Weighted Aggregation Operator Research Articles

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.

Picture Hesitant Fuzzy Set and Its Application to Multiple Criteria Decision-Making

To address the complex multiple criteria decision-making (MCDM) problems in practice, this article proposes the picture hesitant fuzzy set (PHFS) theory based on the picture fuzzy set and the hesitant fuzzy set. First, the concept of PHFS is put forward, and its operations are presented, simultaneously. Second, the generalized picture hesitant fuzzy weighted aggregation operators are developed, and some theorems and reduced operators of them are discussed. Third, the generalized picture hesitant fuzzy prioritized weighted aggregation operators are put forward to solve the MCDM problems that the related criteria are at different priorities. Fourth, two novel MCDM methods combined with the proposed operators are constructed to determine the best alternative in real life. Finally, two numerical examples and an application of web service selection are investigated to illustrate the effectiveness of the proposed methods. The sensitivity analysis shows that the different values of the parameter λ affect the ranking of alternatives, and the proposed operators are compared with several existing MCDM methods to illustrate their advantages.

Group Decision-Making Approach without Weighted Aggregation Operators

This paper introduces an approach for group decision-making problems (GDMP) without weighted aggregation operators. This approach is more suitable for scenarios with infinite number of individuals. A mathematical model approach is established based on the new concept of s⁎-optimal concession equilibrium solution without weighted aggregation operators for group decision-making problems. It is of practical significance for all decision-makers (experts) to find an optimal solution or to sort out all the candidate solutions. We prove that the s⁎-optimal concession equilibrium solution is equivalent to solving a single objective optimization problem, and, under certain conditions, the s⁎-optimal equilibrium solution always exists. Moreover, it is proven that the s⁎-optimal concession equilibrium solution is equivalent to the robust optimal solution of the group weight aggregation and the optimal solution under the worst weighted aggregation operators.

Multiple Attributes Group Decision-Making under Interval-Valued Dual Hesitant Fuzzy Unbalanced Linguistic Environment with Prioritized Attributes and Unknown Decision-Makers’ Weights

Aiming at a special type of ill-defined complicate multiple attributes group decision-making (MAGDM) problem, which exhibits hybrid complexity features of decision hesitancy, prioritized evaluative attributes, and unknown decision-makers’ weights, we investigate an effective approach in this paper. To accommodate decision hesitancy, we employ a compound expression tool of interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS) to help decision-makers elicit their assessments more comprehensively and completely. To exploit prioritization relations among evaluating attributes, we develop a prioritized weighted aggregation operator for IVDHFUBLS-based decision-making scenarios and then analyze its properties and special cases. To objectively derive unknown decision-makers’ weighting vector, we next develop a hybrid model that simultaneously takes into account the overall accuracy measure of the individual decision matrix and maximizing deviation among all decision matrices. Furthermore, on the strength of the above methods, we construct an MAGDM approach and demonstrate its practicality and effectiveness using applied study on a green supplier selection problem.

Hesitant Probabilistic Fuzzy Linguistic Sets with Applications in Multi-Criteria Group Decision Making Problems

Uncertainties due to randomness and fuzziness comprehensively exist in control and decision support systems. In the present study, we introduce notion of occurring probability of possible values into hesitant fuzzy linguistic element (HFLE) and define hesitant probabilistic fuzzy linguistic set (HPFLS) for ill structured and complex decision making problem. HPFLS provides a single framework where both stochastic and non-stochastic uncertainties can be efficiently handled along with hesitation. We have also proposed expected mean, variance, score and accuracy function and basic operations for HPFLS. Weighted and ordered weighted aggregation operators for HPFLS are also defined in the present study for its applications in multi-criteria group decision making (MCGDM) problems. We propose a MCGDM method with HPFL information which is illustrated by an example. A real case study is also taken in the present study to rank State Bank of India, InfoTech Enterprises, I.T.C., H.D.F.C. Bank, Tata Steel, Tata Motors and Bajaj Finance using real data. Proposed HPFLS-based MCGDM method is also compared with two HFL-based decision making methods.

