Weighted Aggregation Operator Research Articles

Neutrality operations-based Pythagorean fuzzy aggregation operators and its applications to multiple attribute group decision-making process

Pythagorean fuzzy sets accommodate more uncertainties than the intuitionistic fuzzy sets and hence it is one of the most important concepts to describe the fuzzy information in the process of decision making. Under this environment, the main objective of the work is to develop some new operational laws and their corresponding weighted aggregation operators. For it, we define some new neutral addition and scalar multiplication operational laws by incorporating the features of a neutral character towards the membership degrees of the set and the probability sum. Some properties of the proposed laws are investigated. Then, associated with these operational laws, we define some novel Pythagorean fuzzy weighted, ordered weighted and hybrid neutral averaging aggregation operators for Pythagorean fuzzy information, which can neutrally treat the membership and non-membership degrees. The various relations and the characteristics of the proposed operators are discussed. Further, in order to ease with the possible application, we present an algorithm to solve the multiple attribute group decision-making problems under the Pythagorean fuzzy environment. Finally, a practical example is provided to illustrate the approach and show its superiority, advantages by comparing their performance with some several existing approaches.

Multi-Attribute Multi-Perception Decision-Making Based on Generalized T-Spherical Fuzzy Weighted Aggregation Operators on Neutrosophic Sets

The framework of the T-spherical fuzzy set is a recent development in fuzzy set theory that can describe imprecise events using four types of membership grades with no restrictions. The purpose of this manuscript is to point out the limitations of the existing intuitionistic fuzzy Einstein averaging and geometric operators and to develop some improved Einstein aggregation operators. To do so, first some new operational laws were developed for T-spherical fuzzy sets and their properties were investigated. Based on these new operations, two types of Einstein aggregation operators are proposed namely the Einstein interactive averaging aggregation operators and the Einstein interactive geometric aggregation operators. The properties of the newly developed aggregation operators were then investigated and verified. The T-spherical fuzzy aggregation operators were then applied to a multi-attribute decision making (MADM) problem related to the degree of pollution of five major cities in China. Actual datasets sourced from the UCI Machine Learning Repository were used for this purpose. A detailed study was done to determine the most and least polluted city for different perceptions for different situations. Several compliance tests were then outlined to test and verify the accuracy of the results obtained via our proposed decision-making algorithm. It was proved that the results obtained via our proposed decision-making algorithm was fully compliant with all the tests that were outlined, thereby confirming the accuracy of the results obtained via our proposed method.

A novel multiple‐attribute group decision‐making method based on q ‐rung orthopair fuzzy generalized power weighted aggregation operators

A novel multiple‐attribute group decision‐making method based on <i>q</i> ‐rung orthopair fuzzy generalized power weighted aggregation operators

Intuitionistic Fuzzy Hybrid Weighted Arithmetic Mean and Its Application in Decision Making

Atanassov’s intuitionistic fuzzy sets (AIFSs), characterized by a membership function, a non-membership function, and a hesitancy function, is a generalization of a fuzzy set. There are various intuitionistic fuzzy hybrid weighted aggregation operators to deal with multi-attribute decision making problems which consider the importance degrees of the arguments and their ordered positions simultaneously. However, these existing hybrid weighed aggregation operators are not monotone with respect to the total order on intuitionistic fuzzy values (AIFVs), which is undesirable. Based on the Łukasiewicz triangular norm, we propose an intuitionistic fuzzy hybrid weighted arithmetic mean, which is monotone with respect to the total order on AIFVs, and therefore is a true generalization of such operations. We give an example that a company intends to select a project manager to illustrate the validity and applicability of the proposed aggregation operator. Moreover, we extend this kind of hybrid weighted arithmetic mean to the interval-valued intuitionistic fuzzy environments.

Some Single-Valued Neutrosophic Power Heronian Aggregation Operators and Their Application to Multiple-Attribute Group Decision-Making

The power Heronian aggregation (PHA) operator can use the advantages of power average and the Heronian mean operator, which together could take into account the interrelationship of the aggregated arguments, and therefore alleviate the effects caused by unreasonable data through considering the support degree between input arguments. However, PHA operators cannot be used to process single-valued neutrosophic numbers (SVNNs), which is significant for extending it to SVNNs. We propose some new PHA operators for SVNNs and introduce a novel MAGDM method on the basis of the proposed operators. Firstly, the definition, properties, comparison method, and operational rules of SVNNs are introduced briefly. Then, some PHA operators are proposed, such as the single-valued neutrosophic power Heronian aggregation (SVNPHA) operator, the single-valued neutrosophic weighted power Heronian aggregation (SVNWPHA) operator, single-valued neutrosophic geometric power Heronian aggregation (SVNGPHA) operator, single-valued neutrosophic weighted geometric power Heronian aggregation (SVNWGPHA) operator. Furthermore, we discuss some properties of these new aggregation operators and several special cases. Moreover, the method to solve the MAGDM problems with SVNNs is proposed, based on the SVNWPHA and SVNWGPHA operators. Lastly, we verified the application and effectiveness of the proposed method by using an example for the MAGDM problem.

