Intuitionistic Fuzzy Multi-attribute Group Decision Research Articles

MAGDM Model Using an Intuitionistic Fuzzy Matrix Energy Method and Its Application in the Selection Issue of Hospital Locations

Matrix energy is a valid mathematical tool for representing collective information. However, it is not used in the existing literature for fuzzy sets, intuitionistic fuzzy sets, and multi-attribute group decision making (MAGDM) problems, which highlights research gaps. Motivated by both matrix energy and the research gaps, this study aims to extend matrix energy to the energy of an intuitionistic fuzzy matrix (IFM) and to utilize the IFM energy method in the MAGDM problem, which fully contains all the IFM information on attribute weights, decision maker weights, and attribute values. To achieve these objectives, this paper first proposes IFM energy in terms of the true matrix energy and false matrix energy; then, it develops a MAGDM model using the IFM energy method and the score and accuracy equations of IFM energy. Then, the developed MAGDM model is applied to the selection problem of hospital locations in Shaoxing City, China to demonstrate the practicality and validity of the developed model. Compared with existing intuitionistic fuzzy MAGDM methods, the developed MAGDM model using the IFM energy method reveals its superiority and novelty in complete IFM information expressions and the MAGDM method because the existing MAGDM methods containing intuitionistic fuzzy set information have difficulty tackling MAGDM problems containing all the IFM information on attribute weights, decision maker weights, and attribute values.

VIKOR method for intuitionistic fuzzy multi-attribute group decision-making and its application to teaching quality evaluation of college English

The results of the nation-wide public college English tests and some other English tests held by the college itself are very valuable data for the assessment of the English teaching level. In the light of the selected and processed data and some other auxiliary approaches, the writer suggests that a modernized monitoring system be established to improve English teaching quality. Under this system, teachers’ and students’ English level can be evaluated in an objective way. Consequently, the subsequent measures such as teachers’ promotion as well as students’ development and employment and the evaluation of the quality of test-papers can be taken scientifically. We can solve the above issues with help of multi-attribute group decision making (MAGDM) method. Depending on the VIKOR steps and given intuitionistic fuzzy sets (IFSs), this paper devises the IF-VIKOR to assess the teaching quality of college English. In addition, the weights of attribute are derived through CRITIC method. Then, the VIKOR method is extended to IFSs to derive the order of each alternative. Therefore, all alternatives could be ranked and the best one can be identified. Eventually, we give an example of college English teaching quality evaluation, according to some comparison with other methods to make an analysis, the results show that the method proposed in such paper is effective and easy to compute.

Grey relational analysis method based on cumulative prospect theory for intuitionistic fuzzy multi-attribute group decision making

The Multi-attribute group decision making (MAGDM) problem is an interesting everyday problem full of complexity and ambiguity. As an extended form of fuzzy sets, intuitionistic fuzzy sets (IFSs) can provide decision-makers (DMs) with a wider range of preferences for MAGDM. The grey relational analysis (GRA) is an effective method for dealing with MAGDM problems. However, in view of the incomplete and asymmetric information and the influence of DMs’ psychological factors on the decision result, we develop a new model that GRA method based on cumulative prospect theory (CPT) under the intuitionistic fuzzy environment. Moreover, the weight of attribute is calculated by entropy weight, so as to distinguish the importance level of attributes, which greatly improves the credibility of the selected scheme. simultaneously, the proposed method is used to the selection of optimal green suppliers for testifying the availability of this new model and the final comparison between this new method and the existing methods further verify the reliability. In addition, the proposed method provides some references for other selection problems.

GRA and CRITIC Method for Intuitionistic Fuzzy Multiattribute Group Decision Making and Application to Development Potentiality Evaluation of Cultural and Creative Garden

