Intuitionistic Multiplicative Preference Relations Research Articles

The strategy of consensus and consistency improving considering bounded confidence for group interval-valued intuitionistic multiplicative best-worst method

To significantly and reasonably enhance the individual consistency and group consensus in group best-worst method (GBWM) under interval-valued intuitionistic multiplicative environment, this study proposes a strategy of consensus and consistency improving considering bounded confidence. Firstly, based on the consistency definition of interval-valued intuitionistic multiplicative preference relations (IVIMPRs), the consistency definition for interval-valued intuitionistic multiplicative reference comparison relations (IVIMRCRs) is proposed. Subsequently, a two-stage consistency improving optimization model is constructed. Then, an interactively iterative consistency improving algorithm considering bounded confidence is designed. For GBWM with IVIMRCRs, the concept of consensus measure is first defined to assess the consensus level among individual IVIMRCRs, and then a two-stage consensus improving optimization model considering bounded confidence is constructed. Additionally, based on the above theories and models, an interactively iterative consensus improving algorithm considering bounded confidence and consistency management is designed for GBWM with IVIMRCRs. Finally, the practicality and effectiveness of the proposed GBWM are verified through an actual application case and simulation analyses. Meanwhile, the advantages of this method are explained through comparative analyses with the existing BWMs and group decision making (GDM) with IVIMPRs.

Generalized correlation coefficients of intuitionistic multiplicative sets and their applications to pattern recognition and clustering analysis

ABSTRACT Intuitionistic multiplicative preference relations (IMPRs) and intuitionistic multiplicative sets (IMSs) play a significant role in real-life problems that contain unsymmetrical and nonuniform information. Correlation coefficients are critical tools for evaluating such information, especially in medical areas and clustering analysis, where the relationship between objects in the given data is required. Despite the importance of this subject, there is only one approach in the literature regarding the correlation coefficients of IMSs and existing coefficients have certain disadvantages. In this paper, we propose a parametric generalisation of these correlation coefficients on IMSs and apply them to medical diagnosis, taxonomy, and clustering. To that end, some disadvantages of existing correlation coefficients are listed first. Then, with some theoretical work, we derive a parametric generalisation of these coefficients and their weighted forms. To better illustrate how the parametric generalisation of correlation coefficients improves the results, numerical parametric solutions of existing examples are presented with detailed comparisons. Moreover, a novel algorithm is introduced for clustering using proposed correlation coefficients in IMSs. Finally, three real-life examples are provided to demonstrate the superiority of the proposed generalised correlation coefficients and the clustering algorithm in specific applications.

A two-objective-optimization-driven group decision making model under the bipolarity of decision information

When building consensus in group decision making (GDM) under uncertainty, an important yet rarely studied issue is to find the Pareto solutions of multi-objective optimization model. This paper reports a two-objective (2Ob) optimization driven consensus model in GDM by describing the bipolarity of judgements through intuitionistic multiplicative preference relations (IMPRs). First, it is realized that the inherent property of IMPRs is the hesitancy degree. A novel inconsistency index of IMPRs is proposed by combining the effects of hesitancy degree and inconsistency of boundary matrices. Second, the compatibility measure between two IMPRs is utilized to quantify the consensus level (CL) of decision makers. The threshold of acceptable group CL is found to decrease with the order of IMPRs for the first time. A 2Ob optimization model is constructed by minimizing group inconsistency degree and group CL, respectively. Third, the method of equipping two flexibility degrees to each expert is proposed for optimizing individual IMPRs. It is interesting to find that the constructed granularity matrix is different from interval-valued IMPRs. A multi-objective particle swarm optimization algorithm is adopted to obtain a set of Pareto solutions to GDM problems. Case studies are carried out to illustrate the proposed consensus reaching model. The results help to identify how to provide flexible decisions in GDM under some complexity and uncertainty of a practical problem.

