Bi-capacities. I: Definition, Möbius transform and interaction
From MaRDI portal
Publication:1770781
DOI10.1016/j.fss.2004.08.012zbMath1106.91023OpenAlexW2018696312MaRDI QIDQ1770781
Christophe Labreuche, Michel Grabisch
Publication date: 7 April 2005
Published in: Fuzzy Sets and Systems (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.fss.2004.08.012
Related Items (64)
Fuzzy bi-cooperative games in multilinear extension form ⋮ Discrete bipolar universal integrals ⋮ Choquet-Integral-Based Evaluations by Fuzzy Rules: Methods for Developing Fuzzy Rule Tables on the Basis of Weights and Interaction Degrees ⋮ \(k\)-additivity and \(\mathcal C\)-decomposability of bi-capacities and its integral ⋮ Stochastic multiobjective acceptability analysis for the Choquet integral preference model and the scale construction problem ⋮ Derivative of functions over lattices as a basis for the notion of interaction between attributes ⋮ Interaction transform for bi-set functions over a finite set ⋮ Entropy of capacities on lattices and set systems ⋮ Entropy of bi-capacities ⋮ Quadratic distances for capacity and bi-capacity approximation and identification ⋮ GAIA-SMAA-PROMETHEE for a hierarchy of interacting criteria ⋮ A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral ⋮ Multi- and multi-polar capacities ⋮ The core of bicapacities and bipolar games ⋮ Bipolar ordered weighted averages: BIOWA operators ⋮ Bipolar OWA operators with continuous input function ⋮ Möbius product-based constructions of aggregation functions ⋮ Sugeno integral based on absolutely monotone real set functions ⋮ New axiomatizations of the Shapley interaction index for bi-capacities ⋮ The 2-Additive Choquet Integral of Bi-capacities ⋮ The SMAA-TWD model: a novel stochastic multi-attribute three-way decision with interrelated attributes in triangular fuzzy information systems ⋮ Discrete bipolar pseudo-integrals ⋮ Incremental preference elicitation with bipolar Choquet integrals ⋮ Algebraic Structures for Bipolar Constraint-Based Reasoning ⋮ Bipolar preference modeling and aggregation in decision support ⋮ A class of fuzzy multisets with a fixed number of memberships ⋮ Bipolar fuzzy integrals ⋮ Decomposition-integral: unifying Choquet and the concave integrals ⋮ Bipolarization of posets and natural interpolation ⋮ Industrial performance measurement: an approach based on the aggregation of unipolar or bipolar expressions ⋮ The bipolar Choquet integral representation ⋮ The core and the Weber set for bicooperative games ⋮ Dealing with interaction between bipolar multiple criteria preferences in PROMETHEE methods ⋮ Belief functions on distributive lattices ⋮ Some properties for bisemivalues on bicooperative games ⋮ Aggregation of ordinal information ⋮ Aggregation on Boolean multi-polar space: knowledge-based vs. category-based ordering ⋮ A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid ⋮ A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid ⋮ Modelling multicriteria value interactions with reasoning maps ⋮ A value for bi-cooperative games ⋮ Finitely additive probability measures on classical propositional formulas definable by Gödel's t-norm and product t-norm ⋮ Bi-cooperative games with fuzzy bi-coalitions ⋮ Evidential reasoning in large partially ordered sets. Application to multi-label classification, ensemble clustering and preference aggregation ⋮ Representing uncertainty on set-valued variables using belief functions ⋮ The Choquet integral with respect to a level dependent capacity ⋮ Bisemivalues for bicooperative games ⋮ The Banzhaf power index for ternary bicooperative games ⋮ The selectope for bicooperative games ⋮ Unnamed Item ⋮ Robust Ordinal Regression ⋮ Decomposable and \(k\)-additive multi-capacities and multi-polar capacities ⋮ Jensen type inequality for the bipolar pseudo-integrals ⋮ CAPACITIES AND GAMES ON LATTICES: A SURVEY OF RESULTS ⋮ An overview of the asymmetric bipolar representation of positive and negative information in possibility theory ⋮ ELECTRE methods with interaction between criteria: an extension of the concordance index ⋮ The interaction transform for functions on lattices ⋮ Non-additive robust ordinal regression: a multiple criteria decision model based on the Choquet integral ⋮ Use and Applications of Non-Additive Measures and Integrals ⋮ Cooperative Game as Non-Additive Measure ⋮ Signed ring families and signed posets ⋮ Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues ⋮ Robust integrals ⋮ Terminological difficulties in fuzzy set theory -- the case of ``intuitionistic fuzzy sets
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Advances in prospect theory: cumulative representation of uncertainty
- \(k\)-order additive discrete fuzzy measures and their representation
- Ternary voting games
- The symmetric and asymmetric Choquet integrals on finite spaces for decision making
- On the extension of pseudo-Boolean functions for the aggregation of interacting criteria.
- An axiomatic approach to the concept of interaction among players in cooperative games
- Generalized Choquet-like aggregation functions for handling bipolar scales
- Theory of capacities
- Equivalent Representations of Set Functions
- Subjective Probability and Expected Utility without Additivity
- [https://portal.mardi4nfdi.de/wiki/Publication:5731810 On the foundations of combinatorial theory I. Theory of M�bius Functions]
This page was built for publication: Bi-capacities. I: Definition, Möbius transform and interaction