In recent years, cultural and creative industry park is becoming a kind of hot industry to promote industrial restructuring and to improve the quality of urban space. For this reason, cultural and creative industrial parks are planning to build across the country. Currently, cultural and creative industrial parks that develop better than others thank to the government’s overall planning, construction, marketing, and management. At the same time, the new cultural and creative industry parks face enormous challenges, such as how to have together the cultural and creative industries and related groups or how to have area cultural creativity. And it is frequently regarded as a multiattribute group decision-making (MAGDM) process. Thus, a novel MAGDM process is needed to tackle it. Depending on the conventional grey relational analysis (GRA) method and intuitionistic fuzzy sets (IFSs), this paper designs a novel intuitive distance-based IF-GRA method for development potentiality evaluation of cultural and creative garden. First of all, some necessary theories related to IFSs are briefly reviewed. In addition, since subjective randomness frequently exists in determining criteria weights, the weights of criteria are decided objectively by utilizing the CRITIC method. Afterwards, relying on novel distance measures between IFSs, the GRA method is extended to the IFSs to calculate assessment score of each alternative. Eventually, an application about development potentiality evaluation of cultural and creative garden and some comparative analysis is given. The results think that the designed method is useful for development potentiality evaluation of cultural and creative garden.

A novel three-way group investment decision model under intuitionistic fuzzy multi-attribute group decision-making environment

Three-way decision (3WD) provides a new research perspective for dealing with uncertain and complex investment decision-making problems. This paper aims to study a novel three-way group investment decision (3WGID) model under intuitionistic fuzzy multi-attribute group decision-making (MAGDM) environment, which can deepen the understanding of 3WD and expand its applications in profit-based investment decision-making problems. Firstly, we design the calculation methods of the relative cost and revenue functions of alternatives with the aid of attribute values expressed by intuitionistic fuzzy values. Subsequently, aiming at multiple attributes in MAGDM problems, we calculate the aggregated cost and revenue functions of alternatives in each evaluation matrix . Then, we integrate the aggregated cost functions and the aggregated revenue functions to obtain the relative profit functions of alternatives in each evaluation matrix. In the context of group decision-making, we determine the overall profit functions of alternatives by fusing the collective opinions of multiple experts. In addition, considering that there is no decision attribute in MAGDM problems, we use intuitionistic fuzzy TOPSIS method to estimate the conditional probability in each evaluation matrix and calculate the comprehensive conditional probability by an aggregation approach. With these discussions, a 3WGID model is established by Bayesian decision procedure and the maximum-profit principle. Meanwhile, the decision rules and associated profits of alternatives are further induced. Ultimately, a coalfield investment case study, along with a sensitivity analysis and a comparative analysis, is adopted to demonstrate the effectiveness and feasibility of the established 3WGID model.

Extended CPT-TODIM method for interval-valued intuitionistic fuzzy MAGDM and its application to urban ecological risk assessment

The urban ecological risk assessment is a new research field, which has been rising and developing with the change of environment management objectives and environment conception. The urban ecological risk assessment could be regarded as a classical multi-attribute group decision making (MAGDM) issue. The interval-valued intuitionistic fuzzy set (IVIFS) can fully describe the uncertain information for the urban ecological risk assessment. Furthermore, the classical TODIM (an acronym in Portuguese for Interactive Multi-Criteria Decision Making) is built on cumulative prospect theory (CPT), which is a selectable method in reflecting the DMs’ psychological behavior. Thus, in this paper, the TODIM method based on the CPT is proposed for MAGDM issue under IVIFS. At the same time, it is enhancing rationality to get the weight information of attributes by using the interval-valued intuitionistic fuzzy entropy weight method. And focusing on hot issues in contemporary society, this article applies the discussed method to urban ecological risk assessment, and demonstrates urban ecological risk assessment model based on the proposed method. Finally, through comparing the outcome of comparative analysis, we conclude that this improved approach is acceptable.

Evidential model for intuitionistic fuzzy multi-attribute group decision making

Due to the uncertainty existing in real-world, intuitionistic fuzzy sets (IFSs) are used to model uncertain information in multi-attribute group decision making (MAGDM). The intuitionistic fuzzy MAGDM problems have gained great popularity recently. But, most of the current methods depend on various aggregation operators that may provide unreasonable collective intuitionistic fuzzy values of alternatives to be ranked. To solve such problem, a new method is developed based on evidence theory and IFSs. First, the mathematical relation between IFSs and evidence theory is analyzed, followed by the transformation from intuitionistic fuzzy evaluation information to basic belief assignment in evidence theory. Then, a new intuitionistic fuzzy weighted evidential (IFWE) average operator is introduced based on the operation of evidence discounting and evidence combination rule. We also develop a possibility-based ranking method for intuitionistic fuzzy values (IFVs) to obtain the linear ordering of IFVs. The proposed evidential model uses the IFWE average operator to aggregate the decision matrix and the attribute weight that is given by each decision maker, based on which each decision maker’s aggregated decision matrix can be obtained. Based on the decision matrices of all decision makers and the weights of the decision makers, the aggregated intuitionistic fuzzy value of each alternative can be obtained by the IFWE average operator. Finally, the preference order of all alternatives can be obtained by the possibility-based ranking method. Comparative analysis based on several application examples of MAGDM demonstrates that the proposed method can overcome the drawbacks of existing methods for MAGDM in intuitionistic fuzzy environments.

