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

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Probabilistic bipartition interaction index of multiple decision criteria associated with the nonadditivity of fuzzy measures

Published on Dec 21, 2018

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...

Nonadditivity index and capacity identification method in the context of multicriteria decision making

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...

Published on Sep 1, 2018

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...

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...

Two kinds of explicit preference information oriented capacity identification methods in the context of multicriteria decision analysis

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...

Published on Jan 1, 2018

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.

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...

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

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 th...

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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...

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...

Multiple Goal Linear Programming-Based Decision Preference Inconsistency Recognition and Adjustment Strategies

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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