Generalization of (∈,∈∨q_k )-fuzzy subnear-rings and (∈,∈∨q_k )-fuzzy ideals of near-rings

2018 ◽  
Vol 7 (1-2) ◽  
pp. 62-76
Author(s):  
T. Manikantan ◽  
S. Ramkumar
Keyword(s):  
Fuzzy Subset ◽  
Fuzzy Ideal

In this paper, we introduce the notions of (∈, ∈∨q_δ^k)-fuzzy subnear-ring and (∈, ∈∨q_δ^k)-fuzzy ideal of a near-ring which are generalization of (∈, ∈∨q_k)-fuzzy subnear-ring and (∈, ∈∨q_k)-fuzzy ideal respectively. We provide the characterizations of (∈, ∈∨q_δ^k)-fuzzy subnear-ring (resp. ideal) of a near-ring and deal with some related properties. Further, we introduce the notion of ∈∨q_δ^k-level subset of a fuzzy subset and obtain some related results.

scholarly journals When do L-fuzzy ideals of a ring generate a distributive lattice?

2016 ◽  
Vol 14 (1) ◽  
pp. 531-542
Author(s):  
Ninghua Gao ◽  
Qingguo Li ◽  
Zhaowen Li
Keyword(s):  
Distributive Lattice ◽  
Heyting Algebra ◽  
Lattice Structures ◽  
Boolean Ring ◽  
Fuzzy Subset ◽  
The Family ◽  
Essential Properties ◽  
Fuzzy Ideal

AbstractThe notion of L-fuzzy extended ideals is introduced in a Boolean ring, and their essential properties are investigated. We also build the relation between an L-fuzzy ideal and the class of its L-fuzzy extended ideals. By defining an operator “⇝” between two arbitrary L-fuzzy ideals in terms of L-fuzzy extended ideals, the result that “the family of all L-fuzzy ideals in a Boolean ring is a complete Heyting algebra” is immediately obtained. Furthermore, the lattice structures of L-fuzzy extended ideals of an L-fuzzy ideal, L-fuzzy extended ideals relative to an L-fuzzy subset, L-fuzzy stable ideals relative to an L-fuzzy subset and their connections are studied in this paper.

scholarly journals IDEAL PRIMA FUZZY DI SEMIGRUP S

2017 ◽  
Vol 2 (2) ◽  
pp. 46
Author(s):  
Abdurahim Abdurahim
Keyword(s):  
Prime Ideal ◽  
Membership Function ◽  
Closed Interval ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Fuzzy Subset ◽  
Fuzzy Ideal ◽  
Function Domain

A fuzzy membership function is a function that maps the nonempty set  to a closed interval . Furthermore, if the function domain is replaced with a semigroup, then the function is called fuzzy subset. A fuzzy subset mapping  to  is denoted by . A fuzzy subset  is called fuzzy ideal if it satisfies both  and . Moreover,  is called a fuzzy prime ideal if for any fuzzy ideal  and , with  implies  or . In this paper be investigated about some characteristics of prime fuzzy ideals and some example of them.

P-F Fuzzy Rings and Normal Fuzzy Ring

2017 ◽  
pp. 82-111
Author(s):  
Manoj Kumar
Keyword(s):  
Fuzzy Subset ◽  
Practical Applications ◽  
Fuzzy Ideal ◽  
The Relationship ◽  
Fuzzy Ring

In 1965, Zadeh introduced the concept of fuzzy subset. Since that time many papers were introduced in different mathematical scopes of theoretical and practical applications. In 1982, Liuformulated the term of fuzzy ring and fuzzy ideal of a ring R. In 2004, Hadi and Abou-Draeb, introduced and studied P-F fuzzy rings and normal fuzzy rings and now we are complete it. In this chapter, the concepts P-F fuzzy rings and normal fuzzy rings have been investigated. Several basic results related to these concepts have given and studied. The relationship between them has also been given. Moreover, some properties of t-pure fuzzy ideal of a fuzzy ring have been given which need it later.

scholarly journals Fuzzy Prime Ideal Theorem in Residuated Lattices

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Pierre Carole Kengne ◽  
Blaise Blériot Koguep ◽  
Celestin Lele
Keyword(s):  
Prime Ideal ◽  
Maximal Ideal ◽  
Residuated Lattice ◽  
Residuated Lattices ◽  
Prime Ideals ◽  
Fuzzy Subset ◽  
Different Types ◽  
Fuzzy Ideal ◽  
Prime Ideal Theorem

This paper mainly focuses on building the fuzzy prime ideal theorem of residuated lattices. Firstly, we introduce the notion of fuzzy ideal generated by a fuzzy subset of a residuated lattice and we give a characterization. Also, we introduce different types of fuzzy prime ideals and establish existing relationships between them. We prove that any fuzzy maximal ideal is a fuzzy prime ideal in residuated lattice. Finally, we give and prove the fuzzy prime ideal theorem in residuated lattice.