An intuitionistic fuzzy multi-attribute group decision making method with incomplete weight information based on improved VIKOR

An intuitionistic fuzzy multi-attribute group decision making method with incomplete weight information based on improved VIKOR

Possibility degree and divergence degree based method for interval-valued intuitionistic fuzzy multi-attribute group decision making

This paper investigates an order relation of interval-valued intuitionistic fuzzy values (IVIFVs) based on possibility degree and divergence degree and applies it to multi-attribute group decision making (MAGDM) problems. Firstly, based on the possibility degree of intuitionistic fuzzy values, the possibility degree and divergence degree of IVIFVs are defined to provide a new order relation of IVIFVs. Subsequently in interval-valued intuitionistic fuzzy MAGDM, an intuitionistic fuzzy linear programming model is constructed to derive decision makers' weights. Depending on the construction of membership and non-membership functions, three approaches are developed to solve the constructed intuitionistic fuzzy linear programming model, including the optimistic, pessimistic and mixed approaches. Utilizing decision makers’ weights, the collective decision matrix is obtained. Combining the possibility and divergence degrees of alternatives on attributes, the adjusted possibility distribution matrix for each attribute is constructed and proved to be an interval fuzzy preference relation. Then the attribute weights are determined by the negative distances and the positive distances of adjusted possibility distribution matrices. Using the interval-valued intuitionistic weighted arithmetic aggregation operator, the collective comprehensive values of alternatives are obtained. The ranking order of alternatives is generated according to the proposed order relation of IVIFVs. Therefore, an interval-valued intuitionistic fuzzy MAGDM method is proposed. Finally, the proposed method is implemented on some examples. Validation discussion and comparative analyses of this method is also done to show the effectiveness of the proposed method.

Divergence-based cross entropy and uncertainty measures of Atanassov’s intuitionistic fuzzy sets with their application in decision making

The uncertainty measure of Atanassov’s intuitionistic fuzzy sets (AIFSs) is important for information discrimination under intuitionistic fuzzy environment. Although many entropy measures and knowledge measures haven been proposed to depict uncertainty of AIFSs, how to measure the uncertainty of AIFSs is still an open topic. The relation between uncertainty and other measures like entropy measures, fuzziness and intuitionism is not clear. This paper introduces uncertainty measures by using new defined divergence-based cross entropy measure of AIFSs. Axiomatic properties of the developed uncertainty measure are analysis, together with the monotony property of uncertainty degree with respect to fuzziness and intuitionism. To adjust the contribution of fuzzy entropy and intuitionistic entropy on the total uncertainty, the proposed cross entropy and uncertainty measures are parameterized. Numerical examples indicate the effectiveness and agility of the biparametric uncertainty measure in quantifying uncertainty degree. Then we apply the cross entropy and uncertainty measures into an optimal model to determine attribute weights in multi-attribute group decision making (MAGDM) problems. A new method for intuitionistic fuzzy MAGDM problems is proposed to show the efficiency of proposed measures in applications. It is demonstrated by application examples that the proposed measures can get reasonable results coinciding with other existing methods.

Commentary on “A geometric approach for ranking interval-valued intuitionistic fuzzy numbers with an application to group decision-making”

Yue (Computers & Industrial Engineering 102 (2016) 233–245) proposed a geometric approach for solving IVIFMAGDM (interval-valued intuitionistic fuzzy multiattribute group decision making) problems and used it to solve a real-life supplier selection problem. In future, the other researchers may use the same approach to solve other real-life IVIFMAGDM problems. However, after a deep study, it is observed that this approach fails to rank the alternatives. Therefore, the aim of this note is to make the researchers aware that it is scientifically incorrect to use this approach for solving real-life IVIFMAGDM problems.