Time Series Data Fusion Based on Evidence Theory and OWA Operator.

Time series data fusion is important in real applications such as target recognition based on sensors’ information. The existing credibility decay model (CDM) is not efficient in the situation when the time interval between data from sensors is too long. To address this issue, a new method based on the ordered weighted aggregation operator (OWA) is presented in this paper. With the improvement to use the Q function in the OWA, the effect of time interval on the final fusion result is decreased. The application in target recognition based on time series data fusion illustrates the efficiency of the new method. The proposed method has promising aspects in time series data fusion.

Towards Human-Centric Aggregation via Ordered Weighted Aggregation Operators and Linguistic Data Summaries: A New Perspective on Zadeh's Inspirations

This work presents a new perspective on how Zadeh's ideas related to fuzzy logic and computing with words have influenced the crucial issue of information aggregation and have led to what may be called a human-centric aggregation. We indicate a need to develop tools and techniques to reflect some fine shades of meaning regarding what can be considered the very purpose of human-centric aggregation, notably stated by various modalities in natural language specifications, in particular the usuality. We advocate the use of the ordered weighted average (OWA) operator, which is a formidable tool that can easily be tailored to a user?s intention as to the purpose and method of aggregation, generalizing many simple and natural aggregation types, such as the arithmetic mean, maximum and minimum, and probability. We show some of the most representative extensions and generalizations, including the induced OWA, the generalized OWA, the probabilistic OWA, and the OWA distance. We show their use in the basic case of the aggregation of numerical values and in social choice (voting) results. Then, we claim that linguistic data summaries in Yager?s sense can be considered an ultimately human consistent form of human-centric aggregation and show how the OWA operators can be used therein.

A Concession Equilibrium Solution Method without Weighted Aggregation Operators for Multiattribute Group Decision-Making Problems

This paper introduces a concession equilibrium solution without weighted aggregation operators to multiattribute group decision-making problems (in short MGDMPs). It is of practical significance for all decision-makers to find an optimal solution to MGDMPs or to sort out all candidate solutions to MGDMPs. It is proved that under certain conditions the optimal concession equilibrium solution does exist, and on this important result the optimal concession equilibrium solution is obtained by solving a single objective optimization problem. Moreover, the optimal concession equilibrium solution is equivalent to the robust optimal solution with the group weight aggregation under the worst weight condition. Finally, it is proved that the concession equilibrium solution is equivalent to a complete order, i.e. all candidate alternatives can be sorted by concession equilibrium solution. By defining the triangular fuzzy numbers of target concession value, the optimal concession equilibrium solution or the order of the alternative solutions can be obtained in the range of objective concession ambiguity. Numerical experiment shows that the solution can balance the evaluations of multiattribute group decision makers. This paper provides a new approach to solving multiattribute group decision-making problems.

Variance measures with ordered weighted aggregation operators

Variance measures with ordered weighted aggregation operators

Some q-rung orthopair fuzzy point weighted aggregation operators for multi-attribute decision making

q-Rung orthopair fuzzy sets, originally proposed by Yager, can dynamically adjust the range of indication of decision information by changing a parameter q based on the different hesitation degree, and point operator is a useful aggregation technology that can control the uncertainty of valuating data from some experts and thus get intensive information in the process of decision making. However, the existing point operators are not available for decision-making problems under q-Rung orthopair fuzzy environment. Thus, in this paper, we firstly propose some new point operators to make it conform to q-rung orthopair fuzzy numbers (q-ROFNs). Then, associated with classic arithmetic and geometric operators, we propose a new class of point weighted aggregation operators to aggregate q-rung orthopair fuzzy information. These proposed operators can redistribute the membership and non-membership in q-ROFNs according to different principle. Furthermore, based on these operators, a novel approach to multi-attribute decision making (MADM) in q-rung orthopair fuzzy context is introduced. Finally, we give a practical example to illustrate the applicability of the new approach. The experimental results show that the novel MADM method outperforms the existing MADM methods for dealing with MADM problems.

