Characterization of Electre I choice procedures

2020 ◽  
Vol 54 (6) ◽  
pp. 1673-1683
Author(s):  
Mustapha Balewa Sanni ◽  
Carlos Ogouyandjou ◽  
Freedath Djibril Moussa
Keyword(s):  
Binary Relations ◽  
Outranking Method ◽  
Outranking Relation ◽  
Choice Procedures ◽  
Outranking Methods ◽  
Electre I

This paper discusses choice procedures that select the set of best alternatives taking into account reflexive binary relations (called pseudo-tournaments in the paper), such as those that can be obtained when constructing an outranking relation à la Electre. The paper contains interesting results which link together the second “exploitation” step in the Electre I outranking method with two choice procedures (Gocha and Getcha choice procedures also known in the literature as Schwartz set and Smith set respectively). A set of results that characterize some properties of the two outranking methods (ElectI and ElectIP choice procedures) is also presented.

scholarly journals ON THE PARTITION MONOID AND SOME RELATED SEMIGROUPS

2010 ◽  
Vol 83 (2) ◽  
pp. 273-288 ◽  
Author(s):  
D. G. FITZGERALD ◽  
KWOK WAI LAU
Keyword(s):  
Transformation Semigroup ◽  
Galois Connection ◽  
Inverse Semigroups ◽  
Natural Order ◽  
Binary Relations ◽  
Ideal Lattices ◽  
New Interpretation ◽  
Semigroup Of Transformations ◽  
The Ideal

AbstractThe partition monoid is a salient natural example of a *-regular semigroup. We find a Galois connection between elements of the partition monoid and binary relations, and use it to show that the partition monoid contains copies of the semigroup of transformations and the symmetric and dual-symmetric inverse semigroups on the underlying set. We characterize the divisibility preorders and the natural order on the (straight) partition monoid, using certain graphical structures associated with each element. This gives a simpler characterization of Green’s relations. We also derive a new interpretation of the natural order on the transformation semigroup. The results are also used to describe the ideal lattices of the straight and twisted partition monoids and the Brauer monoid.

scholarly journals Sequentially Rationalizable Choice

2007 ◽  
Vol 97 (5) ◽  
pp. 1824-1839 ◽  
Author(s):  
Paola Manzini ◽  
Marco Mariotti
Keyword(s):  
Choice Function ◽  
Binary Relations ◽  
Choice Functions ◽  
Choice Problem ◽  
Full Characterization ◽  
Human Choice ◽  
Fixed Set ◽  
Rationalizable Choice

A sequentially rationalizable choice function is a choice function that can be retrieved by applying sequentially to each choice problem the same fixed set of asymmetric binary relations (rationales) to remove inferior alternatives. These concepts translate into economic language some human choice heuristics studied in psychology and explain cyclical patterns of choice observed in experiments. We study some properties of sequential rationalizability and provide a full characterization of choice functions rationalizable by two and three rationales. (JEL D01).

A leximin characterization of strategy-proof and non-resolute social choice procedures

2002 ◽  
Vol 20 (4) ◽  
pp. 809-829 ◽  
Author(s):  
Donald E. Campbell ◽  
Jerry S. Kelly
Keyword(s):  
Social Choice ◽  
Choice Procedures ◽  
Strategy Proof

scholarly journals A generalization of Tong's theorem and properties of pairwise perfectly normal spaces

1985 ◽  
Vol 39 (3) ◽  
pp. 353-359
Author(s):  
Manuel López-Pellicer ◽  
Angel Gutiérrez
Keyword(s):  
Topological Spaces ◽  
Binary Relations ◽  
Closed Set ◽  
Perfect Normality ◽  
Semicontinuous Functions ◽  
Perfectly Normal

AbstractIn this paper we give some properties of the pairwise perfectly normal spaces defined by Lane. In particular we prove that a space (X, P, Q) is pairwise perfectly normal if and only if every P(Q)–closed set is the zero of a P(Q)–l.s.c. and Q(P)–u.s.c. function. Also we characterize the pairwise perfect normality in terms of sequences of semicontinuous functions by means of a result which contains the known Tong's characterization of perfectly normal topological spaces, whose proof we modify by using the technique of binary relations.

scholarly journals Generalized Fitch Graphs III: Symmetrized Fitch maps and Sets of Symmetric Binary Relations that are explained by Unrooted Edge-labeled Trees

