Intuitionistic Fuzzy Geometric Aggregation Operators Research Articles

Intuitionistic fuzzy geometric aggregation operators based on Yager’s triangular norms and its application in multi-criteria decision making

Intuitionistic fuzzy (IF) information aggregation in multi-criteria decision making (MCDM) is a substantial stream that has attracted significant research attention. There are various IF aggregation operators have been suggested for extracting more informative data from imprecise and redundant raw information. However, some of the aggregation techniques that are currently being applied in IF environments are non-monotonic with respect to the total order, and suffer from high computational complexity and inflexibility. It is necessary to develop some novel IF aggregation operators that can surpass these imperfections. This paper aims to construct some IF aggregation operators based on Yager’s triangular norms to shed light on decision-making issues. At first, we present some novel IF operations such as Yager sum, Yager product and Yager scalar multiplication on IF sets. Based on these new operations, we propose the IF Yaeger weighted geometric operator and the IF Yaeger ordered weighted geometric operator, and prove that they are monotone with respect to the total order. Then, the focus on IF MCDM have motivated the creation of a new MCDM model that relies on suggested operators. We show the applicability and validity of the model by using it to select the most influential worldwide supplier for a manufacturing company and evaluate the most efficient method of health-care disposal. In addition, we discuss the sensitivity of the proposed operator to decision findings and criterion weights, and also analyze it in comparison with some existing aggregation operators. The final results show that the proposed operator is suitable for aggregating both IF information on “non-empty lattice" and IF data on total orders.

Intuitionistic fuzzy geometric aggregation operators in the framework of Aczel-Alsina triangular norms and their application to multiple attribute decision making

The aggregation of fuzzy information is a new area of “intuitionistic fuzzy set (IFS)” theory that has piqued the attention of scholars in the past few years. This study aims to construct intuitionistic fuzzy (IF) aggregation operators as a result of Aczel-Alsina (AA) operations in order to shed light on decision-making issues. To begin with, some novel IFS operations are provided, such as AA sum, AA product, and AA scalar multiplication. Based on these new operations, a number of novel aggregation operators for IF information has been suggested. These operators include the IF AA weighted geometric operator, the IF AA ordered weighted geometric operator, and the IF AA hybrid geometric operator. Different properties of these operators are established. Concerns about IF “multi-attribute decision-making (MADM)” has led to the creation of a new strategy that depends on such operators. Two case studies are examined to demonstrate the applicability and efficacy of the developed method in real-world applications. The first case study focuses on the selection of the most influential worldwide supplier for one of the most critical components used in the assembly process of a manufacturing company. The second case study focuses on selecting the most effective method for health-care waste (HCW) disposal. The suggested aggregation operators have a single variable parameter that has an impact on the decision-making method. The sensitivity of the proposed aggregation operators to decision-making findings is investigated. A sensitivity analysis of the criteria weights is presented to ensure the permanence of the introduced framework. In addition, a detailed comparison of existing models is made to show how the new framework is better than them. Finally, the findings show that the new strategy is more effective and reliable than the existing models.

Algorithm for T-spherical fuzzy MADM based on associated immediate probability interactive geometric aggregation operators

The purpose of writing this manuscript is to point out some limitations of existing associated immediate probability intuitionistic fuzzy geometric aggregation operators as these existing operators fail under some conditions such as the existing operators cannot handle the information given in Pythagorean fuzzy sets, picture fuzzy sets, spherical fuzzy sets, and T-spherical fuzzy sets and the existing aggregation operators also cannot aggregate the membership value when membership value of anyone intuitionistic fuzzy number become zero. To overcome these shortcomings associated immediate probability geometric aggregation operators have been developed for T-spherical fuzzy sets and associated immediate probability interactive geometric aggregation operators are proposed. Then a comparison between these operators is developed with the help of an example. The existing score function for T-spherical fuzzy sets does not involve abstinence so a new score function is developed which provides a better comparison between any two T-spherical fuzzy numbers. To demonstrate the presented algorithm, a decision-making process algorithm is presented with T-SFS features. The advantages of the proposed work are also discussed in which it is shown that under some conditions the proposed operators can be reduced to other tools of uncertainty. The comparison between existing and proposed work is also developed with the help of an example.

A Generalized Triangular Intuitionistic Fuzzy Geometric Averaging Operator for Decision-Making in Engineering and Management

Triangular intuitionistic fuzzy number (TIFN) is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multi-criteria decision-making problems, as well as for expressing and reflecting the evaluation information in several dimensions. In this paper, the TIFN has been applied for solving multi-criteria decision-making (MCDM) problems, first, by defining some existing triangular intuitionistic fuzzy geometric aggregation operators, and then developing a new triangular intuitionistic fuzzy geometric aggregation operator, which is the generalized triangular intuitionistic fuzzy ordered weighted geometric averaging (GTIFOWGA) operator. Based on these operators, a new approach for solving multicriteria decision-making problems when the weight information is fixed is proposed. Finally, a numerical example is provided to show the applicability and rationality of the presented method, followed by a comparative analysis using similar existing computational approaches.

