Interval Computation as an Important Part of Granular Computing: An Introduction

2008 ◽  
pp. 1-31 ◽  
Author(s):  
Vladik Kreinovich
Author(s):  
M. R. Delavar ◽  
M. Bahrami ◽  
M. Zare

Several faults exist in the vicinity of Tehran, the capital of Iran such as North Tehran, Ray, Mosha and Kahrizak. One way to assist reducing the damage caused by the earthquake is the production of a seismic vulnerability map. The study area in this research is Tehran, based on the assumption of the activation of North Tehran fault. Degree of Physical seismic vulnerability caused by the earthquake depends on a number of criteria. In this study the intensity of the earthquake, land slope, numbers of buildings’ floors as well as their materials are considered as the effective parameters. Hence, the production of the seismic vulnerability map is a multi criteria issue. In this problem, the main source of uncertainty is related to the experts’ opinions regarding the seismic vulnerability of Tehran statistical units. The main objectives of this study are to exploit opinions of the experts, undertaking interval computation and interval Dempster-Shafer combination rule to reduce the uncertainty in the opinions of the experts and customizing granular computing to extract the rules and to produce Tehran physical seismic vulnerability map with a higher confidence. Among 3174 statistical units of Tehran, 150 units were randomly selected and using interval computation, their physical vulnerabilities were determined by the experts in earthquake-related fields. After the fusion of the experts’ opinions using interval Dempster-Shafer, the information table is prepared as the input to granular computing and then rules are extracted with minimum inconsistency. Finally, the seismic physical vulnerability map of Tehran was produced with % 72 accuracy.


2021 ◽  
Vol 219 ◽  
pp. 106880
Author(s):  
Nana Liu ◽  
Zeshui Xu ◽  
Hangyao Wu ◽  
Peijia Ren
Keyword(s):  

2020 ◽  
Vol 39 (3) ◽  
pp. 2797-2816
Author(s):  
Muhammad Akram ◽  
Anam Luqman ◽  
Ahmad N. Al-Kenani

An extraction of granular structures using graphs is a powerful mathematical framework in human reasoning and problem solving. The visual representation of a graph and the merits of multilevel or multiview of granular structures suggest the more effective and advantageous techniques of problem solving. In this research study, we apply the combinative theories of rough fuzzy sets and rough fuzzy digraphs to extract granular structures. We discuss the accuracy measures of rough fuzzy approximations and measure the distance between lower and upper approximations. Moreover, we consider the adjacency matrix of a rough fuzzy digraph as an information table and determine certain indiscernible relations. We also discuss some general geometric properties of these indiscernible relations. Further, we discuss the granulation of certain social network models using rough fuzzy digraphs. Finally, we develop and implement some algorithms of our proposed models to granulate these social networks.


Author(s):  
JIYE LIANG ◽  
ZHONGZHI SHI

Rough set theory is a relatively new mathematical tool for use in computer applications in circumstances which are characterized by vagueness and uncertainty. In this paper, we introduce the concepts of information entropy, rough entropy and knowledge granulation in rough set theory, and establish the relationships among those concepts. These results will be very helpful for understanding the essence of concept approximation and establishing granular computing in rough set theory.


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