Henry Sharp · Proceedings of the American Mathematical Society · 1970
H. Minc has constructed an upper bound on the permanent of any relation on a finite set. In this paper the permanent of any transitive relation on a finite set is calculated. The work in part is based upon the interpretation of a reflexive, transitive relation as a finite topology. The relationship to (finite) Borel fields is discussed briefly. In an example it is shown how results here may be combined with Mincâs inequality to produce an improved upper bound on the permanent of any relation.
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Henry Sharp · Proceedings of the American Mathematical Society · 1970
H. Minc has constructed an upper bound on the permanent of any relation on a finite set. In this paper the permanent of any transitive relation on a finite set is calculated. The work in part is based upon the interpretation of a reflexive, transitive relation as a finite topology. The relationship to (finite) Borel fields is discussed briefly. In an example it is shown how results here may be combined with Minc’s inequality to produce an improved upper bound on the permanent of any relation.
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Miloud Gorine, Djamila Boutaleb · مجلة الحوار الثقافي · 2023
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Osama Sayed, Nabil Hassan Sayed · SHILAP Revista de lepidopterología · 2022
In the study of partially ordered sets, topologies such as Scott-topology have shown to be of paramount importance. In order to have analogous topology-like tools in the more general setting of quantitative domains, we introduce a method to construct Scotttopology on a set equipped with a transitive binary relation which we call t-set. As an application of this result there is a Scott-topology associated to any topology induced by its specialization pre-ordered relation. Some relations between this topology and the original topology are investigated.
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Ryo Kashima, Ryo Kashima · 2009
A proof of the completeness theorem for the modal logic with transitive closure of accessibility relation
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Sourav Chakraborty, Susmita Ghosh, Nitesh Jha et al. · Lecture notes in computer science · 2015
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Yu-Fen Wu · Journal of Algebra · 1998
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Luigi Santocanale, Friedrich Wehrung · European Journal of Combinatorics · 2014
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Edsger W. Dijkstra · 2000
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Guannan Deng, Yanli Jiang · 2012
Fuzzy relation plays an important role in many applications. In this work, I-fuzzy equivalence relation and I-transitive approximations are studied. Firstly, the methods for judging an I-fuzzy equivalence relation are investigated. Secondly, the relationship between I-fuzzy equivalence relation and T-fuzzy equivalence relation is discussed. Finally, the I-transitive approximations of fuzzy similarity relation are defined and studied.
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E. Roy Weintraub · 1997
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Junzo Watada, Hideo Tanaka, Kiyoji Asai · Transactions of the Society of Instrument and Control Engineers · 1981
The fuzzy transitive relation is very essential for a fuzzy ordering relation in fuzzy decision problems and also for a fuzzy equivalence relation in fuzzy clustering problems. But data of binary relation given by questionnaires do not usually satisfy the transitivity condition. Then the transitive closures of binary relation are used to be transitive. This paper deals with a heuristic method for finding a fuzzy transitive relation which is a good approximation to a given relation. The fuzzy transitive relation obtained by this method is closer to the relation in the system under consideration than the transitive closure is in the sense of the error sum of squares.
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E. Roy Weintraub · South Atlantic Quarterly · 1995
Research Article| April 01 1995 Is “Is a Precursor of” a Transitive Relation? E. Roy Weintraub E. Roy Weintraub Search for other works by this author on: This Site Google South Atlantic Quarterly (1995) 94 (2): 571–589. https://doi.org/10.1215/00382876-94-2-571 Cite Icon Cite Share Icon Share Facebook Twitter LinkedIn MailTo Permissions Search Site Citation E. Roy Weintraub; Is “Is a Precursor of” a Transitive Relation?. South Atlantic Quarterly 1 April 1995; 94 (2): 571–589. doi: https://doi.org/10.1215/00382876-94-2-571 Download citation file: Zotero Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search Books & JournalsAll JournalsSouth Atlantic Quarterly Search Advanced Search The text of this article is only available as a PDF. Copyright © 1995 by Duke University Press1995 Article PDF first page preview Close Modal You do not currently have access to this content.
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E. Roy Weintraub · Edward Elgar Publishing eBooks · 1997
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Machtinger, Lawrence · Open Scholarship Institutional Repository (Washington University in St. Louis) · 2025
The main objective of this paper is the study of rings with a relation which has all the properties of an order relation on a ring except, perhaps, for one: transitivity. Consequently, many of the results presented here are generalizations of well-known facts about transitively ordered rings; and most, but not all, of the conclusions of this paper are applicable to such rings.
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Garmendia Salvador, Luis, Recasens Ferrés, Jorge · RECERCAT (Consorci de Serveis Universitaris de Catalunya)
Three ways to approximate a proximity relation R (i.e., a reflexive and symmetric fuzzy relation) by a T -transitive one where T is a continuous Archimedean t-norm are given. The first one aggregates the transitive closure R macr of R with a (maximal) T-transitive relation B contained in R . The second one computes the closest homotecy of R macr or B to better fit their entries with the ones of R. The third method uses nonlinear programming techniques to obtain the best approximation with respect to the Euclidean distance for T the Lukasiewicz or the product t-norm. The previous methods do not apply for the minimum t-norm. An algorithm to approximate a given proximity relation by a min-transitive relation (a similarity) is given in the last section of the paper.
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Derek J. S. Robinson · Mathematical Proceedings of the Cambridge Philosophical Society · 1964
A group is said to have the property T or to be a T-group if every subnormal subgroup is normal. Thus the class of T-groups is just the class of all groups in which normality is a transitive relation. Finite T-groups have been studied by Best and Taussky (l), Gaschütz (4) and Zacher (11). Gaschütz has shown that if G is a finite soluble T-group and G/L is the unique maximal nilpotent quotient group of G , then G/L is Abelian or Hamiltonian and L is an Abelian group of odd order prime to | G:L | ((4), Satz 1). Our aim is to study infinite T-groups and more especially infinite soluble T-groups with a view to extending Gaschütz's results. One of the simplest results on soluble T-groups is THEOREM 2.3.1. Every soluble T-group is metabelian .
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E. Roy Weintraub · 1997
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Mikhail A. Mikhaylov · Book Publisher International (a part of SCIENCEDOMAIN International) · 2021
In this study the reasons obliging a relation to be transitive were established. Unified definitions of different symmetry and reflexivity manifests were made. It was shown that among relations’ properties only transitivity has the direct negation.
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Katarzyna Kuhlmann, Franz‐Viktor Kuhlmann · Fixed Point Theory · 2017
We present general fixed point theorems for spaces that are equipped with a transitive relation. We apply them to prove corresponding theorems for ultrametric spaces, topological spaces, complete lattices, and ordered abelian groups and fields.
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