𝔖 Bobbio Scriptorium
✦   LIBER   ✦

The fuzzy integral on product spaces for NSA measures

✍ Scribed by E.Suárez Díaz; F.Suárez García

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
417 KB
Volume
103
Category
Article
ISSN
0165-0114

No coin nor oath required. For personal study only.

✦ Synopsis

This paper deals with the study of fuzzy integrals defined as a generalization of Kruse's fuzzy integral , for fuzzy NSA measures given by Weber as opposed to Sugeno's measures. Several properties and convergence theorems, such as the monotone convergence theorem, the dominated convergence theorem and Fatou's lemma are shown for this fuzzy integral.

A fuzzy NSA measure will be constructed on a product space, based on product of these kinds of measures with the same additive generator and we extend the above integral on to a product space.

Further, a version of Fubini's theorem will be proved.

📜 SIMILAR VOLUMES

A further investigation for fuzzy measur
A further investigation for fuzzy measures on metric spaces
✍ Qingshan Jiang; Shengrui Wang; Diemel Ziou 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 341 KB

The pseudometric generating property of non-additive set functions also plays an important role as the autocontinuity in fuzzy measure theory (Jiang, Ph.D.

Choquet integral and fuzzy measures on l
Choquet integral and fuzzy measures on locally compact space
✍ Michio Sugeno; Yasuo Narukawa; Toshiaki Murofushi 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 372 KB

The concept of outer regular fuzzy measures is proposed, and it is shown that a functional of certain type on the cone of positive continuous functions with compact supports is represented as a Choquet integral with respect to a outer regular fuzzy measure. It is also shown that the Choquet integral

Integral Operators on the Product of C(K
Integral Operators on the Product of C(K) Spaces
✍ Fernando Bombal; Ignacio Villanueva 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 131 KB

We study and characterize the integral multilinear operators on a product of C K spaces in terms of the representing polymeasure of the operator. Some applications are given. In particular, we characterize the Borel polymeasures that can be extended to a measure in the product σ-algebra, generalizin

On the integrable noncompact fuzzy numbe
On the integrable noncompact fuzzy number space
✍ Degang Chen; XiaoPing Xue; Liangkuan Zhu 📂 Article 📅 2008 🏛 Elsevier Science 🌐 English ⚖ 232 KB

In this paper an extension of the existing fuzzy number, called integrable noncompact fuzzy number, is proposed. The representation theorems of integrable noncompact fuzzy number by intervals and functions are also presented. All the integrable noncompact fuzzy numbers form an integrable noncompact

On the completeness of fuzzy measure-spa
On the completeness of fuzzy measure-space
✍ Yian-Kui Liu; Guang-Quan Zhang 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 394 KB

In this paper, we first discuss the completeness of fuzzy measure space. The measurability of analytic sets is also discussed in fuzzy measure space. In the last part of the paper a measurable projection theorem is proved.