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Combining analytical hierarchy process and Choquet integral within non-additive robust ordinal regression ☆

Published on Jun 1, 2016in Omega-international Journal of Management Science5.34
· DOI :10.1016/j.omega.2015.07.003
Salvatore Corrente15
Estimated H-index: 15
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Alessio Ishizaka23
Estimated H-index: 23
(University of Portsmouth)
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Abstract
We consider multiple criteria decision aiding in the case of interaction between criteria. In this case the usual weighted sum cannot be used to aggregate evaluations on different criteria and other value functions with a more complex formulation have to be considered. The Choquet integral is the most used technique and also the most widespread in the literature. However, the application of the Choquet integral presents two main problems being the necessity to determine the capacity, which is the function that assigns a weight not only to all single criteria but also to all subset of criteria, and the necessity to express on the same scale evaluations on different criteria. While with respect to the first problem we adopt the recently introduced Non-Additive Robust Ordinal Regression (NAROR) taking into account all the capacities compatible with the preference information provided by the DM, with respect to the second one we build the common scale for the considered criteria using the Analytic Hierarchy Process (AHP). We propose to use AHP on a set of reference points in the scale of each criterion and to use an interpolation to obtain the other values. This permits to reduce considerably the number of pairwise comparisons usually required by the DM when applying AHP. An illustrative example details the application of the proposed methodology.
  • References (66)
  • Citations (23)
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References66
Newest
Published on Dec 1, 2014in European Journal of Operational Research3.81
Salvatore Greco52
Estimated H-index: 52
(University of Catania),
Vincent Mousseau26
Estimated H-index: 26
(ECP: École Centrale Paris),
Roman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
We present a new method called UTAGMS–INT for ranking a finite set of alternatives evaluated on multiple criteria. It belongs to the family of Robust Ordinal Regression (ROR) methods which build a set of preference models compatible with preference information elicited by the Decision Maker (DM). The preference model used by UTAGMS–INT is a general additive value function augmented by two types of components corresponding to ‘‘bonus’’ or ‘‘penalty’’ values for positively or negatively interactin...
Published on Nov 1, 2014in Group Decision and Negotiation2.01
Elena Rokou4
Estimated H-index: 4
(NTUA: National Technical University of Athens),
Konstantinos Kirytopoulos13
Estimated H-index: 13
(NTUA: National Technical University of Athens)
In practice most organisational decisions are made by groups that bring into the problem multiple perspectives, both complementary and contradictory. When having a group of decision makers, usually individuals’ preferences are either led to consensus or are aggregated with the use of some function like the median, the arithmetic or geometric mean. We focus in the second case, where individual’s preferences need to be aggregated. Our approach is based on the fact that when two decision makers are...
Published on Sep 29, 2014
Theodor J. Stewart32
Estimated H-index: 32
(UCT: University of Cape Town)
The multiattribute utility function is a means of systematically analyzing preferences in the context of multiattribute or multicriteria decision making under conditions of uncertain or risky outcomes, and thus integrates concepts from multiattribute value measurement and expected utility theory. The process starts by eliciting utility functions for each individual attribute in turn, which then have to be aggregated in some sense in order to form the overall multiattribute utility function. A we...
Published on Jan 17, 2014
Salvatore Corrente15
Estimated H-index: 15
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania)
+ 1 AuthorsRoman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
Within disaggregation–aggregation approach, ordinal regressionaims at inducing parameters of a preference model, for example, parameters of a value function, which represent some holistic preference comparisons of alternatives given by the Decision Maker (DM). Usually, from among many sets of parameters of a preference model representing the preference information given by the DM, only one specific set is selected and used to work out a recommendation. For example, while there exist many value f...
Published on Nov 1, 2013in Machine Learning2.81
Salvatore Corrente15
Estimated H-index: 15
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Portsmouth)
+ 1 AuthorsRoman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
Multiple Criteria Decision Aiding (MCDA) offers a diversity of approaches designed for providing the decision maker (DM) with a recommendation concerning a set of alternatives (items, actions) evaluated from multiple points of view, called criteria. This paper aims at drawing attention of the Machine Learning (ML) community upon recent advances in a representative MCDA methodology, called Robust Ordinal Regression (ROR). ROR learns by examples in order to rank a set of alternatives, thus conside...
