Quantitative analysis of properties and spatial relations of fuzzy image regions

Properties of objects and spatial relations between objects play an important role in rule-based approaches for high-level vision. The partial presence or absence of such properties and relationships can supply both positive and negative evidence for region labeling hypotheses. Similarly, fuzzy labeling of a region can generate new hypotheses pertaining to the properties of the region, its relation to the neighboring regions, and finally, the labels of the neighboring regions. In this paper, we present a unified methodology to characterize properties and spatial relationships of object regions in a digital image. The proposed methods can be used to arrive at more meaningful decisions about the contents of the scene

Rough matroids based on coverings

The introduction of covering-based rough sets has made a substantial contribution to the classical rough sets. However, many vital problems in rough sets, including attribution reduction, are NP-hard and therefore the algorithms for solving them are usually greedy. Matroid, as a generalization of linear independence in vector spaces, it has a variety of applications in many fields such as algorithm design and combinatorial optimization. An excellent introduction to the topic of rough matroids is due to Zhu and Wang. On the basis of their work, we study the rough matroids based on coverings in this paper. First, we investigate some properties of the definable sets with respect to a covering. Specifically, it is interesting that the set of all definable sets with respect to a covering, equipped with the binary relation of inclusion $\subseteq$, constructs a lattice. Second, we propose the rough matroids based on coverings, which are a generalization of the rough matroids based on relations. Finally, some properties of rough matroids based on coverings are explored. Moreover, an equivalent formulation of rough matroids based on coverings is presented. These interesting and important results exhibit many potential connections between rough sets and matroids.Comment: 15page

Parametric matroid of rough set

Rough set is mainly concerned with the approximations of objects through an equivalence relation on a universe. Matroid is a combinatorial generalization of linear independence in vector spaces. In this paper, we define a parametric set family, with any subset of a universe as its parameter, to connect rough sets and matroids. On the one hand, for a universe and an equivalence relation on the universe, a parametric set family is defined through the lower approximation operator. This parametric set family is proved to satisfy the independent set axiom of matroids, therefore it can generate a matroid, called a parametric matroid of the rough set. Three equivalent representations of the parametric set family are obtained. Moreover, the parametric matroid of the rough set is proved to be the direct sum of a partition-circuit matroid and a free matroid. On the other hand, since partition-circuit matroids were well studied through the lower approximation number, we use it to investigate the parametric matroid of the rough set. Several characteristics of the parametric matroid of the rough set, such as independent sets, bases, circuits, the rank function and the closure operator, are expressed by the lower approximation number.Comment: 15 page

Extending Qualitative Spatial Theories with Emergent Spatial Concepts: An Automated Reasoning Approach

Qualitative Spatial Reasoning is an exciting research field of the Knowledge Representation and Reasoning paradigm whose application often requires the extension, refinement or combination of existent theories (as well as the associated calculus). This paper addresses the issue of the sound spatial interpretation of formal extensions of such theories; particularly the interpretation of the extension and the desired representational features. The paper shows how to interpret certain kinds of extensions of Region Connection Calculus (RCC) theory. We also show how to rebuild the qualitative calculus of these extensions.Junta de Andalucía TIC-606

A unified theory of granularity, vagueness and approximation

Abstract: We propose a view of vagueness as a semantic property of names and predicates. All entities are crisp, on this semantic view, but there are, for each vague name, multiple portions of reality that are equally good candidates for being its referent, and, for each vague predicate, multiple classes of objects that are equally good candidates for being its extension. We provide a new formulation of these ideas in terms of a theory of granular partitions. We show that this theory provides a general framework within which we can understand the relation between vague terms and concepts and the corresponding crisp portions of reality. We also sketch how it might be possible to formulate within this framework a theory of vagueness which dispenses with the notion of truth-value gaps and other artifacts of more familiar approaches. Central to our approach is the idea that judgments about reality involve in every case (1) a separation of reality into foreground and background of attention and (2) the feature of granularity. On this basis we attempt to show that even vague judgments made in naturally occurring contexts are not marked by truth-value indeterminacy. We distinguish, in addition to crisp granular partitions, also vague partitions, and reference partitions, and we explain the role of the latter in the context of judgments that involve vagueness. We conclude by showing how reference partitions provide an effective means by which judging subjects are able to temper the vagueness of their judgments by means of approximations

Grounding spatial relations in natural language by fuzzy representation for human-robot interaction

Additional file 1. Fourier coefficient decomposition for the first guess of the Newton’s method

Spatial analysis of suicide attack incidences in Kabul City

Dissertation submitted in partial fulfillment of the requirements for the Degree of Master of Science in Geospatial Technologies.In the last two decades, suicide bombings became quite common among some communities in Iraq, Afghanistan, Pakistan, India, USA, and a few African and European countries. The modeling of reported suicide bombings has been the subject of a few studies, but the pattern of incidents turned out to be difficult to assess. Nevertheless, to uncover the bombing patterns in past incident locations is of major importance because it can improve social security and save human lives. The Capital city of Afghanistan, Kabul, has experienced on average around one suicide attack in every month since 2001. The overall objective of this study is to characterize the spatial and temporal patterns of suicide attacks in Kabul City. This research primarily used last 5 years descriptive spatial information on suicide attacks in Kabul that brought to public by some local and international news paper to generate geographic point data. Suicide attack location points and potential target group establishment point’s data analyzed separately to explore inherent spatial point pattern in terms of intensity and interaction. Finally it analyzed spatial tendency between suicide attack location points on target group establishment locations. It has been explored that both suicide attack locations that occurred from year 2006 to 2010 within the urban habitat of Kabul and target group’s establishment locations are characterized by inhomogeneous intensity and clustered interaction pattern at 98% level of significance. Moreover, there is a tendency of choosing location for suicide attacks close to target group’s establishment location. Finally some interesting temporal characteristics of suicide attack incidences also presented in this study

A physical effort-based model for pedestrian movement in topographic urban environments

This paper presents a topography-sensitive cognitive model for analysis and prediction of pedestrian movement in urban settings. Topography affects visibility and therefore the spatial awareness of pedestrians. It also accentuates the role of physical effort during travel and route selection. The existing models fall short in their reference to these issues. A thorough description of the proposed model is followed by a validation - the model was tested against two existing models in three case studies in Haifa and Jerusalem, Israel. The proposed model outperformed the others in the steeper parts of the case studies. Future model development is discussed

Fuzzy qualitative trigonometry

AbstractThis paper presents a fuzzy qualitative representation of conventional trigonometry with the goal of bridging the gap between symbolic cognitive functions and numerical sensing & control tasks in the domain of physical systems, especially in intelligent robotics. Fuzzy qualitative coordinates are defined by replacing a unit circle with a fuzzy qualitative circle; a Cartesian translation and orientation are defined by their normalized fuzzy partitions. Conventional trigonometric functions, rules and the extensions to triangles in Euclidean space are converted into their counterparts in fuzzy qualitative coordinates using fuzzy logic and qualitative reasoning techniques. This approach provides a promising representation transformation interface to analyze general trigonometry-related physical systems from an artificial intelligence perspective.Fuzzy qualitative trigonometry has been implemented as a MATLAB toolbox named XTRIG in terms of 4-tuple fuzzy numbers. Examples are given throughout the paper to demonstrate the characteristics of fuzzy qualitative trigonometry. One of the examples focuses on robot kinematics and also explains how contributions could be made by fuzzy qualitative trigonometry to the intelligent connection of low-level sensing & control tasks to high-level cognitive tasks