Interval-valued Intuitionistic Fuzzy Information Research Articles

A multicriteria group decision-making approach based on interval-valued intuitionistic fuzzy sets: A comparative perspective

This study develops an approach to tackle multiple criteria group decision-making problems in the context of interval-valued intuitionistic fuzzy sets. Due to conflicting evaluations and insufficient information about the criteria, an interval-valued intuitionistic fuzzy preference relation matrix is employed to determine the relative importance of criteria in terms of pairwise comparisons. The decision matrix, which indicates the degree of alternatives with respect to each criterion, is expressed by interval-valued intuitionistic fuzzy numbers (IVIFNs). In order to integrate interval-valued intuitionistic fuzzy information, some special aggregation operators are created by altering the aggregation operation of IVIFNs. The three families of parametric fuzzy unions and fuzzy intersections are applied in the aggregation operation with comparisons of the ranking results of alternatives. With a linear programming method, the proposed approach uses an optimization model to obtain criterion weights in exact numbers rather than intervals, and subsequently calculates an aggregated IVIFN for each alternative. The score function and accuracy function assist in discriminating between the aggregated IVIFNs, and in generating a final rank of alternatives. Finally, an illustrative supplier selection problem is used to demonstrate how to apply the proposed approach and to observe the computational consequences resulting from various aggregation operators. The results reveal that the parameters of the aggregation operators indeed have an impact on the ranks of alternatives.

An approach to aggregating interval numbers into interval-valued intuitionistic fuzzy information for group decision making

In this paper, we investigate the multiple attribute group decision making (MAGDM) problems, of which the attribute values in the group decision matrices provided by each decision maker (DM) is characterized by interval numbers. First, we define the concepts of attribute satisfactory interval and attribute dissatisfactory interval, respectively, according to each attribute values. Then we develop an approach for aggregating attribute satisfactory interval and attribute dissatisfactory interval into the collective attribute interval-valued intuitionistic fuzzy number (IVIFN), and then we obtain the collective interval-valued intuitionistic fuzzy decision matrix for group decision making. Next, we use the interval-valued intuitionistic fuzzy weighted averaging operator to aggregate all attribute values characterized by interval-valued intuitionistic fuzzy information to get the overall IVIFNs of alternatives. And then we use the score function and accuracy function to calculate the score and accuracy degree of each alternative value, and then rank the alternatives according to the score and accuracy degree of each alternative and select the most desirable one(s). And finally, we give an example for comprehensive pre-evaluation of air quality in Guangzhou, China during 16th Asian Olympic Games to illustrate in detail the decision process by the developed approach.

Fuzzy cross entropy of interval-valued intuitionistic fuzzy sets and its optimal decision-making method based on the weights of alternatives

A fuzzy cross entropy of the interval-valued intuitionistic fuzzy sets (IVIFSs) (so-called IVIFS cross entropy) is proposed by analogy with the intuitionistic fuzzy cross entropy. In its application to decision-making problems, its optimal decision-making method based on the weights of alternatives is established in which criterion values for alternatives are IVIFSs and the criterion weights are known information. We utilize the interval-valued intuitionistic fuzzy weighted aggregation operators to aggregate the interval-valued intuitionistic fuzzy information corresponding to each alternative, and then with the ideal and anti-ideal information measures of IVIFS cross entropy, an objective function is constructed to derive the optimal evaluation for the weight of each alternative. The ranking of alternatives and the best one can be determined directly on the basis of the weights of alternatives. Finally, two illustrative examples demonstrate the efficiency of the proposed decision-making method.

An interval-valued rough intuitionistic fuzzy set model

Rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. This paper presents an interval-valued rough intuitionistic fuzzy (IF) set model by means of integrating the classical Pawlak rough set theory with the interval-valued IF set theory. In this paper, we first introduce some concepts and properties of interval-valued IF set theory. Then, the rough approximations of an interval-valued IF set in the classical Pawlak approximation space and the generalised Pawlak approximation space are respectively defined, and some fundamental properties of the approximation operators are studied. Furthermore, by employing cut sets of interval-valued IF sets, classical representations of interval-valued rough IF approximation operators are presented, and the connections between special binary relations and interval-valued rough IF approximation operators are constructed. Finally, we discuss the knowledge reduction and knowledge discovery of the interval-valued IF information systems.

Generalized aggregation operators for intuitionistic fuzzy sets

The generalized ordered weighted averaging (GOWA) operators are a new class of operators, which were introduced by Yager (Fuzzy Optim Decision Making 2004;3:93–107). However, it seems that there is no investigation on these aggregation operators to deal with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. In this paper, we first develop some new generalized aggregation operators, such as generalized intuitionistic fuzzy weighted averaging operator, generalized intuitionistic fuzzy ordered weighted averaging operator, generalized intuitionistic fuzzy hybrid averaging operator, generalized interval-valued intuitionistic fuzzy weighted averaging operator, generalized interval-valued intuitionistic fuzzy ordered weighted averaging operator, generalized interval-valued intuitionistic fuzzy hybrid average operator, which extend the GOWA operators to accommodate the environment in which the given arguments are both intuitionistic fuzzy sets that are characterized by a membership function and a nonmembership function, and interval-valued intuitionistic fuzzy sets, whose fundamental characteristic is that the values of its membership function and nonmembership function are intervals rather than exact numbers, and study their properties. Then, we apply them to multiple attribute decision making with intuitionistic fuzzy or interval-valued intuitionistic fuzzy information. © 2009 Wiley Periodicals, Inc.

