Arithmetic Aggregation Operators Research Articles

Group decision making based on dice similarity measure and 2-dimension linguistic fuzzy weighted arithmetic aggregation operator for 2-dimension linguistic fuzzy variables

In the process of decision-making, it usually applies 2-dimension linguistic fuzzy variable (2DLFV) to describe the uncertainty caused by the decision objects and the decision makers. This proposal aims to design group decision making method based on dice similarity measure (DSM) and 2-dimension linguistic fuzzy weighted arithmetic aggregation (2DLFWAA) operator for 2-dimension linguistic fuzzy framework. Based on the psychological theory and prospect theory, 2-dimension linguistic scale function (2DLSF) about 2DLFV is firstly proposed, and new operational rules of 2DLFV are introduced. Two forms of DSM are proposed to measure the closeness between two 2-dimension linguistic fuzzy sets (2DLFSs). A definition is given for 2DLFWAA operator and some of its properties are studied. Based on the DSM and the 2DLFWAA operator for 2DLFSs, the technique for order of preference by similarity to ideal solution (TOPSIS) method is extended to handle the multiple attribute group decision making (MAGDM) problems under 2-dimension linguistic fuzzy environments. Finally, an illustrative example is provided to show the concrete process of the proposed method. Comparative analysis and sensitivity analysis are conducted to test the rationality and robust of the proposed method. The results suggest that the proposed method offers a flexible and reliable approach in 2-dimension linguistic fuzzy scenarios.

Group decision making based on linguistic interval-valued Atanassov intuitionistic fuzzy Yager weighted arithmetic aggregation operator of linguistic interval-valued Atanassov intuitionistic fuzzy numbers

In this paper, we propose a noval addition operation (AOP) and a novel scalar multiplication operation (SMOP) of linguistic interval-valued Atanassov intuitionistic fuzzy numbers (LIVAIFNs) based on Yager’s t-conorm and t-norm. The proposed AOP and the proposed SMOP of LIVAIFNs can conquer the shortcomings of the existing AOP and the existing SMOP of LIVAIFNs. Based on the proposed AOP and the proposed SMOP of LIVAIFNs, we propose the linguistic interval-valued Atanassov intuitionistic fuzzy Yager weighted arithmetic (LIVAIYFWA) aggregation operator (AO) of LIVAIFNs. We also prove some properties of the proposed LIVAIFYWA AO of LIVAIFNs. Moreover, by using the proposed LIVAIFYWA AO of LIVAIFNs, we propose a noval group decision making (GDM) method. The proposed GDM method can conquer the drawbacks of the existing GDM methods in the context of LIVAIFNs.

QNN-MAGDM strategy for E-commerce site selection using quadripartition neutrosophic neutrality aggregative operators

In this paper, we define the Quadripartition Neutrosophic Weighted Neutrality Aggregative (QNWNA) operator and Quadripartition Neutrosophic Ordered Weighted Neutrality Aggregative (QNOWNA) operator for solving Multi-Attribute Group Decision Making (MAGDM) problems. The basic properties of both operators are discussed thoroughly. A new MAGDM strategy is developed using these developed operators. A case study of e-commerce site selection in India is discussed to show the applicability of the proposed MADM strategy. Moreover, the performance of the QNWNA and QNOWNA operators are compared with Quadripartition Neutrosophic Weighted Arithmetic Aggregation (QNWAA) operator and Quadripartition Neutrosophic Weighted Geometric Aggregation (QNWGA), Quadripartition Single valued Neutrosophic Dombi Weighted Arithmetic Aggregation (QSVNDWAA) and QSVN Dombi Weighted Geometric Aggregation (QSVNDWAA) operator.

Multiattribute decision making based on q-rung orthopair fuzzy Yager prioritized weighted arithmetic aggregation operator of q-rung orthopair fuzzy numbers

This paper proposes a new approach for multiattribute decision making (MADM) using the proposed q-rung orthopair fuzzy Yager prioritized weighted arithmetic (q-ROFYPWA) aggregation operator (AO) of q-rung orthopair fuzzy numbers (q-ROFNs). Firstly, we propose the q-ROFYPWA AO of q-ROFNs based on Yager’s t-conorm and t-norm and the concept of prioritized average AO. The proposed q-ROFYPWA AO consider the prioritized relationship among aggregating q-ROFNs. Moreover, we present several properties of the proposed q-ROFYPWA AO. Then, we propose a new MADM approach based on the proposed q-ROFYPWA AO of q-ROFNs. The propsoed MADM approach considers the prioritization among the attributes to overcome the drawbacks of the existing MADM approaches, where they cannot distinguish the ranking orders of the alternatives in some situations. The proposed MADM approach is very useful for MADM in the environment of q-ROFNs.

