In this paper, a new multi-criteria problem solving method—the Full Consistency Method (FUCOM)—is proposed. The model implies the definition of two groups of constraints that need to satisfy the optimal values of weight coefficients. The first group of constraints is the condition that the relations of the weight coefficients of criteria should be equal to the comparative priorities of the criteria. The second group of constraints is defined on the basis of the conditions of mathematical transitivity. After defining the constraints and solving the model, in addition to optimal weight values, a deviation from full consistency (DFC) is obtained. The degree of DFC is the deviation value of the obtained weight coefficients from the estimated comparative priorities of the criteria. In addition, DFC is also the reliability confirmation of the obtained weights of criteria. In order to illustrate the proposed model and evaluate its performance, FUCOM was tested on several numerical examples from the literature. The model validation was performed by comparing it with the other subjective models (the Best Worst Method (BWM) and Analytic Hierarchy Process (AHP)), based on the pairwise comparisons of the criteria and the validation of the results by using DFC. The results show that FUCOM provides better results than the BWM and AHP methods, when the relation between consistency and the required number of the comparisons of the criteria are taken into consideration. The main advantages of FUCOM in relation to the existing multi-criteria decision-making (MCDM) methods are as follows: (1) a significantly smaller number of pairwise comparisons (only n − 1), (2) a consistent pairwise comparison of criteria, and (3) the calculation of the reliable values of criteria weight coefficients, which contribute to rational judgment.

https://www.mdpi.com/2073-8994/10/9/393/pdf

A New Model for Determining Weight Coefficients of Criteria in MCDM Models: Full Consistency Method (FUCOM)

Application of the GIS-DANP-MABAC multi-criteria model for selecting the location of wind farms: A case study of Vojvodina, Serbia

This paper presents a new approach for the treatment of uncertainty which is based on interval-valued fuzzy-rough numbers (IVFRN). It is shown that by integrating the rough approach with the traditional fuzzy approach, the subjectivity that exists when defining the borders of fuzzy sets is eliminated. IVFRN make decision making possible using only the internal knowledge in the operative data available to the decision makers. In this way objective uncertainties are used and there is no need to rely on models of assumptions. Instead of different external parameters in the application of IVFRN, the structure of the given data is used. On this basis an original multi-criteria model was developed based on an IVFRN approach. In this multi-criteria model the traditional steps of the BWM (Best–Worst method) and MABAC (Multi-Attributive Border Approximation area Comparison) methods are modified. The model was tested and validated on a study of the optimal selection of fire fighting helicopters. Testing demonstrated that the model based on IVFRN enabled more objective expert evaluation of the criteria in comparison with traditional fuzzy and rough approaches. A sensitivity analysis of the IVFRN BWM-MABAC model was carried out by means of 57 scenarios, the results of which showed a high degree of stability. The results of the IVFRN model were validated by comparing them with the results of the fuzzy and rough extension of the MABAC, COPRAS and VIKOR models.

Modification of the Best–Worst and MABAC methods: A novel approach based on interval-valued fuzzy-rough numbers

Decision Theory: An Introduction to the Mathematics of Rationality.

An analysis of barriers affecting the implementation of e-waste management practices in India: A novel ISM-DEMATEL approach

This study provides a model for result consistency evaluation of multicriterial decision making (MDM) methods and selection of the optimal one. The model is based on the analysis of results of MDM methods, that is, the analysis of changes in rankings of MDM methods that occur as a result of alterations in input parameters. In the recommended model, we examine sensitivity analysis of MDM methods to changes in criteria weight and result consistency of methods to changes in measurement scale and the way in which we formulate criteria. In the final phase of the model, we select the most suitable method to solve the observed problem and the optimal alternative. The model is tested on an example, when the optimal MDM method selection was required in order to determine the location of the logistical center. During the selection process, TOPSIS, COPRAS, VIKOR and ELECTRE methods were considered. VIKOR method demonstrated the biggest stability of rankings and was selected as the most fit method for ranking the locations of the logistical center. Results of the demonstrated analysis indicate sensitivity of standard MDM methods to criteria considered in this work. Therefore, it is necessary, to take into account stability of the considered method during the selection process of the optimal method.

