Decomposition integrals

Convergence theorems for monotone measures

“…The basic concept in this survey will be that of a monotone measure (see, e.g., [8,29,[39][40][41][42]57,58,62,73,96]). …”

“…Various other names have been used for them (and slight variations thereof) over the years: monotone measures, non-additive measures, capacities, etc. (see, e.g., [39,40,57,58,62,96]). But the essential feature, namely, for nonnegative set functions to drop any form of additivity and to replace it by the (usually weaker) monotonicity (and the vanishing in the empty set) was a significant step toward a generalization of the theory of measures.…”

Ordered Weighted Averaging Operators and their Generalizations with Applications in Decision Making

“…Let ℋ ( ) = {ℬ|ℬ is a chain in of length }, ∈ {1, … , }. As shown in [12], these decomposition systems yield the only kind of decomposition integrals which are also universal integrals in the sense of Klement et al [10]. Note that ℋ (1) , is the Shilkret integral [19], while ℋ ( ) , = Ch is the Choquet integral [3].…”

“…Recall that due to [12], ℋ, ( ) = 1, for each capacity , whenever the decomposition system ℋ is complete (i.e., each non-empty subset of is contained in at least one collection from ℋ) and any of its collections is formed by logically independent subsets of (i.e., their intersection is nonempty). Now, we introduce some decomposition systems and related decomposition integrals.…”

Fuzzy orness measure and new orness axioms

“…Aggregation function (or operator) [1,6] is essential in a variety of theoretical and application areas [7,10,16,17,18,19,23]. Ordered Weighted Averaging (OWA) operators (proposed by Yager [25]) which generalize the or-like and and-like aggregation functions with the aggregation result lying between the Min (and) and Max (or) operators, built a well-known class of aggregation functions.…”