Group decision making based on linguistic intuitionistic fuzzy Yager weighted arithmetic aggregation operator of linguistic intuitionistic fuzzy numbers

In this paper, we propose two new group decision making (GDM) approaches based on the proposed linguistic intuitionistic fuzzy Yager weighted arithmetic (LIYFWA) aggregation operator (AO) of linguistic intuitionistic fuzzy numbers (LIFNs), where the proposed first GDM considers the situation that experts’ weights and attributes’ weights are completely known; the proposed second GDM approach considers the situation that experts’ weights and attributes’ weights are completely unknown. Firstly, we propose new operational laws for LIFNs based on Yager’s norm, namely, the addition operation operation and the scalar multiplication operation. The proposed addition operation and the proposed scalar multiplication operation of LIFNs can conquer the drawbacks of the existing addition operation and the existing scalar multiplication operation of LIFNs. Then, based on the proposed addition operation and the proposed scalar multiplication operation of LIFNs, we propose the LIYFWA AO of LIFNs. We also prove some properties of the proposed LIFYWA AO. Finally, based on the proposed LIFYWA AO, we propose two new GDM approaches of LIFNs. The proposed GDM approaches can conquer the drawbacks of existing GDM methods, where they cannot distinguish the ranking orders of alternatives in some situations.

An extension of CODAS method for multi-criteria group decision making with complex intuitionistic fuzzy information via Dombi sine weighted arithmetic aggregation operators

An extension of CODAS method for multi-criteria group decision making with complex intuitionistic fuzzy information via Dombi sine weighted arithmetic aggregation operators

Novel decision aid model for green supplier selection based on extended EDAS approach under pythagorean fuzzy Z-numbers

The main objective of this study is to identify the green suppliers that would most effectively assist manufacturing producers in implementing green manufacturing production while including uncertainty and reliability in their decision-making. For this firstly, we justify and manifest the idea of Pythagorean Fuzzy Z-numbers (PyFZNs). It has significant implications for improving the effectiveness of decision-making processes in several theories of uncertainty. It can more flexibly explain real-world data and human cognition due to its capacity to express imprecise and reliable information. Thus it is a more accurate mathematical tool for addressing accuracy and uncertainty. Secondly, we defined the Pythagorean fuzzy Z-number arithmetic aggregation operators and geometric aggregation operators. Thirdly, based on the proposed operators and EDAS (Evaluation based on distance from average solution) approach, a fast decision model is designed to deal with the issue of multi-criteria decision-making. Finally, using PyFZN data we also provide a numerical example to demonstrate the usability of the created multicriteria decision-making (MDM) approach. Moreover, a case study also proves its efficacy.

A multiattribute group decision-making method based on a new aggregation operator and the means and variances of interval-valued intuitionistic fuzzy values

The development of information measures associated with interval-valued intuitionistic fuzzy values (IVIFVs) has been an important research area over the past few decades. In the literature, the existing decision -making method using IVIFVs has some drawbacks, and the identification degree and information utilization suffer from a gap in the evaluation of alternatives. Therefore, the need for a reliable, useful, and comprehensive decision method is obvious. To obtain more accurate and reliable evaluation results, multiattribute group decision-making (MAGDM) problems, where the same attribute weights given by different decision-makers are different, are studied in this paper. First, the novel operational laws of IVIFVs and a new interval-valued intuitionistic fuzzy weighted arithmetic aggregation operator are defined to overcome the drawbacks of the IIFWA aggregation operator and avoid losing or distorting the original decision information in the process of aggregation. Second, the mean and variance of the possibility degrees of IVIFVs are defined based on the concept of a definite integral. Third, a novel MAGDM method based on the new aggregation operator and the mean and variance of the possibility degrees of IVIFVs is proposed to improve the identification of the evaluation results and ensure the effectiveness of the ranking order. Finally, the effectiveness and practicability of the proposed method are verified by an air combat training accuracy assessment example. This example can be used to assist decision-makers in evaluating air combat training hits in a timely and efficient manner, providing an objective, scientific basis for the realization and application of air combat training hit assessment and a new method and idea for MAGDM problems in an interval-valued intuitionistic fuzzy environment.

