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- Sorooshian, Shahryar, 1980, et al.
(författare)
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Performance of the decision-making trial and evaluation laboratory
- 2023
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Ingår i: AIMS Mathematics. - : American Institute of Mathematical Sciences (AIMS). - 2473-6988. ; 8:3, s. 7490-7514
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Tidskriftsartikel (refereegranskat)abstract
- Multiple attribute decision-making (MADM) techniques constitute a practical approach for solving complex problems involving multiple and often conflicting criteria. Decision-making trial and evaluation laboratory (DEMATEL) is a popular MADM technique with both admirers and critics. This study presents a comprehensive review of DEMATEL through bibliometric analysis using the Scopus database. This article examined 3,521 papers published in journals, conferences or books between 1981 and 2023. We examined a few parameters for commenting on the performance of the technique. Among them are research outputs, the network of DEMATEL users, implementation subject areas, research zones, financing opportunities and publication hosts and their impact trends. We conclude from the findings of this study that the DEMATEL is capable of dealing with modern problem-solving in future environments. Although the growth of new MADMs is obvious, based on the gathered data, we forecast that more than 776 documents will be published in 2025 using DEMATEL for problem-solving. This expanding tendency will continue in the future. As distinct MADMs have diverse constraints, foundations, computing complexity and standpoints, which result in different performances, outmoded low-performance MADM techniques must be reported by researchers to continue this paper’s objective to minimize ambiguity among decision-makers and practitioners. To facilitate such a comparison in the future, a quantitative performance coefficient was also developed here.
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| 2. |
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| 3. |
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| 4. |
- Hegarty, Peter, 1971
(författare)
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On the notion of balance in social network analysis
- 2012
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The notion of ``balance'' is fundamental for sociologists who study social networks. In formal mathematical terms, it concerns the distribution of triad configurations in actual networks compared to random networks of the same edge density. On reading Charles Kadushin's recent book ``Understanding Social Networks'', we were struck by the amount of confusion in the presentation of this concept in the early sections of the book. This confusion seems to lie behind his flawed analysis of a classical empirical data set, namely the karate club graph of Zachary. Our goal here is twofold. Firstly, we present the notion of balance in terms which are logically consistent, but also consistent with the way sociologists use the term. The main message is that the notion can only be meaningfully applied to undirected graphs. Secondly, we correct the analysis of triads in the karate club graph. This results in the interesting observation that the graph is, in a precise sense, quite ``unbalanced''. We show that this lack of balance is characteristic of a wide class of starlike-graphs, and discuss possible sociological interpretations of this fact, which may be useful in many other situations.
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| 5. |
- Haukkanen, Pentti, et al.
(författare)
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The Arithmetic Jacobian Matrix and Determinant
- 2017
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Ingår i: Journal of Integer Sequences. - : University of Waterloo. - 1530-7638. ; 20:9
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Tidskriftsartikel (refereegranskat)abstract
- Let a1,..., am be real numbers that can be expressed as a finite product of prime powers with rational exponents. Using arithmetic partial derivatives, we define the arithmetic Jacobian matrix Ja of the vector a = (a1,..., am) analogously to the Jacobian matrix Jf of a vector function f. We introduce the concept of multiplicative independence of {a1,..., am} and show that Ja plays in it a similar role as Jf does in functional independence. We also present a kind of arithmetic implicit function theorem and show that Ja applies to it somewhat analogously as Jf applies to the ordinary implicit function theorem.
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| 6. |
- Mattila, Mika, et al.
(författare)
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Maximal perpendicularity in certain Abelian groups
- 2017
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Ingår i: Acta Universitatis Sapientiae, Mathematica. - : Walter de Gruyter. - 2066-7752. ; 9:1, s. 235-247
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Tidskriftsartikel (refereegranskat)abstract
- We define perpendicularity in an Abelian group G as a binary relation satisfying certain five axioms. Such a relation is maximal if it is not a subrelation of any other perpendicularity in G. A motivation for the study is that the poset (P, ⊆) of all perpendicularities in G is a lattice if G has a unique maximal perpendicularity, and only a meet-semilattice if not. We study the cardinality of the set of maximal perpendicularities and, on the other hand, conditions on the existence of a unique maximal perpendicularity in the following cases: G ≅ ℤn, G is finite, G is finitely generated, and G = ℤ ⊕ ℤ ⊕⋯. A few such conditions are found and a few conjectured. In studying ℝn, we encounter perpendicularity in a vector space.
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| 7. |
- Baltz, Andreas, et al.