A contribution to the identification in fuzzy-logic control

1990 ◽  
Vol 55 (4) ◽  
pp. 951-963 ◽  
Author(s):  
Josef Vrba ◽  
Ywetta Purová
Keyword(s):  
Time Series ◽  
Fuzzy Logic ◽  
Fuzzy Logic Control ◽  
Fuzzy Logic Controller ◽  
Automatic Generation ◽  
Linguistic Variable ◽  
Fuzzy Subset ◽  
Input Output ◽  
Logic Control ◽  
Correlation Tables

A linguistic identification of a system controlled by a fuzzy-logic controller is presented. The information about the behaviour of the system, concentrated in time-series, is analyzed from the point of its description by linguistic variable and fuzzy subset as its quantifier. The partial input/output relation and its strength is expressed by a sort of correlation tables and coefficients. The principles of automatic generation of model statements are presented as well.

scholarly journals L-fuzzy ideals and L-fuzzy subalgebras of Novikov algebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1538-1546
Author(s):  
Xin Zhou ◽  
Liangyun Chen ◽  
Yuan Chang
Keyword(s):  
Fuzzy Sets ◽  
Homomorphic Image ◽  
Quotient Algebra ◽  
Algebraic Properties ◽  
Novikov Algebras ◽  
Fuzzy Ideal

Abstract In this paper, we apply the concept of fuzzy sets to Novikov algebras, and introduce the concepts of L-fuzzy ideals and L-fuzzy subalgebras. We get a sufficient and neccessary condition such that an L-fuzzy subspace is an L-fuzzy ideal. Moreover, we show that the quotient algebra A/μ of the L-fuzzy ideal μ is isomorphic to the algebra A/Aμ of the non-fuzzy ideal Aμ. Finally, we discuss the algebraic properties of surjective homomorphic image and preimage of an L-fuzzy ideal.

Fuzzy 𝛿-𝐼-continuity in mixed fuzzy ideal topological spaces

2018 ◽  
Vol 24 (2) ◽  
pp. 233-239
Author(s):  
Binod Chandra Tripathy ◽  
Gautam Chandra Ray
Keyword(s):  
Topological Spaces ◽  
Fuzzy Ideal

Abstract The aim of this paper is to introduce a new concept of fuzzy δ-I-continuity between mixed fuzzy ideal topological spaces and investigate some properties of this mapping.

scholarly journals Generalized Fuzzy Interior Ideals in Abel Grassmann's Groupoids

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Asghar Khan ◽  
Young Bae Jun ◽  
Tahir Mahmood
Keyword(s):  
Fuzzy Subset ◽  
Fuzzy Point ◽  
New Concepts

Using the notion of a fuzzy point and its belongness to and quasicoincidence with a fuzzy subset, some new concepts of a fuzzy interior ideal in Abel Grassmann's groupoidsSare introduced and their interrelations and related properties are invesitigated. We also introduce the notion of a strongly belongness and strongly quasicoincidence of a fuzzy point with a fuzzy subset and characterize fuzzy interior ideals ofSin terms of these relations.

scholarly journals Bipolar Fuzzy Implicative Ideals of BCK-Algebras

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
G. Muhiuddin ◽  
D. Al-Kadi
Keyword(s):  
Fuzzy Set ◽  
Extension Property ◽  
Fuzzy Ideal

The notion of bipolar fuzzy implicative ideals of a BCK-algebra is introduced, and several properties are investigated. The relation between a bipolar fuzzy ideal and a bipolar fuzzy implicative ideal is studied. Characterizations of a bipolar fuzzy implicative ideal are given. Conditions for a bipolar fuzzy set to be a bipolar fuzzy implicative ideal are provided. Extension property for a bipolar fuzzy implicative ideal is stated.

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