Power Average Operator Research Articles

A Novel Approach to Multi-Attribute Group Decision-Making based on Interval-Valued Intuitionistic Fuzzy Power Muirhead Mean

This paper focuses on multi-attribute group decision-making (MAGDM) course in which attributes are evaluated in terms of interval-valued intuitionistic fuzzy (IVIF) information. More explicitly, this paper introduces new aggregation operators for IVIF information and further proposes a new IVIF MAGDM method. The power average (PA) operator and the Muirhead mean (MM) are two powerful and effective information aggregation technologies. The most attractive advantage of the PA operator is its power to combat the adverse effects of ultra-evaluation values on the information aggregation results. The prominent characteristic of the MM operator is that it is flexible to capture the interrelationship among any numbers of arguments, making it more powerful than Bonferroni mean (BM), Heronian mean (HM), and Maclaurin symmetric mean (MSM). To absorb the virtues of both PA and MM, it is necessary to combine them to aggregate IVIF information and propose IVIF power Muirhead mean (IVIFPMM) operator and the IVIF weighted power Muirhead mean (IVIFWPMM) operator. We investigate their properties to show the strongness and flexibility. Furthermore, a novel approach to MAGDM problems with IVIF decision-making information is introduced. Finally, a numerical example is provided to show the performance of the proposed method.

On extended power average operators for decision-making: A case study in emergency response plan selection of civil aviation

The classical Power Average (PA) operator proposed by Yager implicitly restricts itself to an assumption that unduly high or low arguments are conceived as “false” or “biased” perceptions, thereby being assigned smaller weights for aggregation. However, on many occasions, these kinds of inputs to a great extent may be of significant importance to the accuracy of the aggregation outcomes, particularly when different sources of information are taken into consideration. The primary purpose of this paper is to adapt the PA operator to model generally various decision making settings where outliers are treated with different aggregation significance. The concept of Extended PA (EPA) operator is therefore proposed to effectively capture heterogeneous interrelationships among aggregation inputs. Several desirable properties of the EPA operator are investigated and their usefulness in practical decision making problems is highlighted. The choice of appropriate values for parameters associated with the EPA operator is likewise investigated. The proposed EPA operator is applied to develop an approach for multi-attribute decision making in which the interrelationships among the attributes and the inputs themselves are simultaneously taken into consideration. Finally, a case study in emergency response plan selection of civil aviation and a comparison analysis are provided to illustrate the feasibility and effectiveness of the proposed method.

T-Spherical Fuzzy Power Muirhead Mean Operator Based on Novel Operational Laws and Their Application in Multi-Attribute Group Decision Making

T-spherical fuzzy set (T-SPFS) is a generalization of several fuzzy concepts such as fuzzy set (FS), intuitionistic FS, picture FS, Pythagorean FS, and q-rung orthopair FS. T-SPFS is a more powerful mathematical tool to handle uncertain, inconsistent, and vague information than the above-defined sets. In this paper, some limitations in the operational laws for SPF numbers (SPFNs) are discussed and some novel operational laws for SPFNs are proposed. Furthermore, two new aggregation operators for aggregating SPF information are proposed and are applied to multiple-attribute group decision-making (MAGDM). To take the advantages of Muirhead mean (MM) operator and power average operator, the SPF power MM (SPFPMM) operator, weighted SPFPMM operator, SPF power dual MM (SPFPDMM) operator, weighted SPFPDMM operator are introduced and their anticipated properties are discussed. The main advantage of these developed aggregation operators is that they take the relationship among fused data and the interrelationship among aggregated values, thereby getting more information in the process of MAGDM. Moreover, a novel approach to MAGDM based on the developed aggregation operators is established. Finally, a numerical example is given to show the effectiveness of the developed approach and comparison with the existing approaches is also given.

Dual Hesitant Fuzzy Linguistic Power-Average Operators Based on Archimedean t-Conorms and t-Norms

This paper introduces some novel power-average (PA) operators of dual hesitant fuzzy linguistic (DHFL) set with the Archimedean t-conorms and t-norms (ATT) functions, such as the weighted DHFL power-average (ATT-WDHFLPA) operator based on ATT functions and the weighted generalized DHFL power-average operator on ATT functions (ATT-WGDHFLPA). Subsequently, the properties of those new operators are studied and the relationships between operators and existing ones are given. Furthermore, an approach of those operators is developed to solve the group decision-making problem with dual hesitant fuzzy linguistic information. Finally, an example is showing the advantages of those operators, and a sensitivity analysis of the main parameters has illustrated the results.

