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Nonadditive robust ordinal regression with nonadditivity index and multiple goal linear programming

Published on Jul 1, 2019in International Journal of Intelligent Systems7.229
· DOI :10.1002/int.22119
Jian-Zhang Wu4
Estimated H-index: 4
,
Gleb Beliakov33
Estimated H-index: 33
Abstract
  • References (29)
  • Citations (4)
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1997
1 Author (Andreas Hilbert)
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References29
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#1Ning CuiH-Index: 1
#2Junhong LiH-Index: 1
This paper formulates a new particle motion system. The dynamic behaviors of the system are studied including the continuous dependence on initial conditions of the system’s solution, the equilibrium stability, Hopf bifurcation at the equilibrium point, etc. This shows the rich dynamic behaviors of the system, including the supercritical Hopf bifurcations, subcritical Hopf bifurcations, and chaotic attractors. Numerical simulations are carried out to verify theoretical analyses and to exhibit th...
2 CitationsSource
#1Jian-Zhang Wu (NBU: Ningbo University)H-Index: 4
#2Gleb Beliakov (Peoples' Friendship University of Russia)H-Index: 33
Abstract Nonadditivity is an essential property of the capacities defined on the sets of decision criteria. Nonadditivity extends the additivity of traditional probability measures and enables capacities to flexibly represent the interaction phenomenon between the decision criteria. We propose the nonadditivity index to quantify the degree and kind of nonadditivity of a capacity, discuss some properties of this index, and present some tools to help decision makers determine the nonadditivity ind...
14 CitationsSource
3 CitationsSource
#1Gleb Beliakov (Deakin University)H-Index: 33
#2Simon James (Deakin University)H-Index: 15
Last. Tomasa Calvo Sánchez (University of Alcalá)H-Index: 21
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We propose a version of ordered weighted averaging (OWA) operators, which are robust against inputs with outliers. Outliers may heavily bias the outputs of the standard OWA. The penalty-based method proposed here comprises both outlier detection and reallocation of weights of the OWA. At the first stage, the outliers are identified based on a robust criterion that can accommodate up to half the inputs being outliers, but at the same time not removing the inputs unnecessarily. Three numerical alg...
6 CitationsSource
#2Lina García-Cabrera (University of Jaén)H-Index: 7
Dynamic multiattribute decision-making (DMADM) problems are very common in real life and meaningful as research topic. In this paper, the focus is the DMADM problems with correlated periods, in which the attribute assessment values take the form of 2-tuple linguistic values. The concept of the discrete time 2-tuple linguistic variable where is introduced to describe a collection of 2-tuple linguistic values collected from different periods. To aggregate 2-tuple information gathered in multiple p...
11 CitationsSource
#1Jian-Zhang Wu (NBU: Ningbo University)H-Index: 1
#2Endre Pap (Óbuda University)H-Index: 34
Last. Aniko Szakal (Óbuda University)H-Index: 5
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The decision maker's preference information on the importance and interaction of decision criteria can be explicitly described by the probabilistic interaction indices in the framework of the capacity based multicriteria decision analysis. In this paper, we first investigate some properties of the probabilistic interaction indices of the empty set, and propose the maximum and minimum empty set interaction principles based capacity identification methods, which can be considered as the comprehens...
9 CitationsSource
#1Ronald R. Yager (Iona College)H-Index: 97
We are interested in the formulation of multi-criteria decision functions based on the use of a measure over the space of criteria. Specifically the relationship between the criteria is expressed using a fuzzy measure. We then use the Choquet integral to construct decision functions based on the measure. We look at a number of different decision functions generated from specific classes of measures.
4 CitationsSource
#1Silvia Angilella (University of Catania)H-Index: 11
#2Marta Carla Bottero (IPN: Instituto Politécnico Nacional)H-Index: 17
Last. Isabella Maria Lami (IPN: Instituto Politécnico Nacional)H-Index: 9
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In this paper we deal with an urban and territorial planning problem by applying the Non Additive Robust Ordinal Regression (NAROR). NAROR is a recent extension of the Robust Ordinal Regression family of Multiple Criteria Decision Aiding methods to the Choquet integral preference model which permits to represent interaction between considered criteria through the use of a set of non-additive weights called capacity or fuzzy measure. The use of NAROR permits the Decision Maker (DM) to give prefer...