(författare)
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Exact and heuristic algorithms for the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection
- 2015
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Ingår i: Journal of the Operational Research Society. - : Informa UK Limited. - 0160-5682 .- 1476-9360. ; 66:4, s. 615-626
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Tidskriftsartikel (refereegranskat)abstract
- We introduce and study the Travelling Salesman Problem with Multiple Time Windows and Hotel Selection (TSP-MTWHS), which generalises the well-known Travelling Salesman Problem with Time Windows and the recently introduced Travelling Salesman Problem with Hotel Selection. The TSP-MTWHS consists in determining a route for a salesman (eg, an employee of a services company) who visits various customers at different locations and different time windows. The salesman may require a several-day tour during which he may need to stay in hotels. The goal is to minimise the tour costs consisting of wage, hotel costs, travelling expenses and penalty fees for possibly omitted customers. We present a mixed integer linear programming (MILP) model for this practical problem and a heuristic combining cheapest insert, 2-OPT and randomised restarting. We show on random instances and on real world instances from industry that the MILP model can be solved to optimality in reasonable time with a standard MILP solver for several small instances. We also show that the heuristic gives the same solutions for most of the small instances, and is also fast, efficient and practical for large instances.
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| 8. |
- Marshall, Stephen, et al.
(författare)
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Street Network Studies: from Networks to Models and their Representations
- 2018
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Ingår i: Networks and Spatial Economics. - : Springer Science and Business Media LLC. - 1572-9427 .- 1566-113X. ; 18:3, s. 735-749
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Tidskriftsartikel (refereegranskat)abstract
- Over the last fifty years, research into street networks has gained prominence with a rapidly growing number of studies across disparate disciplines. These studies investigate a wide range of phenomena using a wealth of data and diverse analytical techniques. Starting within the fields of transport or infrastructure engineering, street networks have commonly been treated as sets of more or less homogeneous linear elements, connecting locations and intersecting at junctions. This view is commonly represented as a graph, which provides a common and rigorous formalisation accessible across disciplines and is particularly well-suited for problems such as flow optimisation and routing. Street networks are, however, complex objects of investigation and the way we model and then represent them as graphs has fundamental effects on the outcomes of a study. Many approaches to modelling street networks have been proposed, each lending itself to different analyses and supporting insights into diverse aspects of the urban system. Yet, this plurality and the relation between different models remains relatively obscure and unexplored. The motivations for adopting a given model of the network are also not always clear and often seem to follow disciplinary traditions. This paper provides an overview of key street network models and the prima facie merits of pertinent alternative approaches. It suggests greater attention to consistent use of terms and concepts, of graph representations and practical applications, and concludes with suggestions for possible ways forward.
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| 9. |
- Carling, Kenneth, et al.
(författare)
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Testing the gravity p-median model empirically
- 2015
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Ingår i: Operations Research Perspectives. - : Elsevier. - 2214-7160. ; 2:124
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Tidskriftsartikel (refereegranskat)abstract
- Regarding the location of a facility, the presumption in the widely used p-median model is that the customer opts for the shortest route to the nearest facility. However, this assumption is problematic on free markets since the customer is presumed to gravitate to a facility by the distance to and the attractiveness of it. The recently introduced gravity p-median model offers an extension to the p-median model that account for this. The model is therefore potentially interesting, although it has not yet been implemented and tested empirically. In this paper, we have implemented the model in an empirical problem of locating vehicle inspections, locksmiths, and retail stores of vehicle spare-parts for the purpose of investigating its superiority to the p-median model. We found, however, the gravity p-median model to be of limited use for the problem of locating facilities as it either gives solutions similar to the p-median model, or it gives unstable solutions due to a non-concave objective function.
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| 10. |
- Darányi, Sándor, et al.
(författare)
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The Sphynx's new riddle : How to relate the canonical formula of myth to quantum interaction
- 2013
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Konferensbidrag (refereegranskat)abstract
- We introduce Claude Lévi Strauss' canonical formula (CF), an attempt to rigorously formalise the general narrative structure of myth. This formula utilises the Klein group as its basis, but a recent work draws attention to its natural quaternion form, which opens up the possibility that it may require a quantum inspired interpretation. We present the CF in a form that can be understood by a non-anthropological audience, using the formalisation of a key myth (that of Adonis) to draw attention to its mathematical structure. The future potential formalisation of mythological structure within a quantum inspired framework is proposed and discussed, with a probabilistic interpretation further generalising the formula.
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