Multiple-Attribute Group Decision-Making Based on q-Rung Orthopair Fuzzy Power Maclaurin Symmetric Mean Operators

To be able to describe more complex fuzzy uncertainty information effectively, the concept of q-rung orthopair fuzzy sets (q-ROFSs) was first proposed by Yager. The q-ROFSs can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree from the decision-makers, where q ≥ 1, so they outperform the traditional intuitionistic fuzzy sets and Pythagorean fuzzy sets. In real decision-making problems, there is often an interaction phenomenon between attributes. For aggregating these complex fuzzy information, the Maclaurin symmetric mean (MSM) operator is more superior by considering interrelationships among attributes. In addition, the power average (PA) operator can reduce the effects of extreme evaluating data from some experts with prejudice. In this paper, we introduce the PA operator and the MSM operator based on q-rung orthopair fuzzy numbers (q-ROFNs). Then, we put forward the q-rung orthopair fuzzy power MSM (q-ROFPMSM) operator and the q-rung orthopair fuzzy power weighed MSM (q-ROFPWMSM) operator of q-ROFNs and present some of their properties. Finally, we present a novel multiple-attribute group decision-making (MAGDM) method based on the q-ROFPWA and the q-ROFPWMSM operators. The experimental results show that the novel MAGDM method outperforms the existing MAGDM methods for dealing with MAGDM problems.

Some Interval Neutrosophic Dombi Power Bonferroni Mean Operators and Their Application in Multi–Attribute Decision–Making

The power Bonferroni mean (PBM) operator is a hybrid structure and can take the advantage of a power average (PA) operator, which can reduce the impact of inappropriate data given by the prejudiced decision makers (DMs) and Bonferroni mean (BM) operator, which can take into account the correlation between two attributes. In recent years, many researchers have extended the PBM operator to handle fuzzy information. The Dombi operations of T-conorm (TCN) and T-norm (TN), proposed by Dombi, have the supremacy of outstanding flexibility with general parameters. However, in the existing literature, PBM and the Dombi operations have not been combined for the above advantages for interval-neutrosophic sets (INSs). In this article, we first define some operational laws for interval neutrosophic numbers (INNs) based on Dombi TN and TCN and discuss several desirable properties of these operational rules. Secondly, we extend the PBM operator based on Dombi operations to develop an interval-neutrosophic Dombi PBM (INDPBM) operator, an interval-neutrosophic weighted Dombi PBM (INWDPBM) operator, an interval-neutrosophic Dombi power geometric Bonferroni mean (INDPGBM) operator and an interval-neutrosophic weighted Dombi power geometric Bonferroni mean (INWDPGBM) operator, and discuss several properties of these aggregation operators. Then we develop a multi-attribute decision-making (MADM) method, based on these proposed aggregation operators, to deal with interval neutrosophic (IN) information. Lastly, an illustrative example is provided to show the usefulness and realism of the proposed MADM method. The developed aggregation operators are very practical for solving MADM problems, as it considers the interaction among two input arguments and removes the influence of awkward data in the decision-making process at the same time. The other advantage of the proposed aggregation operators is that they are flexible due to general parameter.

Power average-based score function and extension rule of hesitant fuzzy set and the hesitant power average operators

Power average-based score function and extension rule of hesitant fuzzy set and the hesitant power average operators

Neutrosophic Cubic Power Muirhead Mean Operators with Uncertain Data for Multi-Attribute Decision-Making

The neutrosophic cubic set (NCS) is a hybrid structure, which consists of interval neutrosophic sets (INS) (associated with the undetermined part of information associated with entropy) and single-valued neutrosophic set (SVNS) (associated with the determined part of information). NCS is a better tool to handle complex decision-making (DM) problems with INS and SVNS. The main purpose of this article is to develop some new aggregation operators for cubic neutrosophic numbers (NCNs), which is a basic member of NCS. Taking the advantages of Muirhead mean (MM) operator and power average (PA) operator, the power Muirhead mean (PMM) operator is developed and is scrutinized under NC information. To manage the problems upstretched, some new NC aggregation operators, such as the NC power Muirhead mean (NCPMM) operator, weighted NC power Muirhead mean (WNCPMM) operator, NC power dual Muirhead mean (NCPMM) operator and weighted NC power dual Muirhead mean (WNCPDMM) operator are proposed and related properties of these proposed aggregation operators are conferred. The important advantage of the developed aggregation operator is that it can remove the effect of awkward data and it considers the interrelationship among aggregated values at the same time. Furthermore, a novel multi-attribute decision-making (MADM) method is established over the proposed new aggregation operators to confer the usefulness of these operators. Finally, a numerical example is given to show the effectiveness of the developed approach.

