In this note an extension-type theorem for null-additive fuzzy measures is proved. AMS Mathematics Subject Classification (2000): 28A25

TCP congestion control is currently based on Jacobson’s algorithms (slow-start and congestion avoidance), devised back in 1988, with improvements such as SACK and NewReno. Although TCP has proved remarkably flexible thus far and managed to adapt to vastly different types of networks, we show in this paper that some of the assumptions behind these algorithms are no longer valid in today’s fast l...

Fuzzy valued measure ([7], [10], [3], [5]) is a natural generalization of a set valued measure ([6]). Infinite addition is defined ([12]) as a Zadeh’s extension principle of continuity. In [9], using an additive fuzzy valued measure, an integral of single valued function is defined and some basic properties are given. In this paper we proceed to investigate specific properties of integrals in f...

AIMD (additive increase and multiplicative decrease) algorithm has been used in many congestion control protocols, including TCP in the Internet. In this paper, we compare AIMD and MAIMD (multiplicative additive increase and multiplicative decrease). Our evaluation shows that the convergence speeds to fair states of AIMD and MAIMD are close to each other. However, MAIMD has some advantages. For...

In group decision-making, experts’ preferences are usually expressed by means of fuzzy preference relations. Because not all experts may be capable of maintaining consistency between all the possible pair of feasible options of the problem, it is worthwhile evaluating the degree of inconsistency of a fuzzy preference relation so that more importance can be given to the more consistent experts. ...

We study the problem of fairly allocating indivisible goods to groups of agents. Agents in the same group share the same set of goods even though they may have different preferences. Previous work has focused on unanimous fairness, in which all agents in each group must agree that their group’s share is fair. Under this strict requirement, fair allocations exist only for small groups. We introd...

This note discusses some mathematical misunderstandings about Savage (1954). It is shown that in his model the probability measure cannot be countably additive, that the set of events must be a u-algebra and not just an algebra, that Savage did not characterize all atomless finitely additive probability measures, and that the state space in his model, while infinite, does not have to be uncount...

We consider the problem of choosing an alternative in a set A = {A1, A2, ..., Am} of alternatives, given a set D = {d1, d2, ..., dh} of decision makers and a set Ω = {O1, O2, ..., On} of objectives. We assume that any decision maker dk assigns to any pair (alternative Ai, objective Oj) a number aijk that measures to what extent Ai satisfies Oj . We assume that Ω is a subset of a universal set U...

This note proves that risk measures obtained by applying the equivalent utility principle in rank-dependent utility are additive if and only if the utility function is linear or exponential and the probability weighting (distortion) function is the identity.

In this note, we study an approximation property of regular fuzzy neural network(RFNN). It is shown that any fuzzy-valued measurable function can be approximated by the four-layer RFNN in the sense of fuzzy integral norm for the finite sub-additive fuzzy measure on R.