Prioritization Relationship Research Articles

A Fermatean fuzzy Fine–Kinney for occupational risk evaluation using extensible MARCOS with prospect theory

The extant Fine–Kinney frameworks are insufficient to tackle the risk evaluation problem with Fermatean fuzzy information, in which the prioritization degrees and psychological characteristics of decision-makers are considered. Hence, this study develops a hybrid Fine–Kinney-based occupational risk evaluation framework with an extended Fermatean fuzzy MARCOS method (measurement of alternatives and ranking to Compromise solution). Such a MARCOS method improves conventional MARCOS by integrating Fermatean fuzzy prioritized weighted average operator and prospect theory. This improved method has the capability to handle the occupational risk analysis problem with Fermatean fuzzy data in the risk ranking procedure considering the prioritization degrees and bounded rational behavior of decision-makers. In addition, the Fermatean fuzzy numbers-based risk rating scales are established to transform the linguistic risk scores from decision-makers, it allows for handling uncertain risk rating information from decision-makers more effectively. Further, the improved MARCOS method is incorporated into the occupational risk ranking procedure, as it considers the decision-maker’s prioritization relationships among decision-makers and their reference point effect in occupational risk priority calculation. After that, an occupational risk analysis case for construction operations is selected to test the applicability and validity of the proposed framework. The result indicates that the occupational risk OR6 (Back injury) is the most serious risk with the lowest utility function value (-0.324), and OR7 (Tendinitis) is the least severe risk with the highest utility function value (0.682). Finally, sensitivity exploration and comparative study are implemented to further test the advantages of the developed framework.

Pythagorean fuzzy prioritized aggregation operators with priority degrees for multi-criteria decision-making

PurposeThe authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined. Further, based on these operators, a decision-making approach is presented under the Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.Design/methodology/approachIn real-world situations, Pythagorean fuzzy numbers are exceptionally useful for representing ambiguous data. The authors look at multi-criteria decision-making issues in which the parameters have a prioritization relationship. The idea of a priority degree is introduced. The aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees.FindingsThe authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined. Further, based on these operators, a decision-making approach is presented under the Pythagorean fuzzy set environment. An illustrative example related to the selection of the best alternative is considered to demonstrate the efficiency of the proposed approach.Originality/valueThe aggregation operators are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, the authors develop some prioritized operators named Pythagorean fuzzy prioritized averaging operator with priority degrees and Pythagorean fuzzy prioritized geometric operator with priority degrees. The properties of the existing method are routinely compared to those of other current approaches, emphasizing the superiority of the presented work over currently used methods. Furthermore, the impact of priority degrees on the aggregate outcome is thoroughly examined.

Sustainable thermal power equipment supplier selection by Einstein prioritized linear Diophantine fuzzy aggregation operators

<abstract><p>Clean energy potential can be used on a large scale in order to achieve cost competitiveness and market effectiveness. This paper offers sufficient information to choose renewable technology for improving the living conditions of the local community while meeting energy requirements by employing the notion of q-rung orthopair fuzzy numbers (q-ROFNs). In real-world situations, a q-ROFN is exceptionally useful for representing ambiguous/vague data. A multi-criteria decision-making (MCDM) is proposed in which the parameters have a prioritization relationship and the idea of a priority degree is employed. The aggregation operators (AOs) are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, some prioritized operators with q-ROFNs are proposed named as "q-rung orthopair fuzzy prioritized averaging ($\text{q-ROFPA} _d $) operator with priority degrees and q-rung orthopair fuzzy prioritized geometric ($\text{q-ROFPG} _d $) operator with priority degrees". The results of the proposed approach are compared with several other related studies. The comparative analysis results indicate that the proposed approach is valid and accurate which provides feasible results. The characteristics of the existing method are often compared to other current methods, emphasizing the superiority of the presented work over currently used operators. Additionally, the effect of priority degrees is analyzed for information fusion and feasible ranking of objects.</p></abstract>

A Novel Green Supplier Selection Method Based on the Interval Type-2 Fuzzy Prioritized Choquet Bonferroni Means