Triangular picture fuzzy linguistic induced ordered weighted aggregation operators and its application on decision making problems

The primary goal of this paper is to solve the investment problem based on linguistic picture decision making method under the linguistic triangular picture linguistic fuzzy environment. First to define the triangular picture linguistic fuzzy numbers. Further, we define operations on triangular picture linguistic fuzzy numbers and their aggregation operator namely, triangular picture fuzzy linguistic induce OWA (TPFLIOWA) and triangular picture fuzzy linguistic induce OWG (TPFLIOWG) operators. Multi-criteria group decision making method is developed based on TPFLIOWA and TPFLIOWG operators and solve the uncertainty in the investment problem. We study the applicability of the proposed decision making method under triangular picture linguistic fuzzy environment and construct a descriptive example of investment problem. We conclude from the comparison and sensitive analysis that the proposed decision making method is more effective and reliable than other existing models.

Interval-Valued Atanassov Intuitionistic Fuzzy CODAS Method for Multi Criteria Group Decision Making Problems

The paper presents a fuzzy extension of CODAS (COmbinative Distance-Based ASsessment) method which is called as interval-valued Atanassov intuitionistic fuzzy CODAS (IVAIF-CODAS) method for group decision making processes. The extended method considers interval-valued Atanassov intuitionistic fuzzy sets (IVAIFSs) to define the judgements of decision-makers and uses interval-valued Atanassov intuitionistic fuzzy weighted aggregation operator to aggregate the evaluations of decision makers. Due to the abilities of IVAIFS in modeling of uncertainty, the extended method can be readily applied to many decision problems under fuzzy circumstances. In the study, a personnel selection problem is handled to show applicability of the IVAIF-CODAS method. Computational analysis is performed by using three different well-known IVAIF-based multi criteria group decision making (MCGDM) methods in order to test the stability and validity of the outputs. The proposed method is an easy to use and an effective tool in terms of producing as robust results as other methods and requiring relatively less effort.

Fermatean fuzzy linguistic set and its application in multicriteria decision making

In this paper, we propose the concept of Fermatean fuzzy linguistic term sets based on linguistic term sets and Fermatean fuzzy sets. The basic operational laws, the score function, and the accuracy function of Fermatean fuzzy linguistic numbers are provided. Then we propose the Fermatean fuzzy linguistic weighted aggregation operator, the Fermatean fuzzy linguistic weighted geometric operator, and the Fermatean fuzzy linguistic distance measures. Furthermore, we extend the TOPSIS method to the proposed distance measures, and the ranking of alternatives is obtained under a Fermatean fuzzy linguistic environment. An example is provided to illustrate the feasibility and effectiveness of the proposed method, and a comparison with the existing method is also analyzed. Finally, the sensitivity analysis of the parameter in the proposed distance measure is also discussed.

M-Polar Fuzzy Soft Weighted Aggregation Operators and Their Applications in Group Decision-Making

Aggregation operators are important tools for solving multi-attribute group decision-making (MAGDM) problems. The main challenging issue for aggregating data in a MAGDM problem is how to develop a symmetric aggregation operator expressing the decision makers’ behavior. In the literature, there are some methods dealing with this difficulty; however, they lack an effective approach for multi-polar inputs. In this study, a new aggregation operator for m-polar fuzzy soft sets (M-pFSMWM) reflecting different agreement scenarios within a group is presented to proceed MAGDM problems in which both attributes and experts have different weights. Moreover, some desirable properties of M-pFSMWM operator, such as idempotency, monotonicity, and commutativity (symmetric), that means being invariant under any permutation of the input arguments, are studied. Further, m-polar fuzzy soft induced ordered weighted average (M-pFSIOWA) operator and m-polar fuzzy soft induced ordered weighted geometric (M-pFSIOWG) operator, which are extensions of IOWA and IOWG operators, respectively, are developed. Two algorithms are also designed based on the proposed operators to find the final solution in MAGDM problems with weighted multi-polar fuzzy soft information. Finally, the efficiency of the proposed methods is illustrated by some numerical examples. The characteristic comparison of the proposed aggregation operators shows the M-pFSMWM operator is more adaptable for solving MAGDM problems in which different cases of agreement affect the final outcome.

Group decision making approach based on possibility degree measure under linguistic interval-valued intuitionistic fuzzy set environment

<p style='text-indent:20px;'>In the present article, we extended the idea of the linguistic intuitionistic fuzzy set to linguistic interval-valued intuitionistic fuzzy (LIVIF) set to represent the data by the interval-valued linguistic terms of membership and non-membership degrees. Some of the desirable properties of the proposed set are studied. Also, we propose a new ranking method named as possibility degree measures to compare the two or more different LIVIF numbers. During the aggregation process, some LIVIF weighted and ordered weighted aggregation operators are proposed to aggregate the collections of the LIVIF numbers. Finally, based on these proposed operators and possibility degree measure, a new group decision making approach is presented to rank the different alternatives. A real-life case has been studied to manifest the practicability and feasibility of the proposed group decision making method.