Published on Jul 1, 2013in Expert Systems With Applications4.29
Alessio Ishizaka23
Estimated H-index: 23
(University of Portsmouth),
Nam Hoang Nguyen1
Estimated H-index: 1
(University of Portsmouth)
Fuzzy AHP is a hybrid method that combines Fuzzy Set Theory and AHP. It has been developed to take into account uncertainty and imprecision in the evaluations. Fuzzy Set Theory requires the definition of a membership function. At present, there are no indications of how these membership functions can be constructed. In this paper, a way to calibrate the membership functions with comparisons given by the decision-maker on alternatives with known measures is proposed. This new technique is illustr...
Published on Mar 1, 2013in Journal of Mathematical Economics0.63
Alfio Giarlotta7
Estimated H-index: 7
(University of Catania),
Salvatore Greco52
Estimated H-index: 52
(University of Catania)
A classical approach to model a preference on a set A of alternatives uses a reflexive, transitive and complete binary relation, i.e. a total preorder. Since the axioms of a total preorder do not usually hold in many applications, preferences are often modeled by means of weaker binary relations, dropping either completeness (e.g. partial preorders) or transitivity (e.g. interval orders and semiorders). We introduce an alternative approach to preference modeling, which uses two binary relations–...
Published on Feb 1, 2013in Fuzzy Sets and Systems2.91
Silvia Bortot3
Estimated H-index: 3
(University of Trento),
Ricardo Alberto Marques Pereira9
Estimated H-index: 9
(University of Trento)
We examine the AHP in the framework of Choquet integration and we propose an extension of the standard AHP aggregation scheme on the basis of the Shapley values associated with the criteria. In our model a measure of dominance inconsistency between criteria is defined in terms of the totally inconsistent matrix associated with the main pairwise comparison matrix of the AHP. The measure of dominance inconsistency is then used to construct a non-additive capacity whose associated Shapley values re...
José Rui Figueira29
Estimated H-index: 29
(Technical University of Lisbon),
Salvatore Greco52
Estimated H-index: 52
(University of Catania)
+ 1 AuthorsRoman Slowifiski67
Estimated H-index: 67
(PUT: Poznań University of Technology)
We present main characteristics of ELECTRE (ELimination Et Choix Traduisant la REalite - ELimination and Choice Expressing the REality) family methods, designed for multiple criteria decision aiding. These methods use as a preference model an outranking relation on the set of actions—it is constructed in result of concordance and nondiscordance tests involving a specific input preference information. After a brief description of the constructivist conception in which the ELECTRE methods are inse...
Published on Jan 1, 2012
Thomas L. Saaty77
Estimated H-index: 77
(University of Pittsburgh),
Luis G. Vargas35
Estimated H-index: 35
(University of Pittsburgh)
ieρa aρχή is the Greek word for hierarchy meaning holy origin or holy rule1. It is the ordering of parts or elements of a whole from the highest to the lowest. A hierarchy is the principle of control that secures the effective functioning of the organization2.
Cited By23
Newest
Published on Jan 1, 2020
Gleb Beliakov31
Estimated H-index: 31
(Deakin University),
Simon James14
Estimated H-index: 14
(Deakin University),
Jian-Zhang Wu2
Estimated H-index: 2
(NBU: Ningbo University)
This chapter is a key contribution of this work in which various computational approaches to learning fuzzy measures are described. The learning problem is framed from the perspective of data fitting, where we aim to define a model that interpolates or approximates a set of observed or user-specified instances. Fitting is performed with respect to different metrics, and by solving different convex and non-convex optimisation problems. The computational complexity of fuzzy measures is addressed b...
Published on Oct 1, 2019in Information Sciences5.52
Gleb Beliakov31
Estimated H-index: 31
(Deakin University),
Marek Gagolewski7
Estimated H-index: 7
(PAN: Polish Academy of Sciences),
Simon James14
Estimated H-index: 14
(Deakin University)
Abstract The Sugeno integral is a function particularly suited to the aggregation of ordinal inputs. Defined with respect to a fuzzy measure, its ability to account for complementary and redundant relationships between variables brings much potential to the field of biomedicine, where it is common for measurements and patient information to be expressed qualitatively. However, practical applications require well-developed methods for identifying the Sugeno integral’s parameters, and this task is...