In view of the environment competencies, selecting the optimal green supplier is one of the crucial issues for enterprises, and multi-criteria decision-making (MCDM) methodologies can more easily solve this green supplier selection (GSS) problem. In addition, prioritized aggregation (PA) operator can focus on the prioritization relationship over the criteria, Choquet integral (CI) operator can fully take account of the importance of criteria and the interactions among them, and Bonferroni mean (BM) operator can capture the interrelationships of criteria. However, most existing researches cannot simultaneously consider the interactions, interrelationships and prioritizations over the criteria, which are involved in the GSS process. Moreover, the interval type-2 fuzzy set (IT2FS) is a more effective tool to represent the fuzziness. Therefore, based on the advantages of PA, CI, BM and IT2FS, in this paper, the interval type-2 fuzzy prioritized Choquet normalized weighted BM operators with λ fuzzy measure and generalized prioritized measure are proposed, and some properties are discussed. Then, a novel MCDM approach for GSS based upon the presented operators is developed, and detailed decision steps are given. Finally, the applicability and practicability of the proposed methodology are demonstrated by its application in the shared-bike GSS and by comparisons with other methods. The advantages of the proposed method are that it can consider interactions, interrelationships and prioritizations over the criteria simultaneously.

Innovative q-rung orthopair fuzzy prioritized aggregation operators based on priority degrees with application to sustainable energy planning: A case study of Gwadar

<abstract><p>Clean energy potential can be used on a large scale in order to achieve cost competitiveness and market effectiveness. This paper offers sufficient information to choose renewable technology for improving the living conditions of the local community while meeting energy requirements by employing the notion of q-rung orthopair fuzzy numbers (q-ROFNs). In real-world situations, a q-ROFN is exceptionally useful for representing ambiguous/vague data. A multi-criteria decision-making (MCDM) is proposed in which the parameters have a prioritization relationship and the idea of a priority degree is employed. The aggregation operators (AOs) are formed by awarding non-negative real numbers known as priority degrees among strict priority levels. Consequently, some prioritized operators with q-ROFNs are proposed named as "q-rung orthopair fuzzy prioritized averaging (q-ROFPA<sub><italic>d</italic></sub>) operator with priority degrees and q-rung orthopair fuzzy prioritized geometric (q-ROFPG<sub><italic>d</italic></sub>) operator with priority degrees". The results of the proposed approach are compared with several other related studies. The comparative analysis results indicate that the proposed approach is valid and accurate which provides feasible results. The characteristics of the existing method are often compared to other current methods, emphasizing the superiority of the presented work over currently used operators. Additionally, the effect of priority degrees is analyzed for information fusion and feasible ranking of objects.</p></abstract>

Prioritized weighted aggregation operators under complex pythagorean fuzzy information

Complex Pythagorean fuzzy (CPF), a worthwhile generalization of Pythagorean fuzzy set, is a powerful tool to deal with two-dimensional or periodic information. In this paper, we develop two prioritized aggregation operators (AOs) under CPF environment, namely, complex Pythagorean fuzzy prioritized weighted averaging (CPFPWA) operator and complex Pythagorean fuzzy prioritized weighted geometric (CPFPWG) operator. We consider the prioritization relationship among criteria and decision makers (DMs) to make our result more accurate as in real decision making (DM) problems, the criteria and DMs have different priority level. Further, we discuss remarkable properties of our proposed AOs. Moreover, we promote the evolution of MCDM problem by investigating an algorithm in CPF environment with its flow chart. Finally, to check the superiority and validity of proposed operators, we compare the computed results with the different existing techniques.

Dual hesitant fuzzy graphs with applications to multi-attribute decision making

In real world, there exist a kind of Multi-Attribute Decision Making (MADM) problems in which correlations and prioritization relationships of attributes can be found. The notion of Fuzzy Graphs (FGs) performs well when expressing correlations between attributes via edges between vertices in fuzzy information systems, which makes it possible for addressing correlational MADM problems. In addition, as a significant information depiction tool, Dual Hesitant Fuzzy Sets (DHFSs) generalize traditional Intuitionistic Fuzzy Sets (IFSs) to the context of hesitations, thus DHFSs excel in recording numerous imprecise and hesitant information. In this paper, we aim to investigate FGs in the Dual Hesitant Fuzzy (DHF) background and further explore efficient approaches to complicated MADM situations. Following the above motivation, we first develop the definition of Dual Hesitant Fuzzy Graphs (DHFGs). Then, some common operational laws and mapping relationships are put forward. Afterwards, we construct a two-stage MADM approach by means of DHFGs for addressing complicated MADM situations with correlations and prioritization relationships. At last, a realistic case study along with a comparative analysis is presented to show the applicability of the established methodology. The proposed model and approach are conducive to addressing DHF MADM problems that are characterized by correlations and prioritization relationships between attributes at the same time, and further enrich the family of DHF MADM methods to a large extent.