Consistency and consensus enhancing in group decision making with interval-valued intuitionistic multiplicative preference relations based on bounded confidence

Consistency and consensus enhancing in group decision making with interval-valued intuitionistic multiplicative preference relations based on bounded confidence

Consensus reaching with minimum adjustment and consistency management in group decision making with intuitionistic multiplicative preference relations

Intuitionistic multiplicative preference relation (IMPR) is an efficient tool for describing the paired comparisons between objectives in group decision making (GDM). Existing GDM methods with IMPRs overlook the hesitancy of IMPRs and lack a feedback mechanism of adjustment in the consensus reaching process (CRP). Thus, to ensure that the adjusted IMPRs can provide reliable information for decision making, the hesitancy measure for IMPRs is first incorporated into the process of enhancing consistency and consensus. A new consistency index for IMPRs is defined based on distance measure. Some goal programming models are constructed for enhancing consistency of IMPR. For a collection of IMPRs with unacceptable consistency and consensus, based on the optimization model and the identification rule and direction rule (IR-DR), an interactive iterative algorithm is designed for enhancing consistency and consensus, which can greatly save the completion time of consensus reaching and maintain primitive information to the maximum. Subsequently, a distance-based aggregation model is constructed to derive the group IMPR by considering different experts’ decision-making principles. Thereby, a new GDM method with IMPRs considering minimum adjustment is proposed. Moreover, the rationality and effectiveness of the proposed method are verified through a numerical example and some related simulation experiments. Meanwhile its merits are illustrated by comparison analyses.

Revisiting the consistency improvement and consensus reaching processes of intuitionistic multiplicative preference relations

Revisiting the consistency improvement and consensus reaching processes of intuitionistic multiplicative preference relations

Consensus Reaching with Minimum Adjustment and Consistency Management in Group Decision Making with Intuitionistic Multiplicative Preference Relations

Consensus Reaching with Minimum Adjustment and Consistency Management in Group Decision Making with Intuitionistic Multiplicative Preference Relations

Consistency and Consensus Enhancing in Group Decision Making with Interval-Valued Intuitionistic Multiplicative Preference Relations Based on Bounded Confidence

Consistency and Consensus Enhancing in Group Decision Making with Interval-Valued Intuitionistic Multiplicative Preference Relations Based on Bounded Confidence

Two different approaches for consistency of intuitionistic multiplicative preference relation using directed graph

Consistency is an important issue that causes wide public concern of decision makers in the decision-making process. The lack of consistency in preference relations results in a vague solution. The main goal of this paper is to achieve the consistent intuitionistic multiplicative preference relation using a graphical approach. We have proposed two different approaches of the consistency for intuitionistic multiplicative preference relation (IMPR). In the first approach, we propose an algorithm to achieve the consistency of IMPR by using the cycles of various lengths in a directed graph. The second approach proves isomorphism between IMPRs and asymmetric multiplicative preference relations. The result explores the methodologies developed for asymmetric multiplicative preference relations in the case of IMPRs and achieves the consistency of asymmetric multiplicative preference relations using a directed graph. Sometimes the decision maker may not be able to provide the complete reference. So the above-said method is applied for an incomplete IMPR; consistency plays an important role here. The examples are provided to illustrate both the ways in all cases.

A new group decision-making method with incomplete intuitionistic multiplicative preference relations

PurposeConsistency and consensus are two important research issues in group decision-making (GDM). Considering some drawbacks associated with these two issues in existing GDM methods with intuitionistic multiplicative preference relations (IMPRs), a new GDM method with complete IMPRs (CIMPRs) and incomplete IMPRs (ICIMPRs) is proposed in this paper.Design/methodology/approachA mathematically programming model is constructed to judge the consistency of CIMPRs. For the unacceptably consistent CIMPRs, a consistency-driven optimization model is constructed to improve the consistency level. Meanwhile, a consistency-driven optimization model is constructed to supplement the missing values and improve the consistency level of the ICIMPRs. As to GDM with CIMPRs, first, a mathematically programming model is built to obtain the experts' weights, after that a consensus-driven optimization model is constructed to improve the consensus level of CIMPRs, and finally, the group priority weights of alternatives are obtained by an intuitionistic fuzzy programming model.FindingsThe case analysis of the international exchange doctoral student selection problem shows the effectiveness and applicability of this GDM method with CIMPRs and ICIMPRs.Originality/valueFirst, a novel consistency definition of CIMPRs is presented. Then, a consistency-driven optimization model is constructed, which supplements the missing values and improves the consistency level of ICIMPRs simultaneously. Therefore, this model greatly improves the efficiency of consistency improving. Experts' weights determination method considering the subjective and objective information is proposed. The priority weights of alternatives are determined by an intuitionistic fuzzy (IF) programming model considering the risk preference of experts, so the method determining priority weights is more flexible and agile. Based on the above theoretical basis, a new GDM method with CIMPRs and ICIMPRs is proposed in this paper.

