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

Floods are natural disasters with significant socio-economic consequences Urban areas with uncontrolled urban development, rapid population growth, an unregulated municipal system and an unplanned change of land use belong to the highly sensitive areas where floods cause devastating economic and social losses The aim of this paper is to present a reliable GIS multi-criteria methodology for hazard zones’ mapping of flood-prone areas in urban areas The proposed methodology is based on the combined application of geographical information systems (GIS) and multi-criteria decision analysis (MCDA) The methodology considers six factors that are relevant to the hazard of flooding in urban areas: the height, slope, distance to the sewage network, the distance from the water surface, the water table and land use The expert evaluation takes into account the nature and severity of observed criteria, and it is tested using three scenarios: the modalities of the analytic hierarchy process (AHP) The first of them uses a new approach to the exploitation of uncertainty in the application of the AHP technique, the interval rough numbers (IR’AHP) The second one uses the fuzzy technique for the exploitation of uncertainty with the AHP method (F’AHP), and the third scenario contemplates the use of the traditional (crisp) AHP method The proposed methodology is demonstrated in Palilula Municipality, Belgrade, Serbia In the last few decades, Palilula Municipality has been repeatedly devastated by extreme flood events These floods severely affected the transportation networks and other infrastructure Historical flood inundation data have been used in the validation process The final urban flood hazard map proves a satisfactory agreement between the flood hazard zones and the spatial distribution of historical floods that happened in the last 58 years The results indicate that the scenario in which the IR’AHP methodology is used provides the highest level of compatibility with historical data on floods The produced map showed that the areas of very high flood hazard are located on the left Danube River bank These areas are characterized by lowland morphology, gentle slope, sewage network, expansion of impermeable locations and intense urbanization The proposed GIS-IR’AHP methodology and the results of this study provide a good basis for developing a system of flood hazard management in urban areas and can be successfully used for spatial city development policy

Application of GIS-Interval Rough AHP Methodology for Flood Hazard Mapping in Urban Areas

An overview of MULTIMOORA for multi-criteria decision-making: Theory, developments, applications, and challenges

Interval rough number is introduced to deal with the vagueness in decision-making.A novel DEMATEL-ANP model based oninterval rough numbers.Application of a new multi-criteria technique called MARICA.An interval rough number based on MARICA is proposed to evaluate the alternatives.Multi-criteria techniques were compared based on interval rough and fuzzy approaches. This paper presents a novel approach for treating uncertainty in the multi-criteria decision making process by introducing interval rough numbers (IRN). The IRN approach enables decision making using only the internal knowledge incorporated in the data provided by the decision maker. A hybrid multi-criteria model was developed based on IRN, and demonstrated using the example of the bidder selection process in the state administration public procurement procedure. The first segment of the hybrid model deals with the rough interval DEMATEL-ANP (IR'DANP) model, which enables more objective expert evaluation of criteria in a subjective environment than the traditional/crisp approach. In the second segment, the evaluation is enabled by applying the new rough interval MAIRCA method, which introduces mathematical tools and shows high stability concerning changes in the nature and characteristics of the criteria. The results of the hybrid IR'DANP-MAIRCA model were analyzed using 36 scenarios of sensitivity analysis, which showed high stability of the results. The results of the interval rough method were compared with the fuzzy extensions of the TOPSIS, VIKOR, MABAC, TODIM, ELECTRE I and DEMATEL-ANP models.

Novel approach to group multi-criteria decision making based on interval rough numbers

Statistical and machine learning models in credit scoring: A systematic literature survey

Granular computing (GrC) is an efficient way to reveal descriptions of data in line with human cognition and plays a critical role in knowledge discovery. Information granules (IGs), the basic computing unit of GrC, are key components of knowledge representation and processing. Rough sets are one of the classical GrC models and generate IGs based on indiscernibility relations. The relations can effectively achieve the granulation of nominal attributes and generate desirable IGs, but they may cause information loss when achieving the granulation of numerical attributes. To overcome this issue, fuzzy rough sets (FRS) and neighborhood rough sets (NRS) were developed based on rough sets. However, to generate high-performance IGs in practice, the FRS model requires prior knowledge to determine a fuzzy operation in advance, and NRS needs to calculate an optimal neighborhood radius. In addition, regardless of FRS or NRS, each object is taken as a computing unit to generate IGs that constitute a covering rather than a partition for the universe. This process is not only time-consuming but also prone to generate redundant IGs. Therefore, in this study, a data-driven interval granulation approach based on the uncertainty principle is proposed to generate justifiable interval neighborhood IGs with flexibility and tolerance. First, the interval granulation of attribute values and interval equivalence relation are defined. Next, with the interval equivalence relation, a novel interval rough sets model is developed to unify numerical and nominal attributes into one framework, and a membership function is developed without requiring prior knowledge in advance. Then, a highly effective classifier named CAR-ING integrating attribute reduction technique is developed from the perspective of interval neighborhood IGs. Finally, experiments and comparisons on 17 widely used UCI benchmark datasets and 3 real Biobank medical datasets from the UK demonstrated that CAR-ING performs significantly better than four state-of-the-art classifiers based on GrC and five classical classifiers in machine learning. Additionally, the efficiency of CAR-ING is demonstrated on 20 datasets. 

Qin Xie

Papers

Data-Driven Interval Granulation Approach Based on Uncertainty Principle for Efficient Classification