Probabilistic Hybrid Linguistic Approaches for Multiple Attribute Group Decision Making with Decision Hesitancy and the Prioritization of Attribute Relationships

Focusing on ill-structured multiple attribute decision-making (MADM) problems, including decision hesitancy and attribute prioritization relationships, this paper investigates appropriate approaches for decision making. Firstly, we introduce the probabilistic hybrid linguistic term set (P-HLTS) for capturing probabilistic preferences about possible linguistic labels belonging to a wide range of hesitant linguistic term sets. Entropy and distance measurements for P-HLTS are developed without arbitrary complementing operations. To facilitate decision making with attribute prioritization relationships, we present a probabilistic uncertain balanced linguistic-prioritized weighted average (PUBL-PWA) operator and the probabilistic uncertain balanced linguistic-induced prioritized ordered weighted average (PUBL-IPOWA) operator. In terms of the strength of the above tools, we further construct two multiple attribute group decision-making (MAGDM) approaches under P-HLTS environments, namely, an approach for decision-making situations where attribute prioritization relationships are known in advance and the relative importance of decision makers (DMs) or decision-making units (DMUs) is not required for consideration, and second approach for decision-making situations where both attribute prioritization relationships and the weighted vectors of DMs or DMUs are explicitly unknown. In general, our proposed approaches are more flexible and practical when considering heterogeneous opinions, avoiding information distortion brought about by complementing operation-based distance measures. Furthermore, illustrative application studies are conducted to verify our developed approaches.

A multi-attribute decision-making method with prioritization relationship and hesitant fuzzy decision information

A multi-attribute decision-making method with prioritization relationship and hesitant fuzzy decision information

Interval-valued intuitionistic fuzzy aggregation methodology for decision making with a prioritization of criteria

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first propose a prioritized arithmetic mean to IVIF multi-criteria decision making (MCDM) problem where there is a linear ordering among the criteria.The proposed aggregation operator overcomes the existing prioritized aggregation operator's shortcomings that it is not monotone with respect to the total order on interval-valued intuitionistic fuzzy values (IVIFVs).We also prove that it is bounded and monotone with respect to the total order on IVIFVs, and therefore is a true generalization of such operations.We finally propose an aggregation operators-based two-step procedure to IVIF MCDM in the situation that more than one criteria exist at some priority level.

Hesitant 2-tuple linguistic Bonferroni operators and their utilization in group decision making

Hesitant 2-tuple linguistic variable realizes a graded information approach to characterize the uncertainty of human cognition. This study is concerned with the development of new aggregation operators and aims to design a new group decision making approach to address the information fusion involving the interrelationship between aggregated terms and the prioritization relationship among decision makers under hesitant 2-tuple linguistic situation. Firstly, hesitant 2-tuple linguistic Bonferroni mean (H2TLBM) operator and prioritized weighted hesitant 2-tuple linguistic Bonferroni mean (PWH2TLBM) operator are established. Subsequently, some pertinent properties and special forms of the developed operators are studied in detail. To employ the proposed operators to solve group decision making problems, a novel TODIM (an acronym in Portuguese of interactive and multiple attribute decision making) method based on possibility degree is developed under the situation of hesitant 2-tuple linguistic information. The designed decision making method not only inherits the merits of the traditional TODIM approach, but also characterizes the interrelationship of criteria. The detailed process of solving problems is exemplified to highlight the practicality and feasibility of the designed method. Furthermore, comparative analysis with other methods is carried out to further offer insights on the designed decision method.