A decision making model based on intuitionistic multiplicative preference relations with approximate consistency

A decision making model based on intuitionistic multiplicative preference relations with approximate consistency

A group decision making method considering both the consistency and consensus of intuitionistic multiplicative preference relations

This paper aims to develop a new group decision making (GDM) approach with intuitionistic multiplicative preference relations (IMPRs) by considering the consistency and consensus. Using the distance between a given IMPR and its corresponding underlying consistent IMPR, the concept of acceptably consistent IMPR is introduced, then an automatic algorithm is designed to repair the inconsistent IMPR to be of acceptable consistency. Meanwhile, each decision maker's consensus level is evaluated by the deviation between his/her individual IMPR and the group IMPR, and another algorithm for reaching acceptable level of consensus is provided. Moreover, the consensus improving process can guarantee that the modified IMPRs still be acceptably consistent, then the normalized intuitionistic multiplicative priority weight vector can be obtained from a mathematical programming model. A step-by-step algorithm based on the consistency and consensus of IMPRs is offered. Finally, two examples and the corresponding comparative analyses are presented to demonstrate the effectiveness of the proposed method.

A novel method to derive the intuitionistic multiplicative priority vector for the intuitionistic multiplicative preference relation

A novel method to derive the intuitionistic multiplicative priority vector for the intuitionistic multiplicative preference relation

A rational and consensual method for group decision making with interval-valued intuitionistic multiplicative preference relations

Interval-valued intuitionistic multiplicative variables (IVIMVs) can conveniently and effectively represent the uncertain multiplicative preferred and non-preferred judgements of decision makers, this paper studies group decision making (GDM) with interval-valued intuitionistic multiplicative preference relations (IVIMPRs). To calculate the interval-valued intuitionistic multiplicative priority weight vector reasonably, a new consistency concept is introduced that satisfies robustness and upper triangular property. Following this concept, models to judge the consistency and obtain consistent IVIMPRs from inconsistent ones are constructed, respectively. To address the problem of incomplete preferences, consistency-based model to determine missing values is built. Furthermore, we study the consensus for GDM with IVIMPRs and provide a new consensus approach. When an acceptable consensus level is not achieved, an interactive and automatic adjustment method is applied to reach a better consensus level. Following discussion about consistency and consensus, an algorithm for GDM is offered that can address inconsistent and incomplete IVIMPRs. Finally, a practical problem about selecting the steel supplier is selected to show the application of the new method.

Two algorithms for group decision making based on the consistency of intuitionistic multiplicative preference relation

Two algorithms for group decision making based on the consistency of intuitionistic multiplicative preference relation

Distance-based consensus reaching process for group decision making with intuitionistic multiplicative preference relations

The intuitionistic multiplicative preference relation uses Saaty’s 1∕9-9 scale to depict people’s opinions from the prior and not prior aspects. Due to its objectivity in representing people’s cognition, the intuitionistic multiplicative preference relation has attracted extensive attentions of scholars. In this paper, we study the distance-based consensus measures in the context of group decision-making with intuitionistic multiplicative preference relations. First of all, some new distance measures between intuitionistic multiplicative numbers/sets are proposed, which contains the improved Hamming distance, the improved Euclidean distance, and their weighted forms. Then, we investigate their desirable properties. To aid the group decision-making process, we further develop a new consensus measures regarding intuitionistic multiplicative preference relations based on the proposed distance measures. Afterwards, a new group decision-making method is proposed to solve the complex group decision-making problems with intuitionistic multiplicative preference relations. Finally, an example concerning the project investment selection is given to demonstrate the proposed group decision-making method, and then we compare the proposed method with other existing group decision-making methods with intuitionistic multiplicative preference relations in detail.

