✦ LIBER ✦

Regular fuzzy measure and representation of comonotonically additive functional

✍ Scribed by Yasuo Narukawa; Toshiaki Murofushi; Michio Sugeno

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 110 KB
Volume: 112
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(98)00138-9

No coin nor oath required. For personal study only.

✦ Synopsis

This paper discusses the functional I deÿned on the class of continuous functions, which is comonotonically additive and monotone. The notion of regular fuzzy measure is proposed and the uniqueness theorem of regular fuzzy measure is shown. It is also shown that I can be represented by the di erence of two Choquet integrals with respect to regular fuzzy measures when the universal set X is a locally compact Hausdor space, and that I can be represented by one Choquet integral with respect to a regular fuzzy measure when X is a compact Hausdor space.

📜 SIMILAR VOLUMES

Boundedness and symmetry of comonotonica

Boundedness and symmetry of comonotonically additive functionals

✍ Yasuo Narukawa; Toshiaki Murofushi; Michio Sugeno 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 115 KB

The relations between a comonotonically additive and monotone functional I and the induced fuzzy measures + I and - I are discussed. We present a necessary and su cient condition of the functional I for + I (X ) ¡ ∞; - I (X ) ¡ ∞ and + I (X ) = -I (X ).

Decomposition and representation of fuzz

Decomposition and representation of fuzzy valued measure

✍ Mila Stojaković 📂 Article 📅 2000 🏛 Elsevier Science 🌐 English ⚖ 100 KB

On measures of fuzziness and their repre

On measures of fuzziness and their representations

✍ Bruce R Ebanks 📂 Article 📅 1983 🏛 Elsevier Science 🌐 English ⚖ 611 KB

Continuous-from-above possibility measur

Continuous-from-above possibility measures and f-additive fuzzy measures on separable metric spaces: Characterization and regularity

✍ Toshiaki Murofushi; Michio Sugeno 📂 Article 📅 1993 🏛 Elsevier Science 🌐 English ⚖ 258 KB

Differential Representation of Measures

Differential Representation of Measures and Functions

✍ G. Isac; D.T. Vuza 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 170 KB

We present in this paper an elementary method of obtaining a differential representation of Radon measures, of rapidly decreasing functions, and of elements of Besov spaces. We apply our results to the study of vaguelette systems.

Integral Representation of Additive Oper

Integral Representation of Additive Operators with Respect to a Vector Measure and its Applications

✍ Werner Fischer; Ulrich Schöler 📂 Article 📅 1979 🏛 John Wiley and Sons 🌐 English ⚖ 879 KB

During the last years representation theory of additive operators on spaces of measurable functions has been of interest for many writers. L. DREWNOWSKI, W. ORLICZ ([4], [5]), and V. MIZEL ([19], [20]) considered scalar valued operators (functionalu) on various function spaces, then in a subsequent