Intuitionistic fuzzy-valued neutrosophic multi-sets and numerical applications to classification

A single-valued neutrosophic multi-set is characterized by a sequence of truth membership degrees, a sequence of indeterminacy membership degrees and a sequence of falsity membership degrees. Nature of a single-valued neutrosophic multi-set allows us to consider multiple information in the truth, indeterminacy and falsity memberships which is pretty useful in multi-criteria group decision making. In this paper, we consider sequences of intuitionistic fuzzy values instead of numbers to define the concept of intuitionistic fuzzy-valued neutrosophic multi-set. In this manner, such a set gives more powerful information. We also present some set theoretic operations and a partial order for intuitionistic fuzzy-valued neutrosophic sets and provide some algebraic operations between intuitionistic fuzzy-valued neutrosophic values. Then, we develop two types of weighted aggregation operators with the help of intuitionistic fuzzy t-norms and t-conorms. By considering some well-known additive generators of ordinary t-norms, we give the Algebraic weighted arithmetic and geometric aggregation operators and the Einstein weighted arithmetic and geometric aggregation operators that are the particular cases of the weighted aggregation operators defined via general t-norms and t-conorms. We also define a simplified neutrosophic valued similarity measure and we use a score function for simplified neutrosophic values to rank similarities of intuitionistic fuzzy-valued neutrosophic multi-values. Finally, we give an algorithm to solve classification problems using intuitionistic fuzzy-valued neutrosophic multi-values and proposed aggregation operators and we apply the theoretical part of the paper to a real classification problem.

Multi Label Feature Selection Through Dual Hesitant q-Rung Orthopair Fuzzy Dombi Aggregation Operators

In this article, the feature selection (FS) process is taken as a multi criteria decision making (MCDM) problem. Also, to consider the impreciseness arising in the real time data, the values of the decision matrix procured after the ridge regression is fuzzified into dual hesitant q-rung orthopair fuzzy set. For the information fusion process, we have proposed various aggregation operators such as the Dual Hesitant q-rung orthopair fuzzy weighted Dombi arithmetic aggregation operator, Dual Hesitant q-rung orthopair fuzzy weighted Dombi geometric aggregation operator, Dual Hesitant q-rung orthopair fuzzy ordered weighted Dombi arithmetic aggregation operator and Dual Hesitant q-rung orthopair fuzzy ordered weighted Dombi geometric aggregation operator. A multi-label feature selection method is proposed using these MCDM techniques formed by the aggregation operators. This algorithm, initially, obtains the values of the decision matrix through the process of ridge regression. The weight vector required for the MCDM process is calculated using entropy. Further, the data are fuzzified and the MCDM process proposed using the aforementioned aggregation operators are utilized. A rank vector is obtained by utilizing the score function to select the desired number of features. It should be noted that through changing the aggregation operator, the algorithm can be altered. Experimental evaluation that compares the proposed method to other existing methods in terms of evaluation metrics demonstrates the effectiveness of the proposed method and their significance is also evaluated.

Density aggregation operators for interval-valued q-rung orthopair fuzzy numbers and their application in multiple attribute decision making

The symmetry between fuzzy evaluations and crisp numbers provides an effective solution to multiple attribute decision making (MADM) problems under fuzzy environments. Considering the effect of information distribution on decision making, a novel approach to MADM problems under the interval-valued q-rung orthopair fuzzy (Iq-ROF) environments is put forward. Firstly, the clustering method of interval-valued q-rung orthopair fuzzy numbers (Iq-ROFNs) is defined. Secondly, Iq-ROF density weighted arithmetic (Iq-ROFDWA) intermediate operator and Iq-ROF density weighted geometric average (Iq-ROFDWGA) intermediate operator are developed based on the density weighted intermediate operators for crisp numbers. Thirdly, combining the density weighted intermediate operators with the Iq-ROF weighted aggregation operators, Iq-ROF density aggregation operators including Iq-ROF density weighted arithmetic (Iq-ROFDWAA) aggregation operator and Iq-ROF density weighted geometric (Iq-ROFDWGG) aggregation operator are proposed. Finally, effectiveness of the proposed method is verified through a numerical example.