Supplier Selection Problem Based on Interval Intuitionistic Fuzzy Multiattribute Group Decision Making

Aiming at the supplier selection problem where the decision information is an interval intuitionistic fuzzy number and completely does know the attribute and decision maker’s weight, this problem is reduced to a multi-attribute group decision problem. A decision method based on information entropy to determine the decision-maker’s weight and the deviation maximization method to determine the attribute weight is proposed. Finally, this method is applied to the selection of automotive parts suppliers, and the results are compared with the relevant methods, which fully illustrates the effectiveness of this method.

Dynamic Intuitionistic Fuzzy Multi-Attribute Group Decision-Making Based on Power Geometric Weighted Average Operator and Prediction Model

With respect to dynamic multi-attribute group decision-making (DMAGDM) problems, where attribute values take the form of intuitionistic fuzzy values (IFVs) and the weights (including expert, attribute and time weights) are unknown, the dynamic intuitionistic fuzzy power geometric weighted average (DIFPGWA) operator and the improved IFVs’ GM(1,1) prediction model (IFVs-GM(1,1)-PM) are proposed. First, the concept of IFVs, the operational rules, the distance between IFVs, and the comparing method of IFVs are defined. Second, the DIFPGWA operator and the improved IFVs-GM(1,1)-PM are defined in detail. Third, corresponding decision-making (D-M) steps are proposed. Three kinds of weights are given by the proposed determination method. Finally, an example is given to prove the effectiveness and superiority of the proposed decision-making method.

A threat assessment method of group targets based on interval-valued intuitionistic fuzzy multi-attribute group decision-making

Group target (GT) is consisted of multi-class weapons that can collaboratively work and it is a basic application unit in the information warfare. Assessing the threat of GT is required for the optimal decision of troop deployment. However, it is difficult to obtain a reasonable and effective threat assessment result of GT due to the uncertain battlefield information and different judgments from various decision makers (DMs). The study aims to investigate the multi-attribute group decision-making (MAGDM) method for solving the interval-valued intuitionistic fuzzy threat assessment problem of GTs without known attribute weights and DM’s preference weights. Based on the assessment information of DMs, attribute weights are determined with the interval-valued intuitionistic fuzzy entropy. To derive the DM’s preference weights objectively, we construct a nonlinear optimization model to minimize decision makers’ overall decision-making conflict. Moreover, the artificial bee colony algorithm is introduced to solve the nonlinear constrained optimization problem in the optimization model. The decision information of multi-DM is aggregated by the interval-valued intuitionistic fuzzy weighted averaging operator (IVIFWA) with the DMs’ preference weights. In order to describe the attribute closeness degree to the ideal solution, the decision-making judgment matrix is constructed according to the ideal solution closeness degree of each GT’s attribute calculated with the cross-entropy distance. Subsequently, based on the decision-making judgment matrix, the threat degree is calculated according to the weighted average method with the attribute weights. Finally, a case of the threat assessment of group targets is provided to illustrate the implementation process and applicability of the method proposed in this paper.

Intuitionistic fuzzy multi-attribute group decision-making with an application to plant location selection based on a new extended VIKOR method

This paper presents a new decision method for multi-attribute group decision-making (MAGDM) problems in general and plant location selection (PLS) problem in particular, with intuitionistic fuzzy information captured through trapezoidal intuitionistic fuzzy numbers (TrIFNs). We assume that the weights of the decision-makers and attributes are completely unknown. The ratings of alternatives with respect to each attribute are considered as linguistic terms, which are mapped to the appropriate TrIFNs. To reduce subjective randomness in the decision-process, we determine attribute weights using the Shannon entropy theory, and weights of the decision-makers by integrating the Evidence theory with Bayes approximation. Furthermore, we extend the classical VIKOR method to solve MAGDM problems under intuitionistic fuzzy environment based on the TrIFNs. Considering that the PLS problem is essentially a MAGDM problem that involves evaluation of the alternatives on several conflicting attributes based on the vague and imprecise assessments of the decision-makers, we demonstrate utility of the proposed decision method by applying it solve the PLS problem. A detailed comparison is presented to demonstrate the advantages of the proposed methodology over the existing methods used for both the intuitionistic fuzzy MAGDM problems and PLS problem.

