitionistic fuzzy Bonferroni mean for aggregating interval-valued intuitionistic fuzzy information. We study its properties and discuss its special cases. For the situations where the input arguments have different importance, we then define a weighted interval-valued intuitionistic fuzzy Bonferroni mean, based on which we give a procedure for multi-criteria decision making under interval-valued intuitionistic fuzzy environments.

A mathematical programming approach to multi-attribute decision making with interval-valued intuitionistic fuzzy assessment information

This article proposes an approach to handle multi-attribute decision making (MADM) problems under the interval-valued intuitionistic fuzzy environment, in which both assessments of alternatives on attributes (hereafter, referred to as attribute values) and attribute weights are provided as interval-valued intuitionistic fuzzy numbers (IVIFNs). The notion of relative closeness is extended to interval values to accommodate IVIFN decision data, and fractional programming models are developed based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to determine a relative closeness interval where attribute weights are independently determined for each alternative. By employing a series of optimization models, a quadratic program is established for obtaining a unified attribute weight vector, whereby the individual IVIFN attribute values are aggregated into relative closeness intervals to the ideal solution for final ranking. An illustrative supplier selection problem is employed to demonstrate how to apply the proposed procedure.

A new multiple attribute group decision making method in intuitionistic fuzzy setting

The multiple attribute group decision making (MAGDM) problem with intuitionistic fuzzy information investigated in this paper is very useful for solving complicated decision problems under uncertain circumstances. Since experts have their own characteristics, they are familiar with some of the attributes, but not others, the weights of the decision makers to different attributes should be different. We derive the weights of the decision makers by aggregating the individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. The expert has a big weight if his evaluation value is close to the mean value and has a small weight if his evaluation value is far from the mean value. For the incomplete attribute weight information, we establish some optimization models to determine the attribute weights. Furthermore, we develop several algorithms for ranking alternatives under different situations, and then extend the developed models and algorithms to the MAGDM problem with interval-valued intuitionistic fuzzy information. Numerical results finally illustrate the practicality and efficiency of our new algorithms.

Approach for aggregating interval-valued intuitionistic fuzzy information and its application to reservoir operation

In this article, we concentrate on the interval-valued intuitionistic fuzzy multiple attribute decision making problems with preference information on schemes and incomplete weight information. First some operational laws, score function and accuracy function of interval-valued intuitionistic fuzzy numbers are defined, and based on these, a method for ranking interval-valued intuitionistic fuzzy numbers is presented, then an optimization model based on the minimizing deviation method, by which the attribute weights can be determined, is established, so an approach for decision making with interval-valued intuitionistic fuzzy information is developed, finally these are applied to practical reservoir operation and the optimal scheme is obtained. This case study shows that the model and corresponding method are scientific and practical.