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View merging in the presence of incompleteness and inconsistency
 Requir. Eng
, 2006
"... View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, ..."
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Cited by 34 (10 self)
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View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, or to perform various types of analysis. View merging is complicated by incompleteness and inconsistency: Stakeholders often have varying degrees of confidence about their statements. Their views capture different but overlapping aspects of a problem, and may have discrepancies over the terminology being used, the concepts being modeled, or how these concepts should be structured. Once views are merged, it is important to be able to trace the elements of the merged view back to their sources and to the merge assumptions related to them. In this paper, we present a framework for merging incomplete and inconsistent graphbased views. We introduce a formalism, called annotated graphs, with a builtin annotation scheme for modeling incompleteness and inconsistency. We show how structurepreserving maps can be employed to express the relationships between disparate views modeled as annotated graphs, and provide a general algorithm for merging views with arbitrary interconnections. We provide a systematic way to generate and represent the traceability information required for tracing the merged view elements back to their sources, and to the merge assumptions giving rise to the elements.
An algebraic framework for merging incomplete and inconsistent views
, 2004
"... View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, ..."
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Cited by 19 (6 self)
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View merging, also called view integration, is a key problem in conceptual modeling. Large models are often constructed and accessed by manipulating individual views, but it is important to be able to consolidate a set of views to gain a unified perspective, to understand interactions between views, or to perform various types of endtoend analysis. View merging is complicated by incompleteness and inconsistency of views. Once views are merged, it is useful to be able to trace the elements of the merged view back to their sources. In this paper, we propose a framework for merging incomplete and inconsistent graphbased views. We introduce a formalism, called posetannotated graphs, which incorporates a systematic annotation scheme capable of modeling incompleteness and inconsistency as well as providing a builtin mechanism for ownership traceability. We show how structurepreserving maps can capture the relationships between disparate views modeled as posetannotated graphs, and provide a general algorithm for merging views with arbitrary interconnections. We use the i ∗ modeling language [26] as an example to demonstrate how our approach can be applied to existing graphbased modeling languages, especially in the domain of early Requirements Engineering. 1
Fuzzy location problems on networks
, 2004
"... Location problems concern a wide set of fields where it is usually assumed that exact data are known. However, in real applications, the location of the facility considered can be full of linguistic vagueness, that can be appropriately modelled using networks with fuzzy values. Thus fuzzy location p ..."
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Cited by 4 (0 self)
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Location problems concern a wide set of fields where it is usually assumed that exact data are known. However, in real applications, the location of the facility considered can be full of linguistic vagueness, that can be appropriately modelled using networks with fuzzy values. Thus fuzzy location problems on networks arise; this paper deals with their general formulation and the description of the ways to solve them. Namely, we show the variety of problems that can be considered in this context and, for some of them, we propose the most operative approaches for their solution.
Isomorphism on Fuzzy Graphs
 WORLD ACADEMY OF SCIENCE, ENGINEERING AND TECHNOLOGY 47
, 2008
"... In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. ..."
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Cited by 2 (0 self)
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In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed.
ii Copyright c○2012
, 2012
"... iii ivI dedicate this thesis to my father Miguel Machado de Simas, my mother Maria de Lurdes de Simas and my wonderful wife Ana Claudia Guerra, who supported me in each step of the way with love and understanding. ..."
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iii ivI dedicate this thesis to my father Miguel Machado de Simas, my mother Maria de Lurdes de Simas and my wonderful wife Ana Claudia Guerra, who supported me in each step of the way with love and understanding.
World Academy of Science, Engineering and Technology 23 2008 Isomorphism on Fuzzy Graphs A.Nagoor Gani and J.Malarvizhi
"... Abstract—In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary ..."
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Abstract—In this paper, the order, size and degree of the nodes of the isomorphic fuzzy graphs are discussed. Isomorphism between fuzzy graphs is proved to be an equivalence relation. Some properties of self complementary and self weak complementary fuzzy graphs are discussed. Keywords—complementary fuzzy graphs, coweak isomorphism, equivalence relation, fuzzy relation, weak isomorphism. I.
doi:10.1006/cviu.2002.0974 Fuzzy Distance Transform: Theory, Algorithms, and Applications
, 2001
"... This paper describes the theory and algorithms of distance transform for fuzzy subsets, called fuzzy distance transform (FDT). The notion of fuzzy distance is formulated by first defining the length of a path on a fuzzy subset and then finding the infimum of the lengths of all paths between two poin ..."
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This paper describes the theory and algorithms of distance transform for fuzzy subsets, called fuzzy distance transform (FDT). The notion of fuzzy distance is formulated by first defining the length of a path on a fuzzy subset and then finding the infimum of the lengths of all paths between two points. The length of a path π in a fuzzy subset of the ndimensional continuous space ℜ n is defined as the integral of fuzzy membership values along π. Generally, there are infinitely many paths between any two points in a fuzzy subset and it is shown that the shortest one may not exist. The fuzzy distance between two points is defined as the infimum of the lengths of all paths between them. It is demonstrated that, unlike in hard convex sets, the shortest path (when it exists) between two points in a fuzzy convex subset is not necessarily a straight line segment. For any positive number θ ≤ 1, the θsupport of a fuzzy subset is the set of all points in ℜ n with membership values greater than or equal to θ. It is shown that, for any fuzzy subset, for any nonzero θ ≤ 1, fuzzy distance is a metric for the interior of its θsupport. It is also shown that, for any smooth fuzzy subset, fuzzy distance is a metric for the interior of its 0support (referred to as support). FDT is defined as a process on a fuzzy subset that assigns to a point its fuzzy distance from the complement of the support. The theoretical framework of FDT in continuous space is extended to digital cubic spaces and it is shown that for any fuzzy digital object, fuzzy distance is a metric for the support of the object. A
DOI: 10.5829/idosi.wasj.22.am.1.2013 Nstructures Applied to Graphs
"... Abstract: In this paper, we introduce the notion of Ngraphs and describe methods of their construction. We prove that the isomorphism between Ngraphs is an equivalence relation (resp. partial order relation). We then introduce the concept ofNline graphs and discuss some of their fundamental prope ..."
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Abstract: In this paper, we introduce the notion of Ngraphs and describe methods of their construction. We prove that the isomorphism between Ngraphs is an equivalence relation (resp. partial order relation). We then introduce the concept ofNline graphs and discuss some of their fundamental properties. Key words: Ngraphs, isomorphism,Nline graphs.
DOI: 10.5829/idosi.wasj.22.am.4.2013 Metric Aspects ofNgraphs
"... Abstract: We first define length, distance, radius, eccentricity, path cover and edge cover of an Ngraph. Then we introduce the concept of self centeredNgraphs and investigate some of their important properties. We also establish the necessary and sufficient conditions for a completeNgraph to hav ..."
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Abstract: We first define length, distance, radius, eccentricity, path cover and edge cover of an Ngraph. Then we introduce the concept of self centeredNgraphs and investigate some of their important properties. We also establish the necessary and sufficient conditions for a completeNgraph to have an Nbridge.