Bipolar Fuzzy Integrals

In decision analysis and especially in multiple criteria decision analysis, several non additive integrals have been introduced in the last sixty years. Among them, we remember the Choquet integral, the Shilkret integral and the Sugeno integral. Recently, the bipolar Choquet integral has been proposed for the case in which the underlying scale is bipolar. In this paper we propose the bipolar Shilkret integral and the bipolar Sugeno integral. Moreover, we provide an axiomatic characterization of all these three bipolar fuzzy integrals.Comment: 15 page

Discrete bipolar universal integrals

Abstract. The concept of universal integral, recently proposed, generalizes the Choquet, Shilkret and Sugeno integrals. Those integrals admit a discrete bipolar formulation, useful in those situations where the underlying scale is bipolar. In this paper we propose the concept of discrete bipolar universal integral, in order to provide a common framework for bipolar discrete integrals, including as special cases the discrete Choquet, Shilkret and Sugeno bipolar integrals. Moreover we provide two different axiomatic characterizations of the proposed discrete bipolar universal integral

A Fairness Relation Based on the Asymmetric Choquet Integral and Its Application in Network Resource Allocation Problems

The recent problem of network resource allocation is studied where pairs of users could be in a favourable situation, given that the allocation scheme is refined by some add-on technology. The general question here is whether the additional effort can be effective with regard to the user’s experience of fairness. The computational approach proposed in this paper to handle this question is based on the framework of relational optimization. For representing different weightings for different pairs of users, the use of a fuzzy measure appears to be reasonable. The generalized Choquet integrals are discussed from the viewpoint of representing fairness and it is concluded that the asymmetric Choquet integral is the most suitable approach. A binary relation using the asymmetric Choquet integral is proposed. In case of a supermodular fuzzy measure, this is a transitive and cycle-free relation. The price of fairness with regard to a wireless channel allocation problem taking channel interference into account is experimentally studied and it can be seen that the asymmetric on relation actually selects allocations that perform on average between maxmin fairness and proportional fairness, and being more close to maxmin fairness as long as channel interference is not high