Published on Aug 1, 2019in Expert Systems With Applications4.29
Francesca Abastante5
Estimated H-index: 5
(Polytechnic University of Turin),
Salvatore Corrente15
Estimated H-index: 15
(University of Catania)
+ 2 AuthorsIsabella Maria Lami7
Estimated H-index: 7
(Polytechnic University of Turin)
Abstract We propose a development of the Analytic Hierarchy Process (AHP) permitting to use the methodology also for decision problems with a very large number of alternatives and several criteria. While the application of the original AHP method involves many pairwise comparisons between considered objects, that can be alternatives with respect to considered criteria or criteria between them, our parsimonious proposal is composed of five steps: (i) direct evaluation of the objects at hand; (ii)...
Published on Aug 1, 2019in Information Sciences5.52
Gleb Beliakov31
Estimated H-index: 31
(Deakin University),
Jian-Zhang Wu2
Estimated H-index: 2
(NBU: Ningbo University)
Abstract Fuzzy measures model interactions between the inputs in aggregation problems. Their complexity grows exponentially with the dimensionality of the problem, and elicitation of fuzzy measure coefficients either from domain experts or from empirical data is a significant challenge. The notions of k -additivity and k -maxitivity simplify the fuzzy measures by limiting interactions to subsets of up to k elements, but neither reduces the complexity of monotonicity constraints. In this paper we...
Jian-Zhang Wu1
Estimated H-index: 1
,
Li Huang1
Estimated H-index: 1
+ 1 AuthorsYi-Ping Zhou1
Estimated H-index: 1
The purpose of this paper is to enrich the decision preference information inconsistency check and adjustment method in the context of capacity-based multiple criteria decision making. We first show that almost all the preference information of a decision maker can be represented as a collection of linear constraints. By introducing the positive and negative deviations, we construct the the multiple goal linear programming (MGLP)-based inconsistency recognition model to find out the redundant an...
Lazim Abdullah12
Estimated H-index: 12
,
Norsyahida Zulkifli2
Estimated H-index: 2
+ 2 AuthorsAbdullah Al-Barakati
Abstract The decision making trial and evaluation laboratory (DEMATEL) is a pragmatic method used to construct the structural correlation of criteria in a multi-criteria decision making (MCDM) problem. This paper proposes modifications to DEMATEL. Different from the typical DEMATEL which utilizes crisp numbers, this modification introduces interval-valued intuitionistic fuzzy numbers to enhance judgements in group decision-making environment. We use the interval-valued intuitionistic fuzzy weigh...
Mengzhuo Guo (CityU: City University of Hong Kong), Xiuwu Liao11
Estimated H-index: 11
(Ministry of Education)
+ 1 AuthorsQingpeng Zhang8
Estimated H-index: 8
(CityU: City University of Hong Kong)
Abstract Multiple criteria approaches can assist the product manager to know the consumer preferences in the context of e-commerce. Consumer preference analysis explains what aspects of a product affect and how they affect a consumer’s purchasing decision. This issue plays an important role in e-commerce platforms from its relevance in marketing decisions such as advertisements, recommendations and promotions. In this regard, we propose a data-driven multiple criteria decision aiding (MCDA) appr...
Published on Mar 24, 2019
Jian-Zhang Wu1
Estimated H-index: 1
,
Yi-Ping Zhou1
Estimated H-index: 1
+ 1 AuthorsJun-Jie Dong1
Estimated H-index: 1
Multicriteria correlation preference information (MCCPI) refers to a special type of 2-dimensional explicit information: the importance and interaction preferences regarding multiple dependent decision criteria. A few identification models have been established and implemented to transform the MCCPI into the most satisfactory 2-additive capacity. However, as one of the most commonly accepted particular type of capacity, 2-additive capacity only takes into account 2-order interactions and ignores...