Generalized intuitionistic fuzzy geometric aggregation operators and their application to multi-criteria decision making

In this paper, we extend the generalized weighted geometric and generalized ordered weighted geometric operators to intuitionistic fuzzy environments, that is, we develop a series of generalized intuitionistic fuzzy geometric operators to aggregate input arguments that are expressed by intuitionistic fuzzy values based on Archimedean t-conorm and t-norm. Then some desired properties of these aggregation operators are investigated. The relations between these operators and some existing intuitionistic fuzzy geometric aggregation operators are discussed in detail. Furthermore, applying these proposed operators, we develop an approach for multi-criteria decision making with intuitionistic fuzzy information. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.

Atanassov’s intuitionistic fuzzy Quasi-Choquet geometric operators and their applications to multicriteria decision making

In this paper, by combining the Archimedean t-conorm and t-norm and Quasi-Choquet averaging operator, we develop an extended Atanassov's intuitionistic fuzzy Quasi-Choquet geometric operator to aggregate input arguments that are Atanassov's intuitionistic fuzzy values, where the inter-dependent or interactive characteristics among input arguments are taken into account. Some of the desirable properties and some special cases are investigated in detail. It is worth pointing out that most of the existing Atanassov's intuitionistic fuzzy geometric aggregation operators are special cases of this proposed aggregation operator. Furthermore, a decision procedure based on the proposed aggregation operator is developed for solving the multicriteria decision making problem in which all decision information is represented by Atanassov's intuitionistic fuzzy values. An illustrative example is given for demonstrating the applicability of the proposed decision procedure.

Multi-criteria trapezoidal valued intuitionistic fuzzy decision making with Choquet integral based TOPSIS

A generalized trapezoidal-valued intuitionistic fuzzy geometric aggregation operator is proposed which is then used to aggregate decision makers’ opinions in group decision making process. An extension of TOPSIS, a multi-criteria trapezoidal-valued intuitionistic fuzzy decision making technique, to a group decision environment is also proposed, where inter-dependent or interactive characteristics among criteria and preference of decision makers are under consideration. Furthermore, Choquet integral-based distance between trapezoidal-valued intuitionistic fuzzy values is defined. Combining the trapezoidal-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based distance, an extension of TOPSIS method is developed to deal with a multi-criteria trapezoidal-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is provided to understand the proposed method.

Intuitionistic fuzzy geometric aggregation operators based on einstein operations

Intuitionistic fuzzy information aggregation plays an important part in Atanassov's intuitionistic fuzzy set theory, which has emerged to be a new research direction receiving more and more attention in recent years. In this paper, we first introduce some operations on intuitionistic fuzzy sets, such as Einstein sum, Einstein product, Einstein exponentiation, etc., and further develop some new geometric aggregation operators, such as the intuitionistic fuzzy Einstein weighted geometric operator and the intuitionistic fuzzy Einstein ordered weighted geometric operator, which extend the weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator to accommodate the environment in which the given arguments are intuitionistic fuzzy values. We also establish some desirable properties of these operators, such as commutativity, idempotency and monotonicity, and give some numerical examples to illustrate the developed aggregation operators. In addition, we compare the proposed operators with the existing intuitionistic fuzzy geometric operators and get the corresponding relations. Finally, we apply the intuitionistic fuzzy Einstein weighted geometric operator to deal with multiple attribute decision making under intuitionistic fuzzy environments. © 2011 Wiley Periodicals, Inc.

A multi-criteria interval-valued intuitionistic fuzzy group decision making with Choquet integral-based TOPSIS

An extension of TOPSIS, a multi-criteria interval-valued intuitionistic fuzzy decision making technique, to a group decision environment is investigated, where inter-dependent or interactive characteristics among criteria and preference of decision makers are taken into account. To get a broad view of the techniques used, first, some operational laws on interval-valued intuitionistic fuzzy values are introduced. Based on these operational laws, a generalized interval-valued intuitionistic fuzzy geometric aggregation operator is proposed which is used to aggregate decision makers’ opinions in group decision making process. In addition, some of its properties are discussed. Then Choquet integral-based Hamming distance between interval-valued intuitionistic fuzzy values is defined. Combining the interval-valued intuitionistic fuzzy geometric aggregation operator with Choquet integral-based Hamming distance, an extension of TOPSIS method is developed to deal with a multi-criteria interval-valued intuitionistic fuzzy group decision making problems. Finally, an illustrative example is used to illustrate the developed procedures.

Generalized intuitionistic fuzzy geometric aggregation operator and its application to multi-criteria group decision making

In general, for multi-criteria group decision making problem, there exist inter-dependent or interactive phenomena among criteria or preference of experts, so that it is not suitable for us to aggregate them by conventional aggregation operators based on additive measures. In this paper, based on fuzzy measures a generalized intuitionistic fuzzy geometric aggregation operator is investigated for multiple criteria group decision making. First, some operational laws on intuitionistic fuzzy values are introduced. Then, a generalized intuitionistic fuzzy ordered geometric averaging (GIFOGA) operator is proposed. Moreover, some of its properties are given in detail. It is shown that GIFOGA operator can be represented by special t-norms and t-conorms and is a generalization of intuitionistic fuzzy ordered weighted geometric averaging operator. Further, an approach to multiple criteria group decision making with intuitionistic fuzzy information is developed where what criteria and preference of experts often have inter-dependent or interactive phenomena among criteria or preference of experts is taken into account. Finally, a practical example is provided to illustrate the developed approaches.