23 CitationsSource
#1Jian-Zhang WuH-Index: 2
#2Liping YuH-Index: 6
Last. Bisheng DuH-Index: 5
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In the literature (40), the authors proposed the sum interaction index and discussed its basic mathematical properties. And by some comparison analyses, the authors demonstrated that the sum interaction index can be taken as an alternative of the probabilistic interaction index to measure the interaction phenomenon of the multiple decision criteria. In this paper, we further investigate the properties of the sum interaction index with respect to some particular families of monotone measures, suc...
8 CitationsSource
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#1Li HuangH-Index: 1
#2Jian-Zhang WuH-Index: 1
Last. Rui-Jie XiH-Index: 1
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The capacity is a powerful tool with exponential coefficients to represent the interaction phenomenon among decision criteria, but its random generation becomes a tough issue for dealing with the monotonicity with all inclusion subsets as well as the complex constraints of decision preference. In this paper, we adopt a kind of explicit interaction index, the nonadditivity index, to construct two types of quasi-random generation methods of capacity under a given decision interaction preference. C...
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#1Gleb Beliakov (Deakin University)H-Index: 33
#2Jian-Zhang Wu (NBU: Ningbo University)H-Index: 4
Last. Dmitriy Divakov (Peoples' Friendship University of Russia)H-Index: 1
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Abstract This paper addresses a methodology for decision support under multiple and correlated decision criteria. Nonadditive robust ordinal regression (NAROR) aims to build capacities that fit the decision makers’ explicit preferences and pairwise rankings of some alternatives. The capacities provide great flexibility to model decision problems accounting for interactions among the decision criteria. The feasible set of capacities helps identifying all the necessary and possible dominance relat...
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#1Jian-Zhang Wu (NBU: Ningbo University)H-Index: 1
#1Jian-Zhang Wu (NBU: Ningbo University)H-Index: 4
Last. Ye Zhu (Deakin University)H-Index: 1
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1 CitationsSource
#1Jian-Zhang Wu (NBU: Ningbo University)H-Index: 4
#2Gleb Beliakov (Deakin University)H-Index: 33
1 CitationsSource
#1Gleb Beliakov (Deakin University)H-Index: 33
#2Marek Gagolewski (PAN: Polish Academy of Sciences)H-Index: 8
Last. Simon James (Deakin University)H-Index: 15
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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...
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#1Jian-Zhang Wu (NBU: Ningbo University)
#2Gleb Beliakov (Deakin University)H-Index: 33
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#1Jian-Zhang Wu (NBU: Ningbo University)H-Index: 4
#2Gleb Beliakov (Peoples' Friendship University of Russia)H-Index: 33
Abstract Nonmodularity is a more general concept than nonadditivity which provides a more inclusive reflection of the relationship between subsets of criteria in multicriteria decision making. In this paper, we construct the nonmodularity index to describe the kind and intensity of interaction within a subset of criteria associated with the nonmodularity, and introduce the total nonmodularity and nonadditivity (amount) index to reflect the interactions within a capacity as a whole. We prove some...
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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...
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#1Rui-Jie Xi (NBU: Ningbo University)H-Index: 1
#2Jian-Zhang Wu (NBU: Ningbo University)H-Index: 4
Last. Gleb Beliakov (Deakin University)H-Index: 33
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Matrix algebra is an efficient way to represent the relationship between different concepts in the multiple criteria decision analysis theory. The main purpose of this paper is to provide a compact and systematic representation of the capacities and nonlinear integrals based decision theory and models from the perspective of matrices or vectors. We first investigate the forms and properties of the matrix representation of some equivalent transformations of capacities and introduce some new types...
1 CitationsSource