An approach to intuitionistic fuzzy multi-attribute group decision making based on hybrid Einstein aggregation operators

With respect to intuitionistic fuzzy information, this paper presents the induced intuitionistic fuzzy hybrid weighted Einstein aggregation I-IFHWEA operator and the induced intuitionistic fuzzy hybrid geometric Einstein aggregation I-IFHGEA operator, which overcome the drawback in the existing reference. To deal with the situations where elements in a set are correlative, the induced intuitionistic fuzzy hybrid Shapley weighted Einstein aggregation I-IFHSWEA operator and the induced intuitionistic fuzzy hybrid Shapley geometric Einstein aggregation I-IFHSGEA operator are defined, which can be seen as an extension of some intuitionistic fuzzy operators based on additive measures. When the information about the weight vector is partly known, models based on the relative projection are established, by which the optimal fuzzy measure can be obtained. After that, an approach to multi-attribute group decision making under intuitionistic fuzzy environment is developed, and an illustrative example is provided to demonstrate its practicality and feasibility.

An approach to intuitionistic fuzzy multi-attribute group decision making based on hybrid Einstein aggregation operators

An approach to intuitionistic fuzzy multi-attribute group decision making based on hybrid Einstein aggregation operators

Soft computing based on maximizing consensus and fuzzy TOPSIS approach to interval-valued intuitionistic fuzzy group decision making

Multi-attribute group decision making (MAGDM) is an important research topic in decision theory. In recent decades, many useful methods have been proposed to solve various MAGDM problems, but very few methods simultaneously take them into account from the perspectives of both the ranking and the magnitude of decision data, especially for the interval-valued intuitionistic fuzzy decision data. The purpose of this paper is to develop a soft computing technique based on maximizing consensus and fuzzy TOPSIS in order to solve interval-valued intuitionistic fuzzy MAGDM problems from such two aspects of decision data. To this end, we first define a consensus index from the perspective of the ranking of decision data, for measuring the degree of consensus between the individual and the group. Then, we establish an optimal model based on maximizing consensus to determine the weights of experts. Following the idea of TOPSIS, we calculate the closeness indices of the alternatives from the perspective of the magnitude of decision data. To identify the optimal alternatives and determine their optimum quantities, we further construct a multi-choice goal programming model based on the derived closeness indices. Finally, an example is given to verify the developed method and to make a comparative analysis.

Possibility Method for Triangular Intuitionistic Fuzzy Multi-attribute Group Decision Making with Incomplete Weight Information

AbstractTriangular intuitionistic fuzzy numbers (TIFNs) are a special kind of intuitionistic fuzzy sets (IFSs) on a real number set. TIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The purpose of this paper is on developing a new ranking method of TIFNs and application to multiattribute group decision making (MAGDM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete. The weighted average operator of TIFNs is defined, the concepts of the possibility mean, variance of TIFNs as well as standard deviation are introduced. Hereby two new ranking indices considering the risk attitude of decision maker are developed to rank TIFNs. In the proposed group decision method, the collective overall attribute values of alternatives are obtained by using the weighted average operator of TIFNs We construct the multi-objective programming of maximizing the ranking indices of membership and non-mem...

Interval-Valued Intuitionistic Fuzzy Multiattribute Group Decision Making Based on Cross Entropy Measure and Choquet Integral

In this paper, a new operator called the arithmetic interval-valued intuitionistic fuzzy Choquet aggregation (AIVIFCA) operator is defined. Since interactions between elements might exist in all their combinations, the generalized Shapley AIVIFCA (GSAIVIFCA) operator is introduced. Further, to simplify the complexity of solving a fuzzy measure, the 2-additive generalized Shapley AIVIFCA (2AGSAIVIFCA) operator is presented. Moreover, a decision procedure to interval-valued intuitionistic fuzzy multiattribute group decision making is developed. When the weight vectors on attribute set and expert set are not exactly known, the models for obtaining the optimal fuzzy measures are established by using the defined cross entropy measure and the Shapley function. Finally, a numerical example is provided to illustrate the developed procedure.