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### Aggregation Operators on Bounded Partially Ordered Sets, Aggregative Spaces and Their Duality [chapter]

Mustafa Demirci
2014 Communications in Computer and Information Science
The present paper introduces aggregative spaces and their category AGS, and then establishes a dual adjunction between AGS and the category Agop of aggregation operators on bounded partially ordered sets  ...  aggregation operators and the full subcategory of AGS consisting of sober aggregative spaces, will also be subjects of this paper.  ...  Every aggregation operator A on L Definition 1 . 1 [5] The category Agop of aggregation operators has as objects all triples (L, ≤, A), where (L, ≤) is a bounded poset and A is an aggregation operator  ...

### Median linear orders: Heuristics and a branch and bound algorithm

J.P. Barthelemy, A. Guenoche, O. Hudry
1989 European Journal of Operational Research
After recalling some facts about the median linear orders problem, two heuristics are studied to solve it. Then, a branch and bound method is designed which computes all the solutions.  ...  Moreover, while OWT is NP-hard, these heuristics are still polynomial (each iteration needs at most O(n 2) operations and the number of iterations is bounded by the number of 3-cycles of the tournament  ...  In the last part, a branch and bound (B&B) method is designed to get all the median linear orders associated with a profile of linear orders.  ...

### Prioritized aggregation operators

Ronald R. Yager
2008 International Journal of Approximate Reasoning
We first introduce a prioritized scoring operator and a closely related prioritized averaging operator. We next introduce a prioritized "anding" and then a prioritized "oring" operator.  ...  We consider a number of aggregation operators in which there exists a prioritization relationship between the arguments.  ...  We now show that this aggregation method is bounded and monotonic.  ...

### Logics with aggregate operators

Lauri Hella, Leonid Libkin, Juha Nurmonen, Limsoon Wong
2001 Journal of the ACM
We consider a powerful counting logic, and extend it with the set of all aggregate operators.  ...  of expressivity bounds, that do not depend on a particular class of arithmetic functions, and that subsume all those previously known.  ...  For example , 27] gives some bounds based on the estimates on the largest number a query can produce; clearly such bounds are not robust and do not withstand adding arithmetic operations.  ...

### Aggregation operators 2003

2003 European Society for Fuzzy Logic and Technology
Several new results in the field of aggregation operators are recalled. Most of them were or will be presented at 24 th Linz Seminar, AGOP'2003, IFSA'2003 and EUSFLAT'2003.  ...  Finally, a personal vision of the future development of the theory of aggregation operators is given.  ...  Acknowledgements The work on this contribution was supported by grants VEGA 1/8331/01 and APVT-20-023402.  ...

### Range-Aggregate Queries Involving Geometric Aggregation Operations [chapter]

Saladi Rahul, Ananda Swarup Das, K. S. Rajan, Kannan Srinathan
2011 Lecture Notes in Computer Science
This paper is the first attempt to provide dynamic solutions to problems involving geometric aggregation operations.  ...  Range-aggregate version of point enclosure queries, 1-d segment intersection, 2-d orthogonal segment intersection (with/without distance constraint) are revisited and we improve the existing results for  ...  An amortized analysis is carried out to get an efficient bound. Assume that we insert n segments and points in an arbitrary order.  ...

### Fuzzy Triangular Aggregation Operators

Ulrich Florian Simo, Henri Gwét
2018 International Journal of Mathematics and Mathematical Sciences
We present a new class of fuzzy aggregation operators that we call fuzzy triangular aggregation operators.  ...  The fuzzy triangular aggregation operators not only cover a wide range of useful existing fuzzy aggregation operators but also provide new interesting cases.  ...  We present a new class of fuzzy aggregation operators that we call fuzzy triangular aggregation operators.  ...

### Measure-based aggregation operators

Erich Peter Klement, Radko Mesiar, Endre Pap
2004 Fuzzy sets and systems (Print)
Several properties of such aggregation operators are investigated, and the relationship with distinguished classes of aggregation operators is discussed.  ...  In analogy to the representation of the standard probabilistic average as an expected value of a random variable, a geometric approach to aggregation is proposed.  ...  Acknowledgment This work was supported by two European actions (CEEPUS network SK-42 and COST action 274) as well as by grants VEGA 1/8331/01 and MNTS (Yugoslavia).  ...

