Rough set theory applied to (fuzzy) ideal theory

نویسنده

  • John N. Mordeson
چکیده

We use covers of the universal set to de-ne approximation operators on the power set of the given set. In Section 1, we determine basic properties of the upper approximation operator and show how it can be used to give algebraic structural properties of certain subsets. We de-ne a particular cover on the set of ideals of a commutative ring with identity in such a way that both the concepts of the (fuzzy) prime spectrum of a ring and rough set theory can simultaneously be brought to bear on the study of (fuzzy) ideals of a ring. c © 2001 Elsevier Science B.V. All rights reserved.

برای دانلود 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

T-Rough Sets Based on the Lattices

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...

متن کامل

Rough ideals based on ideal determined varieties

The paper is devoted to concern a relationship between rough set theory and universal algebra. Notions of lower and upper rough approximations on an algebraic structure induced by an ideal are introduced and some of their properties are studied. Also, notions of rough subalgebras and rough ideals with respect to an ideal of an algebraic structure, which is an extended notion of subalgebras and ...

متن کامل

Rough Intuitionistic Fuzzy Ideals in a Ring

he theory of fuzzy sets was ntroduced by Zadeh [22] in 1965 as an attempt to study the vagueness and uncertainity in real world problems. A.Rosenfeld [16] applied the notion of fuzzy sets and introduced the notion of fuzzy subgroups in groups. Since then various classical algebraic systems have been fuzzified. The theory of rough sets introduced by Z.Pawlak [14] in 1982 is another independent m...

متن کامل

Application of Fuzzy-rough Set Theory for Feature Subset Selection

Fuzzy Set Theory and Rough Set Theory are the most popular mathematical tools for dealing with uncertainties. During past decades, these set theories are being applied successfully in several areas for solving many complex tasks. This paper is concerned with the application of hybrid Fuzzy-Rough set based approach for feature subset selection. Keywords— Fuzzy set theory, Rough Set theory, Fuzzy...

متن کامل

A New Approach for Knowledge Based Systems Reduction using Rough Sets Theory (RESEARCH NOTE)

Problem of knowledge analysis for decision support system is the most difficult task of information systems. This paper presents a new approach based on notions of mathematical theory of Rough Sets to solve this problem. Using these concepts a systematic approach has been developed to reduce the size of decision database and extract reduced rules set from vague and uncertain data. The method ha...

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

برای دانلود 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

عنوان ژورنال:
  • Fuzzy Sets and Systems

دوره 121  شماره 

صفحات  -

تاریخ انتشار 2001