Some Partitioned Maclaurin Symmetric Mean Based on q-Rung Orthopair Fuzzy Information for Dealing with Multi-Attribute Group Decision Making

In respect to the multi-attribute group decision making (MAGDM) problems in which the evaluated value of each attribute is in the form of q-rung orthopair fuzzy numbers (q-ROFNs), a new approach of MAGDM is developed. Firstly, a new aggregation operator, called the partitioned Maclaurin symmetric mean (PMSM) operator, is proposed to deal with the situations where the attributes are partitioned into different parts and there are interrelationships among multiple attributes in same part whereas the attributes in different parts are not related. Some desirable properties of PMSM are investigated. Then, in order to aggregate the q-rung orthopair fuzzy information, the PMSM is extended to q-rung orthopair fuzzy sets (q-ROFSs) and two q-rung orthopair fuzzy partitioned Maclaurin symmetric mean (q-ROFPMSM) operators are developed. To eliminate the negative influence of unreasonable evaluation values of attributes on aggregated result, we further propose two q-rung orthopair fuzzy power partitioned Maclaurin symmetric mean (q-ROFPPMSM) operators, which combine the PMSM with the power average (PA) operator within q-ROFSs. Finally, a numerical instance is provided to illustrate the proposed approach and a comparative analysis is conducted to demonstrate the advantage of the proposed approach.

Some power Maclaurin symmetric mean aggregation operators based on Pythagorean fuzzy linguistic numbers and their application to group decision making

The power average (PA) operator and Maclaurin symmetric mean (MSM) operator are two important tools to handle the multiple attribute group decision-making (MAGDM) problems, and the combination of two operators can eliminate the influence of unreasonable information from biased decision makers (DMs) and can capture the interrelationship among any number of arguments. The Pythagorean fuzzy linguistic set (PFLS) is parallel to the intuitionistic linguistic set (ILS), which is more powerful to convey the uncertainty and ambiguity of the DMs than ILS. In this paper, we propose some power MSM aggregation operators for Pythagorean fuzzy linguistic information, such as Pythagorean fuzzy linguistic power MSM operator and Pythagorean fuzzy linguistic power weighted MSM (PFLPWMSM) operator. At the same time, we further discuss the properties and special cases of these operators. Then, we propose a new method to solve the MAGDM problems with Pythagorean fuzzy linguistic information based on the PFLPWMSM operator. Finally, some illustrative examples are utilized to show the effectiveness of the proposed method.

Approach to Multiple Attribute Group Decision Making Based on Hesitant Fuzzy Linguistic Aggregation Operators

Abstract Inspired by the nonlinear weighted average operator, this paper proposes several generalized power average operators to aggregate hesitant fuzzy linguistic decision information. It is worth noting that the new operators take both the location and date weight information and the relative closeness of the decision-making information into consideration, a characteristic that results in objectivity and fairness in a group decision making. Moreover, we demonstrate some useful properties of the operators and discuss their associations. A new approach based on the designed operators is then proposed for hesitant fuzzy linguistic multiple attribute group decision-making problems, in which the attribute weights are known or unknown. Finally, this paper demonstrates the efficiency and feasibility of the proposed method through a numerical example.

Some interval-valued intuitionistic fuzzy Schweizer–Sklar power aggregation operators and their application to supplier selection

ABSTRACTSupplier selection is an important multiple attribute group decision-making (MAGDM) problem. How to choose a suitable supplier is an evaluation process with different alternatives of multiple attributes, and it also relates to the expression of the evaluation value. Considering Schweizer–Sklar t-conorm and t-norm (SSTT) can make the information aggregation process more flexible than others, and the power average (PA) operator can eliminate effects of unreasonable data from biased decision-makers. So, we extend SSTT to interval-valued intuitionistic fuzzy numbers (IVIFNs) and define Schweizer–Sklar operational rules of IVIFNs. Then, we combine the PA operator with Schweizer–Sklar operations, and propose the interval-valued intuitionistic fuzzy Schweizer–Sklar power average operator, the interval-valued intuitionistic fuzzy Schweizer–Sklar power weighted average (IVIFSSPWA) operator, the interval-valued intuitionistic fuzzy Schweizer–Sklar power geometric operator and the interval-valued intuitionistic fuzzy Schweizer–Sklar power weighted geometric (IVIFSSPWG) operator, respectively. Furthermore, we study some desirable characteristics of them and develop two methods on the basis of IVIFSSPWA and IVIFSSPWG operators. At the same time, we apply the two methods to deal with the MAGDM problems based on supplier selection. Finally, an illustrative example of supplier selection problem is given to testify the availability of the presented operators.