2021 ◽  
Vol vol. 23 no. 1 (Graph Theory) ◽  
Author(s):  
Marc Hellmuth ◽  
Carsten R. Seemann ◽  
Peter F. Stadler
Keyword(s):  
Natural Generalization ◽  
Formal Models ◽  
Binary Relations ◽  
Transfer Event ◽  
Graph Representations ◽  
Labeled Trees ◽  
Unique Path ◽  
Alternative Characterization ◽  
Np Complete

Binary relations derived from labeled rooted trees play an import role in mathematical biology as formal models of evolutionary relationships. The (symmetrized) Fitch relation formalizes xenology as the pairs of genes separated by at least one horizontal transfer event. As a natural generalization, we consider symmetrized Fitch maps, that is, symmetric maps $\varepsilon$ that assign a subset of colors to each pair of vertices in $X$ and that can be explained by a tree $T$ with edges that are labeled with subsets of colors in the sense that the color $m$ appears in $\varepsilon(x,y)$ if and only if $m$ appears in a label along the unique path between $x$ and $y$ in $T$. We first give an alternative characterization of the monochromatic case and then give a characterization of symmetrized Fitch maps in terms of compatibility of a certain set of quartets. We show that recognition of symmetrized Fitch maps is NP-complete. In the restricted case where $|\varepsilon(x,y)|\leq 1$ the problem becomes polynomial, since such maps coincide with class of monochromatic Fitch maps whose graph-representations form precisely the class of complete multi-partite graphs.

Characterization of Certain Binary Relations on Connected Ordered Spaces

1963 ◽  
Vol 15 ◽  
pp. 397-411
Author(s):  
James E. L'Heureux
Keyword(s):  
Natural Setting ◽  
Binary Relations ◽  
Identity Function ◽  
Minimal Sets ◽  
End Point ◽  
Ordered Space

In an earlier paper (2) reflexive transitive binary relations were considered on a connected ordered space. These relations were topologically restricted and their minimal sets were either an end point of the space or empty. It was shown that these relations could be characterized as one of the two orders of the space. Viewing the situation somewhat differently as suggested by I. S. Krule, one could say that this class of relations was characterized in terms of the identity function on the space. In this case the relations are considered in their natural setting, the product of the space with itself.

scholarly journals Multiple-Attribute Decision Making ELECTRE II Method under Bipolar Fuzzy Model

Algorithms ◽  
2019 ◽  
Vol 12 (11) ◽  
pp. 226 ◽  
Author(s):  
Shumaiza ◽  
Muhammad Akram ◽  
Ahmad N. Al-Kenani
Keyword(s):  
Decision Making ◽  
Optimization Technique ◽  
Multiple Criteria Decision Making ◽  
Fuzzy Model ◽  
Multiple Attribute Decision Making ◽  
Business Location ◽  
Outranking Relation ◽  
Fuzzy Environment ◽  
Multiple Attribute ◽  
Electre I

The core aim of this paper is to provide a new multiple-criteria decision making (MCDM) model, namely bipolar fuzzy ELimination and Choice Translating REality (ELECTRE) II method, by combining the bipolar fuzzy set with ELECTRE II technique. It can be used to solve the problems having bipolar uncertainty. The proposed method is established by defining the concept of bipolar fuzzy strong, median and weak concordance as well as discordance sets and indifferent set to define two types of outranking relations, namely strong outranking relation and weak outranking relation. The normalized weights of criteria, which may be partly or completely unknown for decision makers, are calculated by using an optimization technique, which is based on maximizing deviation method. A systematic iterative procedure is applied to strongly outrank as well as weakly outrank graphs to determine the ranking of favorable actions or alternatives or to choose the best possible solution. The implementation of the proposed method is presented by numerical examples such as selection of business location and to chose the best supplier. A comparative analysis of proposed ELECTRE II method is also presented with already existing multiple-attribute decision making methods, including Technique for the Order of Preference by Similarity to an Ideal Solution (TOPSIS) and ELECTRE I under bipolar fuzzy environment by solving the problem of business location.