### Aggregation operators for fuzzy ontologies

Fernando Bobillo, Umberto Straccia
2013 Applied Soft Computing
Some examples of aggregation operators are weighted sums, Ordered Weighting Averaging operators and fuzzy integrals. In this work, we integrate fuzzy ontologies and aggregation operators.  ...  As a theoretical formalism, we provide the syntax and semantics of a fuzzy Description Logic with fuzzy aggregation operators.  ...  In the current paper, we order them in decreasing order for coherence with the case of aggregation operators.  ...

### Operator-scaling Gaussian random fields via aggregation [article]

Yi Shen, Yizao Wang
2019 arXiv   pre-print
We propose an aggregated random-field model, and investigate the scaling limits of the aggregated partial-sum random fields.  ...  rates different operator-scaling Gaussian random fields appear as the region area tends to infinity.  ...  YS's research was supported in part by the Natural Sciences and Engineering Research Council of Canada (RGPIN-2014-04840).  ...

### Aggregate Operators in Constraint Query Languages

Michael Benedikt, Leonid Libkin
2002 Journal of computer and system sciences (Print)
We then give a set of results showing that it is impossible to get constraint-based languages that admit definable aggregation operators, both for exact operators and for approximate ones.  ...  We deal with standard relational aggregation, and also with aggregates specific to spatial data, such as volume.  ...  constraints) and not finite, the aggregation operators cannot be allowed to be applied to any constraint query output.  ...

### Aggregation issues in operational risk

Rosella Giacometti, Svetlozar Rachev, Anna Chernobai, Marida Bertocchi
2008 The Journal of Operational Risk
In this paper we study copula-based models for aggregation of operational risk capital across business lines in a bank.  ...  The problem can be further aggravated by the persistence of heavy tails in operational loss data; in some cases, the subadditivity property of value-at-risk may fail and the capital charge becomes underestimated  ...  As a result, the aggregate measure of risk represents an upper bound for a bank's true total level of risk.  ...

### Absorbent tuples of aggregation operators

G. Beliakov, T. Calvo, A. Pradera
2007 Fuzzy sets and systems (Print)
We examine the most important classes of aggregation operators in respect to their absorbent tuples, and also construct new aggregation operators with predefined sets of absorbent tuples.  ...  We generalize the notion of an absorbent element of aggregation operators. Our construction involves tuples of values that decide the result of aggregation.  ...  Acknowledgements This work was supported by the projects MTM2004-3175, BFM2003-05308, TIC2002-11942-E and TIC2003-09001-C02-02 from Ministerio de Educación y Ciencia, Spain, and PRIB-2004-9250, Govern  ...

### Aggregating operational risk across matrix structured loss data

Paul Embrechts, Giovanni Puccetti
2008 The Journal of Operational Risk
In the Basel II regulatory setup for operational risk in banking, we analyse how interdependencies between individual loss random variables within the matrix may influence different estimates for the minimum  ...  In order to investigate the consequences of the Basel II guidelines for LDA-based risk capital aggregation across the OR loss matrix L, in Table 3 we include upper and lower bounds on the Value-at-Risk  ...  Lower (LB) and upper (UB) bounds are given; bold face values indicate sharpness of these bounds.for rowwise aggregated losses.  ...

### Aggregation operators and Fuzzy OWL 2

Fernando Bobillo, Umberto Straccia
2011 2011 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2011)
In particular, the integration of aggregation operators (AOs) in fuzzy DLs has received little attention so far. In this work, we show how to support aggregation operators in fuzzy DLs.  ...  We provide syntax and semantics of a fuzzy DL extended with AOs, and provide a calculus for a family of AOs (weighted sum, OWA and quantifier-guided OWA).  ...  Section II recalls basic notions on mathematical fuzzy logic and aggregation operators. Then, Section III introduces fuzzy DLs that support aggregation operators.  ...
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