Hesitant fuzzy linguistic prioritized superiority and inferiority ranking method and its application in sustainable energy technology evaluation

The aim of this study is to develop a hesitant fuzzy linguistic prioritized superiority and inferiority ranking method, which is used to solve multi-criteria decision making (MCDM) problems. In the MCDM problems, all criteria are expressed at different priority levels and the importance degrees of criteria and the evaluation values of alternatives are both expressed by hesitant fuzzy linguistic term sets (HFLTSs). The contribution of this study concerns the following: (1) A novel algorithm is proposed to determine the real-valued relative weights of criteria according to the given importance degrees of criteria, which are expressed by HFLTSs; (2) We model the prioritization relationships among criteria by revising the real-valued weights of criteria. The revision is based on the satisfaction degrees of evaluation values of alternatives under higher priority criteria to the decision maker (DM)’s requirements; (3) Based on the intrinsic characteristics of HFLTSs, we propose a hesitant fuzzy linguistic prioritized superiority and inferiority ranking method, in which the prioritization relationships among criteria and the DM's requirements for criteria are taken into account; (4) The proposed method is applied to the sustainable energy technology evaluation, and then, a comparative analysis is completed to show its practicability and availability.

Group Decision-Making Approach Based on Generalized Grey Linguistic 2-Tuple Aggregation Operators

To address complexity information fusion problems involving fuzzy and grey uncertainty information, we develop prioritized averaging aggregation operator and Bonferroni mean aggregation operator with grey linguistic 2-tuple variables and apply them to design a new decision-making scheme. First, the grey linguistic 2-tuple prioritized averaging (GLTPA) operator is developed to characterize the prioritization relationship among experts and employed to fuse experts’ information into an overall opinion. Second, we establish dual generalized grey linguistic 2-tuple weighted Bonferroni mean (DGGLTWBM) operator to capture the interrelationship among any attribute subsets, which can be reduced to some conventional operators by adjusting parameter vector. On that basis, a flexible group decision-making approach with fuzzy and grey information is designed and applied to an evaluation problem, in which grey relationship analysis (GRA) method and a linear programming model are combined to extract attribute weights from partially known attribute information. Furthermore, an illustrative example is employed to illustrate the practicality and flexibility of the designed method by conducting the related comparative studies.

Pythagorean fuzzy prioritized aggregation operators and their application to multi-attribute group decision making

Pythagorean fuzzy set is a useful tool to deal with the fuzziness and vagueness. Many aggregation operators have been proposed by many researchers based on Pythagorean fuzzy sets. But the current methods are under the assumption that the decision makers and the attributes are at the same priority level. However, in real group decision-making problems the attribute and decision makers may have different priority level. Therefore, in this paper, we develop multi-attribute group decision-making based on Pythagorean fuzzy sets where there exists a prioritization relationship over the attributes and decision makers. First, we develop Pythagorean fuzzy prioritized weighted average operator and Pythagorean fuzzy prioritized weighted geometric operator. Then we study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Moreover, we propose a multi-attribute group decision-making approach based on the developed operators under Pythagorean fuzzy environment. Finally, a numerical example is provided to illustrate the practicality of the proposed approach.

Prioritized Aggregation Operators and Correlated Aggregation Operators for Hesitant 2-Tuple Linguistic Variables

The aggregation operator is a potential tool to fuse the information derived from multisources, which has been applied in group decision, combination classification and scheduling clusters successfully. To better characterize complex decision situations and capture complex opinions of decision-makers (DMs), aggregation operators are required to be explored from different viewpoints. In view of information fusion of hesitant 2-tuple linguistic variables, this paper establishes four new aggregation operators, which are called the hesitant 2-tuple linguistic prioritized weighted averaging (H2TLPWA) aggregation operator, hesitant 2-tuple linguistic prioritized weighted geometric (H2TLPWG) aggregation operator, hesitant 2-tuple linguistic correlated averaging (H2TLCA) aggregation operator, and hesitant 2-tuple linguistic correlated geometric (H2TLCG) aggregation operator, respectively. The H2TLPWA aggregation operator and H2TLPWG aggregation operator can characterize the prioritization relationship of the aggregated arguments. The H2TLCA aggregation operator and H2TLCG aggregation operator can describe dependencies between criteria in decision-making problem solving. Moreover all aggregation operation operators have the properties of idempotency, boundedness and monotonicity, and the H2TLCA aggregation operator and H2TLCG aggregation operator are also verified to be symmetric functions. In addition, the H2TLPWA aggregation operator and H2TLCA aggregation operator are employed to settle multicriteria decision-making problems with hesitant 2-tuple linguistic terms. By virtue of predefining discrete initial linguistic labels with symmetrical distribution, the detailed steps of the decision-making process with an example are given to illustrate their practicality and effectiveness.