CONCURRENT AUTOMATA AND DOMAINS

1992 ◽  
Vol 03 (04) ◽  
pp. 389-418 ◽  
Author(s):  
MANFRED DROSTE
Keyword(s):  
Concurrent Systems ◽  
Equivalence Classes ◽  
Binary Relations ◽  
Transition Systems ◽  
Operational Model ◽  
Locally Finite ◽  
Natural Domain ◽  
Theoretic Characterization ◽  
Natural Way

We introduce an operational model of concurrent systems, called automata with concurrency relations. These are labeled transition systems [Formula: see text] in which the event set is endowed with a collection of symmetric binary relations which describe when two events at a particular state of [Formula: see text] commute. This model generalizes the recent concept of Stark’s trace automata. A permutation equivalence for computation sequences of [Formula: see text] arises canonically, and we obtain a natural domain [Formula: see text] comprising the induced equivalence classes. We give a complete order-theoretic characterization of all such partial orders [Formula: see text] which turn out to be particular finitary domains. The arising domains [Formula: see text] are particularly pleasant Scott-domains, if [Formula: see text] is assumed to be concurrent, i.e. if the concurrency relations of [Formula: see text] depend (in a natural way) locally on each other, but not necessarily globally. We show that both event domains and dI-domains arise, up to isomorphism, as domains [Formula: see text] with well-behaved such concurrent automata [Formula: see text]. We introduce a subautomaton relationship for concurrent automata and show that, given two concurrency domains (D, ≤), (D′, ≤), there exists a nice stable embedding-projection pair from D to D′ iff D, D′ can be generated by concurrent automata [Formula: see text] such that [Formula: see text] is a subautomaton of [Formula: see text]. Finally, we introduce the concept of locally finite concurrent automata as a limit of finite concurrent automata and show that there exists a universal homogeneous locally finite concurrent automaton, which is unique up to isomorphism.

scholarly journals Binary Relations-based Rough Sets – an Automated Approach

2016 ◽  
Vol 24 (2) ◽  
pp. 143-155 ◽  
Author(s):  
Adam Grabowski
Keyword(s):  
Binary Relation ◽  
Rough Sets ◽  
The State ◽  
General Mechanism ◽  
Binary Relations ◽  
Approximation Spaces ◽  
Approximation Operators ◽  
Mizar Mathematical Library ◽  
Almost All

Summary Rough sets, developed by Zdzisław Pawlak [12], are an important tool to describe the state of incomplete or partially unknown information. In this article, which is essentially the continuation of [8], we try to give the characterization of approximation operators in terms of ordinary properties of underlying relations (some of them, as serial and mediate relations, were not available in the Mizar Mathematical Library [11]). Here we drop the classical equivalence- and tolerance-based models of rough sets trying to formalize some parts of [18]. The main aim of this Mizar article is to provide a formal counterpart for the rest of the paper of William Zhu [18]. In order to do this, we recall also Theorem 3 from Y.Y. Yao’s paper [17]. The first part of our formalization (covering first seven pages) is contained in [8]. Now we start from page 5003, sec. 3.4. [18]. We formalized almost all numbered items (definitions, propositions, theorems, and corollaries), with the exception of Proposition 7, where we stated our theorem only in terms of singletons. We provided more thorough discussion of the property positive alliance and its connection with seriality and reflexivity (and also transitivity). Examples were not covered as a rule as we tried to construct a more general mechanism of finding appropriate models for approximation spaces in Mizar providing more automatization than it is now [10]. Of course, we can see some more general applications of some registrations of clusters, essentially not dealing with the notion of an approximation: the notions of an alliance binary relation were not defined in the Mizar Mathematical Library before, and we should think about other properties which are also absent but needed in the context of rough approximations [9], [5]. Via theory merging, using mechanisms described in [6] and [7], such elementary constructions can be extended to other frameworks.

AGGREGATING TRANSITIVE FUZZY BINARY RELATIONS

1995 ◽  
Vol 03 (01) ◽  
pp. 47-55 ◽  
Author(s):  
SERGEI OVCHINNIKOV
Keyword(s):  
Binary Relation ◽  
Arithmetic Mean ◽  
Geometric Characterization ◽  
Binary Relations ◽  
Aggregation Procedure ◽  
Aggregation Problem ◽  
Fuzzy Binary Relation ◽  
Finite Set

We discuss the aggregation problem for transitive fuzzy binary relations. An aggregation procedure assigns a group fuzzy binary relation to each finite set of individual binary relations. Individual and group binary relations are assumed to be transitive fuzzy binary relation with respect to a given continuous t-norm. We study a particular class of aggregation procedures given by quasi-arithmetic (Kolmogorov) means and show that these procedures are well defined if and only if the t-norm is Archimedean. We also give a geometric characterization of t-norms for which the arithmetic mean is a well-defined aggregation procedure.

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