Applications of Bipolar Fuzzy Theory to Hemirings

نویسندگان

  • Min Zhou
  • Shenggang Li
چکیده

In our real life, bipolar fuzzy theory is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. In this paper, we provide a general algebraic framework for handling bipolar information by combining the theory of bipolar fuzzy sets with hemirings. First, we present the concepts of bipolar fuzzy h-ideals and normal bipolar fuzzy h-ideals. Meanwhile, some illustrative examples are given to show the rationality of the definitions introduced in the present paper. Second, the characterizations of bipolar fuzzy h-ideals are investigated by means of positive t-cut, negative s-cut, homomorphism and equivalence relation. Third, we give the range of the values of the non-constant maximal element of all normal bipolar fuzzy h-ideals.

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

Characterizations of Hemirings Based on Probability Spaces

Starting from a unified treatment of uncertainty by combining probability and fuzzy set theory [1], Goodman [2] put forward the equivalence between a fuzzy set and a class of random sets. Falling shadow representation theory was established based on the collection of Wang and Sanchez [3], which is directly related to the concept of probabilistic fuzzy set membership function. The theory shows t...

متن کامل

A robust aggregation operator for multi-criteria decision-making method with bipolar fuzzy soft environment

Molodtsov initiated soft set theory that provided a general mathematicalframework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory.The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in ...

متن کامل

Applications of soft union sets to hemirings via SU-h-ideals

The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, we introduce the concepts of soft union hemirings (soft union h-ideals) of hemirings by soft intersection-union product and obtain some related results. Finally, we investigate some characterizations of h...

متن کامل

On Fuzzy h-Ideals of Hemirings

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is considered. In fact, this concept is a generalized concept of the quasi-coincidence of a fuzzy point in a fuzzy set. By using this new concept, the authors define the notion of interval valued (∈,∈ ∨q)fuzzy h-ideals of hemirings and study their related properties. In addition, the authors also extend t...

متن کامل

ON INTUITIONISTIC FUZZY H - IDEALS IN H - HEMIREGULAR HEMIRINGS AND h ∗ - DUO - HEMIRINGS

Abstract. In this paper, intuitionistic fuzzy h-bi-ideals and intuitionistic fuzzy hquasi-ideals of hemirings are studied and some related properties are investigated. We characterize fully idempotent hemirings by the properties of their intuitionistic fuzzy h-ideals.We also characterize h-hemiregularity, h-intra-hemiregularity and h-quasi-hemiregularity in hemirings by the properties of their ...

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:

دوره   شماره 

صفحات  -

تاریخ انتشار 2013