Interval-valued Fuzzy Sets, Possibility Theory and Imprecise Probability

نویسندگان

  • Didier Dubois
  • Henri Prade
چکیده

Interval-valued fuzzy sets were proposed thirty years ago as a natural extension of fuzzy sets. Many variants of these mathematical objects exist, under various names. One popular variant proposed by Atanassov starts by the specification of membership and non-membership functions. This paper focuses on interpretations of such extensions of fuzzy sets, whereby the two membership functions that define them can be justified in the scope of some information representation paradigm. It particularly focuses on a recent proposal by Neumaier, who proposes to use intervalvalued fuzzy sets under the name “clouds”, as an efficient method to represent a family of probabilities. We show the connection between clouds, interval-valued fuzzy sets and possibility theory.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Handling Grey Information in Object Oriented Databases

Efficient handling of inexact (grey) information is an important issue for the new emerging database technology. Inexact or imprecise information has been represented and manipulated by using different techniques, including fuzzy set theory, possibility theory, IVF (Interval Valued Fuzzy) Sets, Time Petri Nets, Fuzzy Clouds, etc. In this paper, different approaches dealing with uncertainty have...

متن کامل

On weighted possibilistic mean and variance of fuzzy numbers

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Carlsson and Fullér defined an interval-valued mean value of fuzzy numbers, viewing them as possibility distributions. In this paper we shall introduce the notation of weighted interval-valued possibilistic mean value of fuzzy numbers and investigate its relationship to the interval-...

متن کامل

Approaches to interval-valued intuitionistic hesitant fuzzy soft sets based decision making

The soft set theory is a newly mathematical tool to deal with uncertain problems. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, we introduce the average function and propose the interval-valued intuitionistic hesitant fuzzy soft sets (IVIHFSSs) which are a combination of the interval-valued intuitionistic hesitant fuzzy sets and...

متن کامل

On Generalised Interval-Valued Fuzzy Soft Sets

Soft set theory, initiated by Molodtsov, can be used as a new mathematical tool for dealing with imprecise, vague, and uncertain problems. In this paper, the concepts of two types of generalised interval-valued fuzzy soft set are proposed and their basic properties are studied. The lattice structures of generalised interval-valued fuzzy soft set are also discussed. Furthermore, an application o...

متن کامل

INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND SIMILARITY MEASURE

In this paper, the problem of measuring the degree of inclusion and similarity measure for two   interval-valued intuitionistic  fuzzy sets is considered. We propose inclusion and similarity measure by using  order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them an...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2005