Multiple Attribute Decision-Making Method Using Linguistic Cubic Hesitant Variables

Linguistic decision making (DM) is an important research topic in DM theory and methods since using linguistic terms for the assessment of the objective world is very fitting for human thinking and expressing habits. However, there is both uncertainty and hesitancy in linguistic arguments in human thinking and judgments of an evaluated object. Nonetheless, the hybrid information regarding both uncertain linguistic arguments and hesitant linguistic arguments cannot be expressed through the various existing linguistic concepts. To reasonably express it, this study presents a linguistic cubic hesitant variable (LCHV) based on the concepts of a linguistic cubic variable and a hesitant fuzzy set, its operational relations, and its linguistic score function for ranking LCHVs. Then, the objective extension method based on the least common multiple number/cardinality for LCHVs and the weighted aggregation operators of LCHVs are proposed to reasonably aggregate LCHV information because existing aggregation operators cannot aggregate LCHVs in which the number of their hesitant components may imply difference. Next, a multi-attribute decision-making (MADM) approach is proposed based on the weighted arithmetic averaging (WAA) and weighted geometric averaging (WGA) operators of LCHVs. Lastly, an illustrative example is provided to indicate the applicability of the proposed approaches.

Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making

Some single-valued neutrosophic dombi prioritized weighted aggregation operators in multiple attribute decision making

Applications of Neutrosophic Bipolar Fuzzy Sets in HOPE Foundation for Planning to Build a Children Hospital with Different Types of Similarity Measures

In this paper we provide an application of neutrosophic bipolar fuzzy sets in daily life’s problem related with HOPE foundation that is planning to build a children hospital, which is the main theme of this paper. For it we first develop the theory of neutrosophic bipolar fuzzy sets which is a generalization of bipolar fuzzy sets. After giving the definition we introduce some basic operation of neutrosophic bipolar fuzzy sets and focus on weighted aggregation operators in terms of neutrosophic bipolar fuzzy sets. We define neutrosophic bipolar fuzzy weighted averaging ( N B FWA ) and neutrosophic bipolar fuzzy ordered weighted averaging ( N B FOWA ) operators. Next we introduce different kinds of similarity measures of neutrosophic bipolar fuzzy sets. Finally as an application we give an algorithm for the multiple attribute decision making problems under the neutrosophic bipolar fuzzy environment by using the different kinds of neutrosophic bipolar fuzzy weighted/fuzzy ordered weighted aggregation operators with a numerical example related with HOPE foundation.

Some hybrid weighted aggregation operators under neutrosophic set environment and their applications to multicriteria decision-making

A single-valued and an interval neutrosophic sets are two instances of the neutrosophic set(NS), which can efficiently deal with uncertain, imprecise and inconsistent information. In the present work, the work has been done under this environment to develop some novel hybrid aggregation operators based on arithmetic and geometric aggregation operators. The preferences related to the attributes are made in the form of single-valued and interval neutrosophic numbers. Their desirable properties such as idempotency, boundedness and monotonicity are also investigated. Furthermore, a decision-making approach presents to investigate the multi-criteria decision-making problem. The effectiveness of the approach is demonstrated through a case study and a comparison analysis with some other existing methods has been done to validate the results.

A multi criteria comprehensive evaluation approach for emergency response capacity with interval 2-tuple linguistic information

Emergency response capacity evaluation (ERCE) is an important and challenging issue in emergency management with the frequent occurrence of emergency events. Because of their different backgrounds and preferences, decision makers (DMs) often prefer to use linguistic variables from different linguistic term sets to express their decision information about the importance and the ratings of multi criteria involved in ERCE issue, some of which may be imprecise and uncertain. Therefore, this paper proposes a multi criteria comprehensive evaluation (MCCE) approach for ERCE with interval 2-tuple linguistic information. First, a new method for comparison between interval 2-tuples is proposed. Then, the classic analytical hierarchy process is extended into the ITL-AHP, in which the interval 2-tuple linguistic preference relation (ITLPR) and its multiplicative consistency are defined. An iterative algorithm to improve the consistency level of an ITLPR is proposed. Based on improved ITLPRs, the priority weights of criteria are derived by the normalizing rank summation method. In individual decision information collecting processes, both subjective weights and objective weights of DMs are considered. Furthermore, some interval 2-tuple interval weighted aggregation operators in which the weight vectors take the form of interval 2-tuple linguistic information are developed. Finally, a numerical illustration and comparison analyses are provided to elucidate the feasibility and superiority of the proposed method. The proposed method can provide a flexible way to perceive and appraise the emergency response capacity (REC) and an effective tool to handle the emergency management performance evaluation and decision making under fuzzy and uncertain information environment.