Dual Hesitant Bipolar Fuzzy Hamacher Prioritized Aggregation Operators in Multiple Attribute Decision Making

In this paper, we investigate the dual hesitant bipolar fuzzy multiple attribute decision making problems in which there exists a prioritization relationship over attributes. Then, motivated by the idea of Hamacher operations and prioritized aggregation operators, we have developed some Hamacher prioritized aggregation operators for aggregating dual hesitant bipolar fuzzy information: dual hesitant bipolar fuzzy Hamacher prioritized average operator, dual hesitant bipolar fuzzy Hamacher prioritized geometric operator, dual hesitant bipolar fuzzy Hamacher prioritized weighted average operator, dual hesitant bipolar fuzzy Hamacher prioritized weighted geometric operator. Then, we have utilized these operators to develop some approaches to solve the dual hesitant bipolar fuzzy multiple attribute decision making problems. Finally, a real-world example is then analyzed to illustrate the relevance and effectiveness of the proposed methodology.

Water Policies and Conflict Resolution of Public Participation Decision-Making Processes Using Prioritized Ordered Weighted Averaging (OWA) Operators

There is a growing interest in environmental policies about how to implement public participation engagement in the context of water resources management. This paper presents a robust methodology, based on ordered weighted averaging (OWA) operators, to conflict resolution decision-making problems under uncertain environments due to both information and stakeholders’ preferences. The methodology allows integrating heterogeneous interests of the general public and stakeholders on account of their different degree of acceptance or preference and level of influence or power regarding the measures and policies to be adopted, and also of their level of involvement (i.e., information supply, consultation and active involvement). These considerations lead to different environmental and socio-economic outcomes, and levels of stakeholders’ satisfaction. The methodology establishes a prioritization relationship over the stakeholders. The individual stakeholders’ preferences are aggregated through their associated weights, which depend on the satisfaction of the higher priority decision maker. The methodology ranks the optimal management strategies to maximize the stakeholders’ satisfaction. It has been successfully applied to a real case study, providing greater fairness, transparency, social equity and consensus among actors. Furthermore, it provides support to environmental policies, such as the EU Water Framework Directive (WFD), improving integrated water management while covering a wide range of objectives, management alternatives and stakeholders.

Digraph-based Requirement Prioritization for Comparisons Reduction

The increasing size of requirements is challenging to requirement prioritization in a large scale software engineering projects. Most existing requirement prioritization methods have high accuracy but suffer a problem of scalability. To overcome the aforementioned shortcomings, this paper proposes a prioritization approach based on Requirement digraph (R-digraph). Via a transformation from requirements to nodes and from prioritization relationships to edges, we propose one algorithm to build the R-digraph with less human interactions, and another algorithm is designed to perform the dominance test and to output the final rank of requirements. A comprehensive experiment is conducted to evaluate the performance of our proposal. The results show that our approach achieves reliable performance in terms of less human interaction than the state-of-the-art.

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>

Normal neutrosophic multiple attribute decision making based on generalized prioritized aggregation operators

Normal neutrosophic set, which allows a combination of the normal fuzzy number and the neutrosophic number, is a powerful tool for handling the incompleteness, indeterminacy and inconsistency of evaluation information. Based on the opinion of prioritized aggregation operators developed to describe the prioritization relationships among several attributes, this paper investigates some prioritized aggregation operators for aggregating the normal neutrosophic information, such as normal neutrosophic prioritized weighted averaging operator and normal neutrosophic prioritized weighted geometric operator, and then extends these operators to the generalized prioritized weighted aggregation operators, including normal neutrosophic generalized prioritized weighted averaging operator and normal neutrosophic generalized prioritized weighted geometric operator, respectively. They can take into account the prioritization facts in the aggregated information. Moreover, some of their desirable properties are investigated in detail. A multiple attribute decision-making method is developed for solving a kind of problems in which the decision attributes have different priority level commonly and they take the form of normal neutrosophic numbers. Finally, an illustrative example based on the prioritization relationship over the evaluation data is given to depict the effectiveness and feasibility of the developed decision-making method, which are then compared to the existing approaches.