Choquet integral-based intuitionistic fuzzy arithmetic aggregation operators in multi-criteria decision-making

Intuitionistic fuzzy set (IFS), a classical extension of fuzzy set, is a powerful tool to describe fuzzy information in multi-criteria decision-making (MCDM) because of its membership and non-membership functions. Intuitionistic fuzzy aggregation operators are the standard mathematical tools for the combination of several inputs with respect to criteria into one unique output. The traditional intuitionistic fuzzy aggregation operator-based methods have been criticized because of reasons that include disregard for comprehensive correlative relationships of criteria and ignorance for combination of fuzzy measures of criteria and weights of positions. In this paper, the effectiveness of traditional aggregation operator-based MCDM techniques is improved by a novel method to select the best alternative(s) under the intuitionistic fuzzy environment. We begin by defining the Choquet integral-based intuitionistic fuzzy arithmetic aggregation (CIIFAA) operator, the remarkable properties of which are proved in details. Further, the Choquet integral based intuitionistic fuzzy hybrid arithmetic aggregation (CIIFHAA) operator is defined as well as the proofs of its properties. The CIIFHAA operator can not only capture the comprehensive correlative relationships of criteria in a simpler manner, but also combine the weights of positions. Then, we put forward a MCDM method based on CIIFHAA operator with intuitionistic fuzzy evaluations. An illustrative example is solved, the best alternative and the ranking of alternatives are obtained, which can verify the feasibility of the proposed method. Finally, two comparisons are conducted to illustrate the stability and advantages of the proposed method.

Optimal resilient distributed data collection in mobile edge environments

A key goal of edge computing is to achieve “distributed sensing” out of data continuously generated from a multitude of interconnected physical devices. The traditional approach is to gather information into sparse collector devices by relying on hop-by-hop accumulation, but issues of reactivity and fragility naturally arise in scenarios with high mobility. We propose novel algorithms for dynamic data summarisation across space, supporting high reactivity and resilience by specific techniques maximising the speed at which information propagates towards collectors. Such algorithms support idempotent and arithmetic aggregation operators and, under reasonable network assumptions, are proved to achieve optimal reactivity. We provide evaluation via simulation: first in multiple scenarios showing improvement over the state of art, and then by a case study in edge data mining, which conveys the practical impact in higher-level distributed sensing patterns.

A novel logarithmic operational law and aggregation operators for trapezoidal neutrosophic number with MCGDM skill to determine most harmful virus.

In the current era, the theory of vagueness and multi-criteria group decision making (MCGDM) techniques are extensively applied by the researchers in disjunctive fields like recruitment policies, financial investment, design of the complex circuit, clinical diagnosis of disease, material management, etc. Recently, trapezoidal neutrosophic number (TNN) draws a major awareness to the researchers as it plays an essential role to grab the vagueness and uncertainty of daily life problems. In this article, we have focused, derived and established new logarithmic operational laws of trapezoidal neutrosophic number (TNN) where the logarithmic base μ is a positive real number. Here, logarithmic trapezoidal neutrosophic weighted arithmetic aggregation (Larm) operator and logarithmic trapezoidal neutrosophic weighted geometric aggregation (Lgeo) operator have been introduced using the logarithmic operational law. Furthermore, a new MCGDM approach is being demonstrated with the help of logarithmic operational law and aggregation operators, which has been successfully deployed to solve numerical problems. We have shown the stability and reliability of the proposed technique through sensitivity analysis. Finally, a comparative analysis has been presented to legitimize the rationality and efficiency of our proposed technique with the existing methods.