A modified TOPSIS method based on vague parameterized vague soft sets and its application to supplier selection problems

In this paper, we propose an intuitively straightforward extension of the vague soft set model called the vague parameterized vague soft set (vp-VSS). This model generalizes the vague soft set by including the opinions of an expert or a moderator regarding the values of the membership function for the parameters that are considered, in the form of a vague set. The values provided by the experts indicate the threshold values for the membership functions of the elements, i.e., the minimum values that must be ideally satisfied by all the elements for each parameter. This provides a clear indication to the users of these information, and forms a pertinent component of the model, particularly in the decision-making process. Subsequently, we define some operations for this model and examine its properties. Subsequently, we introduce two algorithms based on a modified TOPSIS approach and a weighted aggregation operator approach, both of which are based on our proposed vp-VSS model. These algorithms are then applied in two multi-attribute decision-making problems involving supplier selection and the evaluation of supplier performance. The performance and utility of these algorithms are compared and contrasted in terms of the computational complexity and discriminative power of the algorithms.

On Intuitionistic Fuzzy Copula Aggregation Operators in Multiple- Attribute Decision Making

Operations of intuitionistic fuzzy values have been widely studied and have attracted significant interest. In this paper, some other operations on intuitionistic fuzzy values on the basis of Archimedean copulas and corresponding co-copulas are introduced. Such novel operations can show the relevance between intuitionistic fuzzy values. A family of weighted aggregation operators are developed according to the proposed operations, i.e., the intuitionistic fuzzy copula aggregation operator. The properties of the novel operations and the weighted aggregation operators are also considered. In the end, we provide a modified maximizing deviation decision procedure for multiple attributes decision making under intuitionistic fuzzy environment, and show a case study to illustrate the application of the proposed approach.

New exponential operational laws and their aggregation operators for interval-valued Pythagorean fuzzy multicriteria decision-making

In this article, we define two new exponential operational laws about the interval-valued Pythagorean fuzzy set (IVPFS) and their corresponding aggregation operators. However, the exponential parameters (weights) of all the existing operational laws of IVPFSs are crisp values in IVPFS decision-making problems. As a supplement, this paper first introduces new exponential operational laws of IVPFS, where bases are crisp values or interval numbers and exponents are interval-valued Pythagorean fuzzy numbers. The prominent characteristic of these proposed operations is studied. Based on these laws, we develop some new weighted aggregation operators, namely the interval-valued Pythagorean fuzzy weighted exponential averaging operator and the dual interval-valued Pythagorean fuzzy weighted exponential averaging. Finally, a decision-making approach is presented based on these operators and illustrated with some numerical examples to validate the developed approach.

Multiple Attributes Group Decision-Making Approaches Based on Interval-Valued Dual Hesitant Fuzzy Unbalanced Linguistic Set and Their Applications

Aiming at multiple attributes group decision-making (MAGDM) problems that characterize uncertainty nature and decision hesitancy, firstly, we propose the interval-valued dual hesitant fuzzy unbalanced linguistic set (IVDHFUBLS) in which two sets of interval-valued hesitant fuzzy membership degrees and nonmembership degrees are employed to supplement the most preferred unbalanced linguistic term, as an effective hybrid expression tool to elicit complicate preferences of decision-makers more comprehensively and flexibly than existing tools based on classic linguistic term set. Basic operations for IVDHFUBLS are further defined; also a novel distance measure is developed to avoid potential information distortion that could be brought about by traditional complementing methodology for hesitant fuzzy set and its derivatives. In view of the fundamental role of aggregation operators in MAGDM modelling, we next develop some extended power aggregation operators for IVDHFUBLS, including power aggregation operator, weighted power aggregation operator, and induced power ordered weighted aggregation operator; their desirable properties and special cases are also analyzed theoretically. Subsequently, with support of the above methods, we develop two effective approaches for our targeted complex decision-making problems and verify their effectiveness and practicality by numerical studies.

Fuzzy Techniques for Decision Making

This book contains the successful invited submissions [1–21] to a Special Issue of Symmetry on the subject area of “Fuzzy Techniques for Decision Making”.[...]