Group decision making with incomplete intuitionistic multiplicative preference relations

Intuitionistic multiplicative preference relations (IMPRs) have been widely applied in decision making for their ability to efficiently express the uncertainty of information. This paper investigates the decision making with incomplete IMPRs. First, a new consistency of incomplete IMPRs is defined. Then, we present some optimization models for estimating missing values by maximizing the consistency level. After that, the group IMPR is derived by using membership degrees in individual intuitionistic multiplicative judgments. Subsequently, a transformation method is offered to build a consistent IMPR through a normalized intuitionistic fuzzy priority weight vector. Moreover, a model is presented to get intuitionistic fuzzy priority weights. Finally, we propose a group decision making (GDM) method with incomplete IMPRs. A practical GDM problem on venue selection for communication drills is offered to indicate the specific application of main theoretical results.

A priority-based intuitionistic multiplicative UTASTAR method and its application in low-carbon tourism destination selection

The intuitionistic multiplicative preference relation extends Saaty’s multiplicative preference relation by membership and non-membership functions to describe decision-makers’ preferences on objects (alternatives or criteria), and the product of pairwise membership and non-membership degrees is less than or equal to one. In recent years, the intuitionistic multiplicative preference relation has attracted increasing attention and many methods have been proposed to handle multiple criteria decision making (MCDM) problems. However, few of the existing methods can be used to tackle the MCDM problems with both quantitative and qualitative criteria. To overcome this challenge, in this paper, a novel MCDM method called the priority-based intuitionistic multiplicative UTASTAR method is proposed, which combines a new intuitionistic multiplicative prioritization method and the UTASTAR method within the context of intuitionistic multiplicative sets. The consistency checking and improving processes are considered in the weight-determining method. A case study regarding the low-carbon tourism destination selection is adopted to illustrate the applicability of the proposed method. The effectiveness and superiority of the proposed method are further verified by comparative analyses and discussions.

Real-Time Performance Evaluation of the Combustion Process of Coke Oven

Real-time performance assessment is one of the main methods to guarantee the steady operation of production during the combustion process of a coke oven. In this study, a real-time assessment method is proposed for this combustion process based on the analytic hierarchy process (AHP) and intuitionistic multiplicative preference relation. Relevant scholars, senior engineers, and elite workers participated in this project to build the AHP model with three aspects (i.e. safety, stability, and economic benefit) and perform pairwise comparisons of criteria and sub-criteria through group decisions. To support real-time, the pairwise comparisons of alternatives were realized by an automated method using measurement values. This comprehensive assessment method demonstrates ability to provide real-time performance evaluation for the combustion process. An experiment was conducted to evaluate the effectiveness and viability of the proposed method.

A Novel Group Decision-Making Method for Interval-Valued Intuitionistic Multiplicative Preference Relations

In this paper, we propose a consistency and consensus-based method to solve the group decision-making (GDM) problems within the framework of interval-valued intuitionistic multiplicative preference relations (IVIMPRs). First, we introduce a similarity measure that expresses the similarity between two decision makers (DMs). Then, a similarity-based consensus index is offered to evaluate closeness between individuals' judgments. Based on the consensus index, the concept of acceptable consensus for IVIMPRs is presented. In the sequel, a consistency and consensus improvement model that aims at retaining original opinions of the DMs is introduced to make consistency and consensus of IVIMPRs acceptable. Moreover, the DMs' comprehensive weights are obtained by combining their subjective weights and objective weights. Afterward, to derive priority weights of alternatives, a programming model is established and solved by three approaches considering DMs' different risk attitudes. Finally, a GDM method with IVIMPRs is offered, and its application to select the partners is offered.