An algorithmic study of relative cardinalities for interval-valued fuzzy sets

ywica, Patryk; Stachowiak, Anna; Wygralak, Maciej

doi:10.1016/j.fss.2015.11.007

Cited by 17 publications

(4 citation statements)

References 37 publications

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“…A large number of authors uses the process of the multi-criteria decision-making benefits of fuzzy sets to exploit ambiguity as their default [66] or through the different types of fuzzy theory extensions [74][75][76][77][78][79]. In addition, fuzzy sets are a very powerful tool for representing imprecision; the choice of membership functions of fuzzy sets is based on subjectivity and shall be based on experience and intuition [80].…”

Section: Interval Rough Numbersmentioning

confidence: 99%

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

Gigović

Pamučar

Bajić

et al. 2017

Water

224

122

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Abstract: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.

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Section: Interval Rough Numbersmentioning

confidence: 99%

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

Gigović

Pamučar

Bajić

et al. 2017

Water

224

122

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“…Measure s T,S,f is defined by the generalized relative cardinality of fuzzy sets, making it possible to simplify the problem of its efficient calculation. For this purpose, we will use the concept of generalized relative cardinality of interval-valued fuzzy sets [36]. σ f (B) > 0}, (33) is called generalized interval-valued relative cardinality.…”

Section: Set Theory Based Similarity Measuresmentioning

confidence: 99%

“…Thanks to the above equation, the value of the extended Jaccard index can be calculated by means of generalized interval-valued relative cardinality. The effective solution of this computational problem was given in [36]. Unfortunately, the problem of effective calculation of the s T,S,f in the general case still remains an open problem.…”

Section: Set Theory Based Similarity Measuresmentioning

confidence: 99%

Uncertainty-aware similarity measures – properties and construction method

Żywica¹,

Stachowiak²

2019

Proceedings of the 2019 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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A concept of uncertainty-aware similarity measure is being defined and discussed. The aim of the paper is to support the opinion that both definition and construction of such measure should take into account the epistemic nature of compared incomplete (uncertain) information. This approach, however, generates new challenges resulted from the computational complexity of the problem. We define a set of properties to be satisfied by uncertainty-aware similarity measure and we propose a new technique of constructing such measures for Interval-Valued Fuzzy Sets.

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“…Just to mention some of the most recent ones, interval-valued fuzzy sets have been used in decision making (see, e.g., the works by Khalil and Hassan [36] and Cheng et al [20]), image processing (see, e.g., the works by Barrenechea et al [2], Pagola et al [45] and Melin et al [39]) or classification (see, e.g., the works by Sanz et al [52,53]). They have also been the origin of rich theoretical studies, as, for instance, the works by Bedregal et al [3,7], Dimuro et al [28], Reiser et al [48] and the recent works by Zywica et al [64] and Takác [55].…”

Section: Introductionmentioning

confidence: 99%

Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions

Bedregal

Bustince

Palmeira

et al. 2017

International Journal of Approximate Reasoning

104

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In this work we extend to the interval-valued setting the notion of an overlap functions and we discuss a method which makes use of interval-valued overlap functions for constructing OWA operators with interval-valued weights. . Some properties of intervalvalued overlap functions and the derived interval-valued OWA operators are analysed. We specially focus on the homogeneity and migrativity properties.

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An algorithmic study of relative cardinalities for interval-valued fuzzy sets

Cited by 17 publications

References 37 publications

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

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

Uncertainty-aware similarity measures – properties and construction method

Generalized interval-valued OWA operators with interval weights derived from interval-valued overlap functions

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