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

https://cyberleninka.org/article/n/688210.pdf

A survey on rough set theory and its applications

In the classical three-way decision (3WD) model with decision-theoretic rough sets (DTRSs), the classification correct rate (CCR) is an important issue. As one of the risk measurement methods, loss functions have been used to calculate thresholds. Using risk measurement methods relevant research has yielded many results. However, for improving the CCR, few research studies have focused on the risk measurement by considering the difference among the equivalence classes. In this paper, from the viewpoint of the difference among the equivalence classes, to improve the CCR, a novel model is proposed to derive the 3WD model with DTRSs by considering the new risk measurement functions through the utility theory. First, the weight of each attribute is calculated based on the knowledge distance. Then, with the aid of utility theory, the improved utility function, which can score the attribute values, is defined. Further, a reasonable model for constructing the utility-based scoring functions is proposed. Then, a decision procedure for calculating the exclusive thresholds is designed and the rules of three-way decisions (3WDs) are deduced. An example is presented to illustrate the proposed model and the trend of change for exclusive thresholds. Finally, our experimental results show that the performance of the proposed model is better than that of current existing models.

A Novel Three-way decision model with decision-theoretic rough sets using utility theory

Attribute reduction based on misclassification cost in variable precision rough set model

Granular ball computing (GBC), as an efficient, robust, and scalable learning method, has become a popular research topic of granular computing. GBC includes two stages: granular ball generation (GBG) and multi-granularity learning based on the granular ball (GB). However, the stability and efficiency of existing GBG methods need to be further improved due to their strong dependence on $k$-means or $k$-division. In addition, GB-based classifiers only unilaterally consider the GB's geometric characteristics to construct classification rules, but the GB's quality is ignored. Therefore, in this paper, based on the attention mechanism, a fast and stable GBG (GBG++) method is proposed first. Specifically, the proposed GBG++ method only needs to calculate the distances from the data-driven center to the undivided samples when splitting each GB, instead of randomly selecting the center and calculating the distances between it to all samples. Moreover, an outlier detection method is introduced to identify local outliers. Consequently, the GBG++ method can significantly improve effectiveness, robustness, and efficiency while being absolutely stable. Second, considering the influence of the sample size within the GB on the GB's quality, based on the GBG++ method, a $k$-nearest neighbors algorithm (GB$k$NN++) which can reduce misclassification at class boundary to some extent is presented. Finally, the experimental results indicate that the proposed method outperforms several existing GB-based classifiers and classical machine learning classifiers on $20$ public benchmark data sets.

GBG++: A Fast and Stable Granular Ball Generation Method for Classification

As one of rapidly developing methodology for dealing with complex problems in line with human cognition, granular computing has made significant achievements in knowledge discovery. Neighborhood classifier, as a typical description of granular computing (GrC), is an effective method for classification of continuous data. However, in the phase of constructing neighborhood rules, the existing neighborhood classifiers are divided into the following two modes and both have defects: (1) The strategy driven by center: There are a lot of overlap and inclusion among neighborhood rules, that is, it need to spend much time to reduce redundancy rules; (2) The strategy driven by rule: There are many rules containing only one object, which cannot form an effective covering, and would affect knowledge acquisition in the incremental environment. Therefore, in this paper, fuzzy quotient space theory is introduced to construct neighborhood rules. Based on optimal granularity of fuzzy quotient space, a neighborhood covering classifier, which has no redundant rules and could form the effective covering, is proposed without any artificial parameter. Second, comprehensively considering the knowledge purity and complexity, the quality measure of granularity is proposed, which guides the optimal granularity selection of HQSS. Third, neighborhood rules are constructed in the optimal granularity. Then, the offset of center is introduced to describe the membership degree of the test object to different neighborhood rules, and the neighborhood allocation strategy is proposed accordingly. Next, an algorithm for the neighborhood covering classifier based on these theories is proposed. Finally, experiments on 13 UCI datasets and 3 real datasets are carried out to verify the performance of the proposed classifier from four common classification indexes. 

Qin Xie

Papers

A survey on rough set theory and its applications

A Novel Three-way decision model with decision-theoretic rough sets using utility theory

Attribute reduction based on misclassification cost in variable precision rough set model

GBG++: A Fast and Stable Granular Ball Generation Method for Classification

A Neighborhood Covering Classifier Based on Optimal Granularity of Fuzzy Quotient Space