Generalized MULTIMOORA method and Dombi prioritized weighted aggregation operators based on T‐spherical fuzzy sets and their applications

In this manuscript, the technique of the generalized MULTIMOORA method is investigated by using the concept of a T-spherical fuzzy set (T-SFS), which is the modified idea of a picture fuzzy set to handle awkward and vague information in daily life problems. T-SFS covers the degree of truth, abstinence, and falsity with a rule that the sum of the qth-powers of all degrees is restricted to the unit interval. Moreover, for examining the interrelationships among any number of T-SFSs, we construct the idea of T-spherical fuzzy Dombi prioritized weighted arithmetic (T-SFDPWA) aggregation operators, T-spherical fuzzy Dombi prioritized arithmetic, T-spherical fuzzy Dombi prioritized geometric, and T-spherical fuzzy Dombi prioritized weighted geometric (T-SFDPWG) aggregation operators are given. Then, the basic properties of T-SFDPWA and T-SFDPWG aggregation operators are investigated and discussed in some of their cases. The investigated operators based on T-SFS are utilized in the environment of multiattribute decision-making problems to find the consistency and proficiency of the developed operators. In last, we illustrated some numerical examples based on explored operators is to examine the reliability and validity of the investigated operators with the help of comparative analysis and graphical representations with some existing ideas to show the presented approaches are extensive powerful.

An Algorithm for Fuzzy Negations Based-Intuitionistic Fuzzy Copula Aggregation Operators in Multiple Attribute Decision Making

In this paper, we develop a novel computation model of Intuitionistic Fuzzy Values with the usage of fuzzy negations and Archimedean copulas. This novel computation model’s structure is based on the extension of the existing operations of intuitionistic fuzzy values with some classes of fuzzy negations. Many properties of the proposed operations are investigated and proved. Additionally, in this paper we introduce the concepts of intuitionistic fuzzy Archimedean copula weighted arithmetic and geometric aggregation operators based on fuzzy negations, including a further analysis of their properties. Finally, using a case study from an already published paper we found that our method has many advantages.

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.

Generalized Hamacher Aggregation Operators for Intuitionistic Uncertain Linguistic Sets: Multiple Attribute Group Decision Making Methods

In this paper, we consider multiple attribute group decision making (MAGDM) problems in which the attribute values take the form of intuitionistic uncertain linguistic variables. Based on Hamacher operations, we developed several Hamacher aggregation operators, which generalize the arithmetic aggregation operators and geometric aggregation operators, and extend the algebraic aggregation operators and Einstein aggregation operators. A number of special cases for the two operators with respect to the parameters are discussed in detail. Also, we developed an intuitionistic uncertain linguistic generalized Hamacher hybrid weighted average operator to reflect the importance degrees of both the given intuitionistic uncertain linguistic variables and their ordered positions. Based on the generalized Hamacher aggregation operator, we propose a method for MAGDM for intuitionistic uncertain linguistic sets. Finally, a numerical example and comparative analysis with related decision making methods are provided to illustrate the practicality and feasibility of the proposed method.

Complex fuzzy arithmetic aggregation operators

Complex fuzzy arithmetic aggregation operators

A New Decision-Making Method Based on Interval-Valued Linguistic Intuitionistic Fuzzy Information

In real decision-making, because of the particularity of human cognition activity, it is difficult to depict the decision information by exact numbers, especially, for complex decision information, how to express and aggregate them is an important work for solving these decision-making problems. In order to express the complex fuzzy information accurately, we proposed the concept of interval-valued linguistic intuitionistic fuzzy numbers (IVLIFNs), where their membership function and non-membership function are represented by interval-valued linguistic terms, and then we developed the operational rules, score function, accuracy function, and comparison method of them. Considering that the Maclaurin symmetric mean (MSM) operator has a good characteristic in dealing with the interrelationships among multi-parameters, and it also is a generalization of arithmetic aggregation operator, Bonferroni mean (BM) operator, and geometric aggregation operator, we further proposed the interval-valued linguistic intuitionistic fuzzy MSM (IVLIFMSM) operator, the weighted interval-valued linguistic intuitionistic fuzzy MSM (WIVLIFMSM) operator, and proved some related properties of them. We gave an illustrative example to demonstrate the steps and the effectiveness of the proposed method by the comparison with existing methods. IVLIFNs can more conveniently express the complex fuzzy information in qualitative environment by considering the cognition of decision-makers, and the proposed method can consider the interrelationship among multiple input arguments, so it can make the decision-making results more reasonable. In a word, the proposed method is more scientific and flexible in solving multiple attribute decision-making (MADM) problems than some existing methods.