Multiple Attribute Group Decision-Making Method Based on Generalized Interval-Valued Hesitant Uncertain Linguistic Power Aggregation Operators and Linguistic-Scale Functions

As an extension of hesitant linguistic term set, interval-valued hesitant uncertain linguistic set can simultaneously express qualitative information and quantitative information, and reflect the uncertainty and hesitancy of assessment experts. The purpose of this paper is to present a new interval-valued hesitant uncertain linguistic MAGDM method, which can take into account changes in the semantic environment and negative effects caused by experts’ extreme assessment values. First, by combining with different linguistic-scale functions, some new operational laws and a new comparison method for IVHULNs are developed to accommodate different semantic environments. Then, several new generalized interval-valued hesitant uncertain linguistic power aggregation operators are proposed, including generalized interval-valued hesitant uncertain linguistic power average operator and its weight form, generalized interval-valued hesitant uncertain linguistic power geometric operator and its weighted form. Some desirable properties and some special cases of these operators are investigated and analyzed. Furthermore, based on the proposed operators, an approach to multiple attribute group decision-making with interval-valued hesitant uncertain linguistic information is developed. Finally, an illustrative example is provided to demonstrate the applicability and feasibility of the proposed approach. A comparative analysis with other existing methods is also conducted to illustrate the effectiveness of the proposed approach.

Multi-attribute group decision making based on power generalized Heronian mean operator under hesitant fuzzy linguistic environment

Generalized Heronian mean (GHM) is a useful aggregation operator with the characteristic of capturing the interrelationship of evaluation information. In this paper, we propose some new operators by combining the power average operator and the GHM operator under hesitant fuzzy linguistic environment, such as the hesitant fuzzy linguistic power generalized Heronian mean (HFLPGHM) operator, the hesitant fuzzy linguistic power generalized geometric Heronian mean (HFLPGGHM) operator, the hesitant fuzzy linguistic weighted power generalized Heronian mean (HFLWPGHM) operator and the hesitant fuzzy linguistic weighted power generalized geometric Heronian mean (HFLWPGGHM) operator. Then, some special cases of the proposed HFLPGHM and HFLPGGHM operators are discussed in detail. Furthermore, based on the proposed operators, we develop a novel method to solve multi-attribute group decision-making problem under hesitant fuzzy linguistic environment. Finally, a numerical example is given to illustrate the application of the developed method and a comparison analysis is also conducted, which further demonstrates the effectiveness and feasibility of the proposed method.

Group Decision Making Based on Power Heronian Aggregation Operators Under Linguistic Neutrosophic Environment

The power average (PA) operator can overcome some effects of awkward data given by predispose decision makers, and Heronian mean (HM) operator can consider the interrelationship of the aggregated arguments. In order to take the full use of these two kinds of operators, in this article, we combined the PA operator with HM operator and extended them to process linguistic neutrosophic information, and presented the linguistic neutrosophic power Heronian aggregation operator, linguistic neutrosophic power weight Heronian aggregation operator. Further, some properties of these new aggregation operators are investigated and some special cases are discussed. Furthermore, we propose new technique based on these operators for multiple attribute group decision making. Finally, an illustrative example was given to illustrate the effectiveness and advantages of the developed method by comparing with the existing method.

Location‐dependent sensing data collection and processing mechanism in vehicular network

AbstractWith the promotion of the Internet of Things, in which a growing number of objects in everyday life are able to communicate with each other, crowdsensing has attracted public attention. Among different devices, vehicles with various sensors can perform the traffic data collection tasks released by the traffic center, which is helpful for monitoring road conditions. Thus, we use crowdsensing between vehicles to improve the precision of traffic state estimation. We also propose a location‐dependent sensing task assignment mechanism for traffic data collection and a multisource data fusion model for traffic data processing in a vehicular network. First, we establish a mathematical model for the sensing task assignment considering the vehicle's time budget constraint, location, and collection task requirements. We then propose a task assignment algorithm consisting of determining the order for vehicle allocation and scheduling the optimal collection path for each vehicle, which aims to achieve maximum platform utility. Furthermore, we put forward a fusion model, including spatial fusion and temporal fusion, to better process the collected data. We use a power average operator for the spatial fusion and a temporal correlation–based data compression algorithm for the temporal fusion. The obtained simulation results validate the accuracy and correctness of our approach.

