𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Inclusion measures, similarity measures, and the fuzziness of fuzzy sets and their relations

✍ Scribed by Wenyi Zeng; Hongxing Li

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
130 KB
Volume
21
Category
Article
ISSN
0884-8173

No coin nor oath required. For personal study only.

✦ Synopsis

The inclusion measure, the similarity measure, and the fuzziness of fuzzy sets are three important measures in fuzzy set theory. In this article, we investigate the relations among inclusion measures, similarity measures, and the fuzziness of fuzzy sets, prove eight theorems that inclusion measures, similarity measures, and the fuzziness of fuzzy sets can be transformed by each other based on their axiomatic definitions, and propose some new formulas to calculate inclusion measures, similarity measures, and the fuzziness of fuzzy sets. These results can be applied in many fields, such as pattern recognition, image processing, fuzzy neural networks, fuzzy reasoning, and fuzzy control.

πŸ“œ SIMILAR VOLUMES

On similarity measures between intuition
On similarity measures between intuitionistic fuzzy sets
✍ Wen-Liang Hung; Miin-Shen Yang πŸ“‚ Article πŸ“… 2008 πŸ› John Wiley and Sons 🌐 English βš– 149 KB πŸ‘ 2 views

In this paper, we first review several popular similarity measures between fuzzy sets and then extend those similarity measures to intuitionistic fuzzy sets. We also propose two new similarity measures between intuitionistic fuzzy sets. These similarity measures have been found to satisfy some simil

Fuzzy Measures and the Entropy of Fuzzy
Fuzzy Measures and the Entropy of Fuzzy Partitions
✍ D. Dumitrescu πŸ“‚ Article πŸ“… 1993 πŸ› Elsevier Science 🌐 English βš– 390 KB

Using an additive fuzzy measure a notion of the entropy of a finite fuzzy partition has been defined [D. Dumitrescu, On fuzzy partitions, in "Itinerant Seminar on Functional Equations, Approximation and Convexity, Cluj-Napoca, 1983;" pp. 57-60; D. Dumitrescu and M. Barbu, Fuzzy entropy and processes

Relationships between entropy and simila
Relationships between entropy and similarity measure of interval-valued intuitionistic fuzzy sets
✍ Qiansheng Zhang; Shengyi Jiang πŸ“‚ Article πŸ“… 2010 πŸ› John Wiley and Sons 🌐 English βš– 299 KB πŸ‘ 2 views

The concept of entropy of interval-valued intuitionistic fuzzy set (IvIFS) is Þrst introduced. The close relationships between entropy and the similarity measure of interval-valued intuitionistic fuzzy sets are discussed in detail. We also obtain some important theorems by which entropy and similari

Fuzzy Measures Defined by Fuzzy Integral
Fuzzy Measures Defined by Fuzzy Integral and their Absolute Continuity
✍ Zhenyuan Wang; George J. Klir; Wei Wang πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 192 KB

Given a measurable space X, F F , a fuzzy measure on X, F F , and a nonnegative function f on X that is measurable with respect to F F, we can define a new set Ε½ . function on X, F F by the fuzzy integral. It is known that is a lower Ε½ . semicontinuous fuzzy measure on X, F F and, moreover, if is fi

The set of fuzzy relative integers and f
The set of fuzzy relative integers and fuzzy bags
✍ Daniel Rocacher; Patrick Bosc πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 169 KB

A characterization of fuzzy bags with conjunctive fuzzy integers (N f ) provides a general framework in which sets, bags, fuzzy sets, and fuzzy bags are treated in a uniform way. In this context, the difference between two fuzzy bags does not always exist and, in such cases, only approximations of t