Bifurcating fuzzy sets: Theory and application

نویسندگان

  • Seyyedeh Fatemeh Molaeezadeh
  • Mohammad Hassan Moradi
چکیده

To overcome the complexities in Type-2 Fuzzy Sets (T2FSs) and to present a general model for chaotic FSs, this paper introduces new FSs called Bifurcating FSs (BFSs). The BFS is inspired from human brain. Mathematically, it is equivalent to the coupled chaotic map in which one of the variables is a fuzzy membership function. Biologically, it is equivalent to the oscillatory neuron in which a fuzzy membership bifurcation-parameter diagram. This diagram demonstrates that a BFS can exhibit a wide range of FSs such as convex or non-convex, T1 or T2 and chaotic or non-chaotic FSs, and also make information processing fast. Using a BFS as an activation function in the neurons of the membership layer of a Fuzzy Neural Network (FNN), a new network called a Bifurcating FNN (BFNN) is presented. The proposed network has a similar design to an Interval T2 FNN (IT2FNN). The BFNN is applied to the problem of forecasting Mackey–Glass chaotic time series under different SNRs and different chaotic degrees. In comparison with T1FNNs and IT2FNNs, results show that BFNNs provide more accurate and robust predictions and handle more uncertainties. & 2013 Elsevier B.V. All rights reserved.

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

A Multi-Criteria Analysis Model under an Interval Type-2 Fuzzy Environment with an Application to Production Project Decision Problems

Using Multi-Criteria Decision-Making (MCDM) to solve complicated decisions often includes uncertainty, which could be tackled by utilizing the fuzzy sets theory. Type-2 fuzzy sets consider more uncertainty than type-1 fuzzy sets. These fuzzy sets provide more degrees of freedom to illustrate the uncertainty and fuzziness in real-world production projects. In this paper, a new multi-criteria ana...

متن کامل

Fuzzy relations, Possibility theory, Measures of uncertainty, Mathematical modeling.

A central aim of educational research in the area of mathematical modeling and applications is to recognize the attainment level of students at defined states of the modeling process. In this paper, we introduce principles of fuzzy sets theory and possibility theory to describe the process of mathematical modeling in the classroom. The main stages of the modeling process are represented as fuzz...

متن کامل

FUZZY SOFT MATRIX THEORY AND ITS APPLICATION IN DECISION MAKING

In this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. We then define products of $fs$-matrices andstudy their properties. We finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

متن کامل

CERTAIN TYPES OF EDGE m-POLAR FUZZY GRAPHS

In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy  sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. W...

متن کامل

POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

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:
  • Neurocomputing

دوره 118  شماره 

صفحات  -

تاریخ انتشار 2013