Probabilistic Linguistic Power Aggregation Operators for Multi-Criteria Group Decision Making

As an effective aggregation tool, power average (PA) allows the input arguments being aggregated to support and reinforce each other, which provides more versatility in the information aggregation process. Under the probabilistic linguistic term environment, we deeply investigate the new power aggregation (PA) operators for fusing the probabilistic linguistic term sets (PLTSs). In this paper, we firstly develop the probabilistic linguistic power average (PLPA), the weighted probabilistic linguistic power average (WPLPA) operators, the probabilistic linguistic power geometric (PLPG) and the weighted probabilistic linguistic power geometric (WPLPG) operators. At the same time, we carefully analyze the properties of these new aggregation operators. With the aid of the WPLPA and WPLPG operators, we further design the approaches for the application of multi-criteria group decision-making (MCGDM) with PLTSs. Finally, we use an illustrated example to expound our proposed methods and verify their performances.

Intuitionistic fuzzy evidential power aggregation operator and its application in multiple criteria decision-making

ABSTRACTThe theory of intuitionistic fuzzy sets (IFS) is widely used for dealing with vagueness and the Dempster--Shafer (D-S) evidence theory has a widespread use in multiple criteria decision-making problems under uncertain situation. However, there are many methods to aggregate intuitionistic fuzzy numbers (IFNs), but the aggregation operator to fuse basic probability assignment (BPA) is rare. Power average (P-A) operator, as a powerful operator, is useful and important in information fusion. Motivated by the idea of P-A power, in this paper, a new operator based on the IFS and D-S evidence theory is proposed, which is named as intuitionistic fuzzy evidential power average (IFEPA) aggregation operator. First, an IFN is converted into a BPA, and the uncertainty is measured in D-S evidence theory. Second, the difference between BPAs is measured by Jousselme distance and a satisfying support function is proposed to get the support degree between each other effectively. Then the IFEPA operator is used for aggregating the original IFN and make a more reasonable decision. The proposed method is objective and reasonable because it is completely driven by data once some parameters are required. At the same time, it is novel and interesting. Finally, an application of developed models to the ‘One Belt, One road’ investment decision-making problems is presented to illustrate the effectiveness and feasibility of the proposed operator.

Using New Version of Extended $t$ -Norms and $s$ -Norms for Aggregating Interval Linguistic Labels

The aim of this paper is to develop some closed algebra operational laws for interval linguistic labels based on extended $\boldsymbol {t}$ -norms and $\boldsymbol {s}$ -norms. We discuss the properties of these operational laws, such as commutative law, associative law, and distribution law. Different kinds of extended $\boldsymbol {t}$ -norms and $\boldsymbol {s}$ -norms, such as the extended algebraic, extended Einstein, extended Hamacher, and extended Frank $\boldsymbol {t}$ -norms and $\boldsymbol {s}$ -norms, have been investigated to produce different operational laws. As an application of such operational laws, we propose some extended $\boldsymbol {t}$ -norms and $\boldsymbol {s}$ -norms based interval linguistic weighted power average operators. We also study some basic properties of such aggregation functions. The cross-entropy of interval linguistic information is proposed and applied to obtain the weights of attributes. An approach to multiple attributes decision making with interval linguistic information is proposed. Finally, two cases of practical decision issues are illustrated to show the application of the proposed method.

Pythagorean fuzzy power aggregation operators in multiple attribute decision making

In this paper, we utilize power aggregation operators to develop some Pythagorean fuzzy power aggregation operators: Pythagorean fuzzy power average operator, Pythagorean fuzzy power geometric operator, Pythagorean fuzzy power weighted average operator, Pythagorean fuzzy power weighted geometric operator, Pythagorean fuzzy power ordered weighted average operator, Pythagorean fuzzy power ordered weighted geometric operator, Pythagorean fuzzy power hybrid average operator, and Pythagorean fuzzy power hybrid geometric operator. The prominent characteristic of these proposed operators are studied. Then, we have utilized these operators to develop some approaches to solve the Pythagorean fuzzy multiple attribute decision-making problems. Finally, a practical example is given to verify the developed approach and to demonstrate its practicality and effectiveness.