A novel group decision-making model based on triangular neutrosophic numbers

In group decision-making (GDM) model, experts often evaluate their opinion by using triangular fuzzy numbers. The preference relations with triangular fuzzy numbers are in consistent in nature, so we turned to neutrosophic in this paper. It is very important to take into account consistency of expert opinion and consensus degree in GDM. In order to distinguish the typical consistency, the concept of additive approximation consistency is proposed for triangular neutrosophic additive reciprocal matrices. The properties of triangular neutrosophic additive reciprocal matrices with additive approximation consistency are studied in detail. Second, by using $$(n-1)$$ restricted preference values, a triangular neutrosophic additive reciprocal preference relation with additive approximation consistency is constructed. The differences among expert’s opinions are measured using consensus degree. For generating a collective triangular neutrosophic additive reciprocal matrix with additive approximation consistency, the neutrosophic triangular weighted aggregation operator is used. Finally, a novel algorithm for the group decision-making problem with triangular neutrosophic additive reciprocal preference relations is presented. A numerical example is carried out to illustrate the proposed definitions and algorithm.

Single-Valued Neutrosophic Hybrid Arithmetic and Geometric Aggregation Operators and Their Decision-Making Method

Single-valued neutrosophic numbers (SVNNs) can express incomplete, indeterminate, and inconsistent information in the real world. Then, the common weighted aggregation operators of SVNNs may result in unreasonably aggregated results in some situations. Based on the hybrid weighted arithmetic and geometric aggregation and hybrid ordered weighted arithmetic and geometric aggregation ideas, this paper proposes SVNN hybrid weighted arithmetic and geometric aggregation (SVNNHWAGA) and SVNN hybrid ordered weighted arithmetic and geometric aggregation (SVNNHOWAGA) operators and investigates their rationality and effectiveness by numerical examples. Then, we establish a multiple-attribute decision-making method based on the SVNNHWAGA or SVNNHOWAGA operator under a SVNN environment. Finally, the multiple-attribute decision-making problem about the design schemes of punching machine is presented as a case to show the application and rationality of the proposed decision-making method.

Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach.

Autocratic decision making using group recommendations based on interval type-2 fuzzy sets, enhanced Karnik–Mendel algorithms, and the ordered weighted aggregation operator

Autocratic decision making using group recommendations (ADMUGRs) is a very important research topic in the research area of multiple attributes group decision making (MAGDM), which automatically modifies the weights of decision makers (DMs) to get MAGDM results. In this paper, a new method for ADMUGRs is proposed based on interval type-2 fuzzy sets (IT2FSs), enhanced Karnik-Mendel (EKM) algorithms, and the ordered weighted aggregation (OWA) operator. Each DM uses linguistic terms represented by IT2FSs to evaluate the attributes of alternatives, where different attributes can have different weights in [0, 1]. The evaluating matrices (EMs) and the weighting vectors (WVs) of the attributes given by the DMs are assessed by linguistic terms represented by IT2FSs. The proposed method can overcome the shortcomings of Chen and Hong's method (2014), Chen and Lee's method (2010) and Cheng et al.’s method (2016) for ADMUGRs in IT2FSs environments.

Adaptive linguistic weighted aggregation operators for multi-criteria decision making

In this paper, we propose new aggregation operators for multi-criteria decision making under linguistic settings. The proposed operators are based on two sets of criteria weights. Besides the primary conventional criteria weights, we introduce a method to deduce secondary criteria weights from the criteria evaluations, which reflect the role of the different criteria in discriminating among the alternatives. The properties of the proposed operators are investigated. An approach for the application of the said operators in a group multi-criteria decision making problem is presented. Following the same, the proposed operators are applied in a case study on supplier selection. The empirical validation of the proposed operators is performed on a set of 12 real datasets.Note: All usages of he, him, his in the paper, also refer to she, and her.

Applications of ordered weighted averaging (OWA) operators in environmental problems

<p>This paper presents an application of a prioritized weighted aggregation operator based on ordered weighted averaging (OWA) to deal with stakeholders' constructive participation in water resources projects. They have different degree of acceptance or preference regarding the measures and policies to be carried out, which lead to different environmental and socio-economic outcomes, and hence, to different levels of stakeholders’ satisfaction. The methodology establishes a prioritization relationship upon the stakeholders, which preferences are aggregated by means of weights depending on the satisfaction of the higher priority policy maker. The methodology establishes a prioritization relationship upon the stakeholders, which preferences are aggregated by means of weights depending on the satisfaction of the higher priority policy maker. The methodology has been successfully applied to a Public Participation Project (PPP) in watershed management, thus obtaining efficient environmental measures in conflict resolution problems under actors’ preference uncertainties.</p>