On the priority vector associated with a fuzzy preference relation and a multiplicative preference relation.

We propose two straightforward methods for deriving the priority vector associated with a fuzzy preference relation. Then, using transformations between multiplicative preference relations and fuzzy preference relations, we study the relationships between the priority vectors associated with these two types of preference relations.pairwise comparison matrix; fuzzy preference relation; priority vector

Least-square method to priority of the fuzzy preference relations with incomplete information

AbstractThe priority problem of incomplete preference relations is investigated. Using the transformation relation between multiplicative preference relation and fuzzy preference relation, we develop a least-square model to obtain the collective priority vector of the incomplete preference relations presented by multiple decision makers, with the existence condition of the solution being developed. Meanwhile, we extend this model to the cases of the fuzzy preference relations with complete information presented by multiple decision makers and the fuzzy preference relation with complete information presented by one decision maker. Finally, it is illustrated by a numerical example that the method proposed is feasible and effective

Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

A fuzzy multi-criteria decision making model for construction contractor prequalification

Selecting an appropriate contractor is essential for the success of any construction project. Contractor prequalification procedure makes it possible to admit for tendering only competent contractor. Prequalification is a multi-criteria decision problem that is, in essence, largely dependent on the uncertainty and vagueness in the nature of construction projects and subjective judgement of the decision-maker. This paper presents a systematic prequalification procedure, based on Fuzzy Set Theory, whose main differences and advantages in comparison with other models are the use of an algorithm to handle the inconsistencies in the fuzzy preference relation when pair-wise comparison judgements are used and the use of linguistic assessment or exact assessment of performance of the contractors on qualitative or quantitative criterion, respectively. Finally, a case study for the rehabilitation project of a building at Technical University of Cartagena is presented to illustrate the use of the proposed model and to demonstrate its effectiveness

A new type of preference relations: Fuzzy preference relations with self-confidence

Preference relations are very useful to express decision makers’ preferences over alternatives in the process of decision-making. However, multiple self-confidence levels are not considered in existing preference relations. In this study, we propose a new type of preference relations: fuzzy preference relations with self-confidence. A linear programming model is proposed for estimating priority vectors of this new type of preference relations. Finally, two numerical examples are provided to demonstrate the linear programming model, and a comparative analysis is used to show the influence of self-confidence levels on the decision-making results

A fuzzy approach to construction project risk assessment

The increasing complexity and dynamism of construction projects have imposed substantial uncertainties and subjectivities in the risk analysis process. Most of the real-world risk analysis problems contain a mixture of quantitative and qualitative data; therefore quantitative risk assessment techniques are inadequate for prioritizing risks. This article presents a risk assessment methodology based on the Fuzzy Sets Theory, which is an effective tool to deal with subjective judgement, and on the Analytic Hierarchy Process (AHP), which is used to structure a large number of risks. The proposed methodology incorporates knowledge and experience acquired from many experts, since they carry out the risks identification and their structuring, and also the subjective judgements of the parameters which are considered to assess the overall risk factor: risk impact, risk probability and risk discrimination. All of these factors are expressed by qualitative scales which are defined by trapezoidal fuzzy numbers to capture the vagueness in the linguistic variables. The most notable differences with other fuzzy risk assessment methods are the use of an algorithm to handle the inconsistencies in the fuzzy preference relation when pair-wise comparison judgements are necessary, and the use of trapezoidal fuzzy numbers until the defuzzification step. An illustrative example on risk assessment of a rehabilitation project of a building is used to demonstrate the proposed methodology

A fuzzy AHP multi-criteria decision-making approach applied to combined cooling, heating and power production systems

Most of the real-world multi-criteria decision-making (MCDM) problems contain a mixture of quantitative and qualitative criteria; therefore quantitative MCDM methods are inadequate for handling this type of decision problems. In this paper, a MCDM method based on the Fuzzy Sets Theory and on the Analytic Hierarchy Process (AHP) is proposed. This method incorporates a number of perspectives on how to approach the fuzzy MCDM problem, as follows: (1) combining quantitative and qualitative criteria (2) expressing criteria pair-wise comparison in linguistic terms and performance of the alternative on each criterion in linguistic terms or exact values when criterion is qualitative or quantitative, respectively, (3) converting all the assessments into trapezoidal fuzzy numbers, (4) using the difference minimization method to calculate the local weight of criteria, employing the algebraic operations of fuzzy numbers based on the concept of α-cuts, (4) calculating the global weight of criteria and the global performance of each alternative using geometric mean and the weighted sum, respectively, (5) using the centroid method to rank the alternatives. Finally, an illustrative example on evaluation of several combined cooling, heat and power production systems is used to demonstrate the effectiveness of the proposed methodology

A chi-square method for priority derivation in group decision making with incomplete reciprocal preference relations

This paper proposes a chi-square method (CSM) to obtain a priority vector for group decision making (GDM) problems where decision-makers’ (DMs’) assessment on alternatives is furnished as incomplete reciprocal preference relations with missing values. Relevant theorems and an iterative algorithm about CSM are proposed. Saaty’s consistency ratio concept is adapted to judge whether an incomplete reciprocal preference relation provided by a DM is of acceptable consistency. If its consistency is unacceptable, an algorithm is proposed to repair it until its consistency ratio reaches a satisfactory threshold. The repairing algorithm aims to rectify an inconsistent incomplete reciprocal preference relation to one with acceptable consistency in addition to preserving the initial preference information as much as possible. Finally, four examples are examined to illustrate the applicability and validity of the proposed method, and comparative analyses are provided to show its advantages over existing approaches

Distance-based consensus models for fuzzy and multiplicative 3 preference relations

This paper proposes a distance-based consensus model for fuzzy preference relations where the weights of fuzzy preference relations are automatically determined. Two indices, an individual to group consensus index (ICI) and a group consensus index (GCI), are introduced. An iterative consensus reaching algorithm is presented and the process terminates until both the ICI and GCI are controlled within predefined thresholds. The model and algorithm are then extended to handle multiplicative preference relations. Finally, two examples are illustrated and comparative analyses demonstrate the effectiveness of the proposed methods

A Local Adjustment Method to Improve Multiplicative Consistency of Fuzzy Reciprocal Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Preferences that verify the transitivity property are usually referred to as rational or consistent preferences. Existent methods to improve the consistency of inconsistent fuzzy reciprocal preference relations (FPRs) fail to retain the original preference values because they always derive a new FPR. This article presents a new inconsistency identification and modification (IIM) method to detect and rectify only the most inconsistent elements of an inconsistent FPR. As such, the proposed IIM can be considered a local adjustment method to improve multiplicative consistency (MC) of FPRs. The case of inconsistent FPRs with missing values, i.e., incomplete FPRs, is addressed with the estimation of the missing preferences with a constrained nonlinear optimization model by the application of the IIM method. The implementation process of the proposed algorithms is illustrated with numerical examples. Simulation experiments and comparisons with existent methods are also included to show that the new method requires fewer iterations than existent methods to improve the MC of FPRs and achieves better MC level, while preserving the original preference information as much as possible than the existent methods. Thus, the results presented in this article demonstrate the correctness, effectiveness, and robustness of the proposed method