A Novel Measured Function for MCDM Problem Based on Interval-Valued Intuitionistic Fuzzy Sets

Several papers have presented measured function to handle multi-criteria fuzzy decision-making problems based on interval-valued intuitionistic fuzzy sets. However, in some cases, the proposed function cannot give sufficient information about alternatives. Consequently, in this paper, we will overcome previous insufficient problem and provide a novel accuracy function to measure the degree of the interval-valued intuitionistic fuzzy information. And a practical example has been provided to demonstrate our proposed approach. In addition, to make computing and ranking results easier and to increase the recruiting productivity, a computer-based interface system has been developed for decision makers to make decisions more efficiently.

Application of correlation coefficient to interval-valued intuitionistic fuzzy multiple attribute decision-making with incomplete weight information

With respect to multiple attribute decision-making problems with interval-valued intuitionistic fuzzy information, some operational laws of interval-valued intuitionistic fuzzy numbers, correlation and correlation coefficient of interval-valued intuitionistic fuzzy sets are introduced. An optimization model based on the negative ideal solution and max-min operator, by which the attribute weights can be determined, is established. We utilize the interval-valued intuitionistic fuzzy weighted averaging operator proposed by Xu (Control Decis 22(2):215–219, 2007) 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 correlation coefficient. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Choquet integrals of weighted intuitionistic fuzzy information

The Choquet integral is a very useful way of measuring the expected utility of an uncertain event [G. Choquet, Theory of capacities, Annales de l’institut Fourier 5 (1953) 131–295]. In this paper, we use the Choquet integral to propose some intuitionistic fuzzy aggregation operators. The operators not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements or their ordered positions. It is worth pointing out that most of the existing intuitionistic fuzzy aggregation operators are special cases of our operators. Moreover, we propose the interval-valued intuitionistic fuzzy correlated averaging operator and the interval-valued intuitionistic fuzzy correlated geometric operator to aggregate interval-valued intuitionistic fuzzy information, and apply them to a practical decision-making problem involving the prioritization of information technology improvement projects.

Correlation coefficient of interval-valued intuitionistic fuzzy sets and its application to multiple attribute group decision making problems

In this paper, we investigate the group decision making 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 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 then we use the obtained attribute weights and the interval-valued intuitionistic fuzzy weighted geometric (IIFWG) operator to fuse the interval-valued intuitionistic fuzzy information in the collective interval-valued intuitionistic fuzzy decision matrix to get the overall interval-valued intuitionistic fuzzy values of alternatives, and then rank the alternatives according to the correlation coefficients between IVIFNs and select the most desirable one(s). Finally, a numerical example is used to illustrate the applicability of the proposed approach.

A Deviation-Based Approach to Intuitionistic Fuzzy Multiple Attribute Group Decision Making

The aim of this article is to investigate the approach to multiple attribute group decision making (MAGDM) with intuitionistic fuzzy information. We first introduce a deviation measure between two intuitionistic fuzzy numbers, and then utilize the intuitionistic fuzzy hybrid aggregation operator to aggregate all individual intuitionistic fuzzy decision matrices into a collective intuitionistic fuzzy decision matrix. Based on the deviation measure, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the intuitionistic fuzzy weighted averaging operator and information theory, we utilize the score function and accuracy function to give an approach to ranking the given alternatives and then selecting the most desirable one(s). In addition, we extend the above results to MAGDM with interval-valued intuitionistic fuzzy information.

Multicriteria fuzzy decision-making method based on a novel accuracy function under interval-valued intuitionistic fuzzy environment

The interval-valued intuitionistic fuzzy weighted arithmetic average operator, the interval-valued intuitionistic fuzzy weighted geometric average operator, and an accuracy function of interval-valued intuitionistic fuzzy value are introduced in this paper. A novel accuracy function for interval-valued intuitionistic fuzzy sets (IVIFSs) is proposed by taking into account the unknown degree (hesitancy degree) of IVIFSs to overcome the situation of difficult decision of existing accuracy functions to the alternatives in some cases. To identify the best alternative in multicriteria decision-making problems, a multicriteria fuzzy decision-making method is established in which criterion values for alternatives are IVIFSs. We utilize the interval-valued intuitionistic fuzzy weighted aggregation operators 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 accuracy degree of the aggregated the interval-valued intuitionistic fuzzy information corresponding to the new accuracy function. Finally, an illustrative example is given to verify the developed approach.

MODELS FOR MULTIPLE ATTRIBUTE DECISION MAKING WITH INTUITIONISTIC FUZZY INFORMATION

The intuitionistic fuzzy set (IFS) characterized by a membership function and a non-membership function, was introduced by Atanassov [K. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems 20 (1986) 87–96] as a generalization of Zadeh' fuzzy set [L. A. Zadeh, "Fuzzy Sets", Information and Control 8 (1965) 338–353] to deal with fuzziness and uncertainty. In this paper, we investigate the multiple attribute decision making (MADM) problems, in which the information about attribute weights is incomplete, and the attribute values are expressed in intuitionistic fuzzy numbers (IFNs). We first define the concept of intuitionistic fuzzy ideal solution (IFIS), and then, based on the IFIS and the distance measure, we establish some optimization models to derive the attribute weights. Furthermore, based on the developed models, we develop some procedures for the rankings of alternatives under different situations, and extend the developed models and procedures to handle the MADM problems with interval-valued intuitionistic fuzzy information. Finally, we give some illustrative examples to verify the effectiveness and practicability of the developed models and procedures.