/pdf/multi-criteria-decision-making-an-example-of-sensitivity-4dv21jamr6.pdf

Multi-criteria decision making: An example of sensitivity analysis

A level crossing, as a point of the crossing of road and rail traffic in the same level, is a place of conflicts subject to traffic accidents. In Serbia, the selection of the level crossings to be secured is mostly done based on the media and society pressure, as a result of an increase of the number of accidents at level crossings. In Serbia, there is no defined methodology for the evaluation of level crossings, respectively, for the development of a strategy for making relevant decision. This paper presents the application of a group multi-criteria FUCOM-MAIRCA (Full Consistency Method – Multi Attributive Ideal-Real Comparative Analysis) model that supports the process of selecting a level crossing in terms of investing in its security equipment. The FUCOM-MAIRCA multi-criteria model is tested in a case study which included the evaluation of ten level crossings within the railway infrastructure in the Republic of Serbia. The evaluation of the crossings is carried out through the assessment according to seven criteria set out on the basis of representative literature and surveys of experts. Sensitivity test of the FUCOM-MAIRCA model is performed by changing the weight coefficients of criteria and statistically processing the results using Spearman’s rank correlation coefficient.

/pdf/multi-criteria-fucom-mairca-model-for-the-evaluation-of-2gfrlqugue.pdf

Multi-criteria FUCOM-MAIRCA model for the evaluation of level crossings: case study in the Republic of Serbia

This paper presents a new approach to the treatment of uncertainty and imprecision in multi-criteria decision-making based on interval rough numbers (IRN). The IRN-based approach provides decision-making using only internal knowledge for the data and operational information of a decision-maker. A new normalized weighted geometric Bonferroni mean operator is developed on the basis of the IRN for the aggregation of the IRN (IRNWGBM). Testing of the IRNWGBM operator is performed through the application in a hybrid IR-DEMATEL-COPRAS multi-criteria model which is tested on real case of selection of optimal direction for the creation of a temporary military route. The first part of hybrid model is the IRN DEMATEL model, which provides objective expert evaluation of criteria under the conditions of uncertainty and imprecision. In the second part of the model, the evaluation is carried out using the new interval rough COPRAS technique.

/pdf/normalized-weighted-geometric-bonferroni-mean-operator-of-3cm665cm0h.pdf

Normalized weighted geometric bonferroni mean operator of interval rough numbers – application in interval rough dematel-copras model

In the paper is presented a model for selecting a location for a brigade command post during combat operations. Considering that this is a very complex model, which can be approached from several aspects, this paper is limited only to the criteria related to the construction or arrangement of the command post, respectively, the engineering aspect. The selection process is conducted using hybrid FUCOM – Z-number – MABAC model. The FUCOM method is used to define the weight coefficients of criteria based on which the selection is made. The MABAC method, modified by applying Z-number, is used to rank alternatives. The end results indicate that the application of Z-number in decision making includes broader set of uncertainties than standard fuzzy numbers, which is very important for deciding in combat situations.

https://dmame.rabek.org/index.php/dmame/article/download/72/53

Darko Božanić

Papers

Application of the GIS-DANP-MABAC multi-criteria model for selecting the location of wind farms: A case study of Vojvodina, Serbia

Multi-criteria decision making: An example of sensitivity analysis

Multi-criteria FUCOM-MAIRCA model for the evaluation of level crossings: case study in the Republic of Serbia

Normalized weighted geometric bonferroni mean operator of interval rough numbers – application in interval rough dematel-copras model

Multicriteria Decision Making Model with Z-Numbers Based on FUCOM and MABAC model