F-Dugundji spaces, F-Milutin spaces and absolute F-valued retracts

Банах, Тарас; Yagasaki, Tatsuhiko

doi:10.1016/j.topol.2014.08.014

Cited by 8 publications

(3 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Suppose the contrary w(X) > ω 1 , then by Theorem 5.6 and Proposition 6.3 from [7], there exists an embedding s : D ω2 → X. It follows from results of [2] that there exists a continuous map f : X → I(D ω2 ) such that Is(f (x)) = δ x for each x ∈ s(D τ ). Since the map Is is an embedding, we have f • s = δD ω2 .…”

Section: Idempotent Measures and Absolute Retractsmentioning

confidence: 93%

Idempotent measures:absolute retracts and soft maps

Radul¹

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Section: Idempotent Measures and Absolute Retractsmentioning

confidence: 93%

Idempotent measures:absolute retracts and soft maps

Radul¹

2018

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…The tensor product operation of probability measures is well known and very useful partially for investigation of the spaces of probability measures on compacta (see for example Chapter 8 from [15]). General categorical definition of tensor product for any functor was given in [3]. Applying this definition to the capacity functor we obtain that a tensor product of capacities on compacta X 1 and X 2 is a continuous map…”

Section: Tensor Products Of Capacitiesmentioning

confidence: 99%

Games in possibility capacities with payoff expressed by fuzzy integral

Radul¹

2019

Preprint

Self Cite

View full text Add to dashboard Cite

This paper studies non-cooperative games where players are allowed to play their mixed non-additive strategies. Expected payoffs are expressed by so-called fuzzy integrals: Choquet integral, Sugeno integral and generalizations of Sugeno integral obtained by using triangular norms. We consider the existence problem of Nash equilibrium for such games. Positive results for Sugeno integral and its generalizations are obtained. However we provide some example of a game with Choquet payoffs which have no Nash equilibrium. Such example demonstrates that fuzzy integrals based on the maximum operation are more suitable for possibility capacities then Choquet integral which is based on the addition operation.

show abstract

“…The tensor product operation of probability measures is well known and very useful partially for investigation of the spaces of probability measures on compacta (see for example Chapter 8 from [12]). General categorical definition of tensor product for any functor was given in [2]. Applying this definition to the capacity functor we obtain that a tensor product of capacities on compacta X 1 and X 2 is a continuous map…”

Section: Tensor Products Of Capacitiesmentioning

confidence: 99%

Equilibrium under uncertainty with Sugeno payoff

Radul

2018

Fuzzy Sets and Systems

Self Cite

View full text Add to dashboard Cite

Abstract. This paper studies n-player games where players beliefs about their opponents behaviour are capacities. The concept of an equilibrium under uncertainty was introduced J.Dow and S.Werlang (J Econ. Theory 64 (1994) 205-224)) for two players and was extended to n-player games by J.Eichberger and D.Kelsey (Games Econ. Behav. 30 (2000) 183-215). Expected utility was expressed by Choquet integral. We consider the concept of an equilibrium under uncertainty in this paper but with expected utility expressed by Sugeno integral. Existence of such an equilibrium is demonstrated using some abstract non-linear convexity on the space of capacities.

show abstract

F-Dugundji spaces, F-Milutin spaces and absolute F-valued retracts

Cited by 8 publications

References 9 publications

Idempotent measures:absolute retracts and soft maps

Idempotent measures:absolute retracts and soft maps

Games in possibility capacities with payoff expressed by fuzzy integral

Equilibrium under uncertainty with Sugeno payoff

Contact Info

Product

Resources

About