On T-fuzzy ideals in nearrings
22 May 2007-International Journal of Mathematics and Mathematical Sciences (Hindawi Publishing Corporation)-Vol. 2007, Iss: 5, pp 1-14
TL;DR: The notion of fuzzy ideals in nearrings with respect to a t-norm T is introduced and some properties of T-fuzzy ideals of the quotient nearrings are considered.
Abstract: We introduce the notion of fuzzy ideals in nearrings with respect to a t-norm T and investigate some of their properties. Using T-fuzzy ideals, characterizations of Artinian and Noetherian nearrings are established. Some properties of T-fuzzy ideals of the quotient nearrings are also considered.
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TL;DR: In this article, the authors discuss the concept of (, ) T S -intuitionistic fuzzy bi-ideals of near-ring using t -norm and t -co-norm and investigate some of their properties.
Abstract: The aim of this paper is to discuss the concept of ( , ) T S -intuitionistic fuzzy bi-ideals of near-ring using t -norm and t -co-norm and to investigate some of their properties. AMS Subject Classification: 03E72, 16Y30
4 citations
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TL;DR: Right ternary near-rings and their ideals are considered and fuzzy soft set technology initiated by Maji et al in 2001 is applied to introduce fuzzy soft right ternaries near- rings, fuzzy soft ideals and study their basic algebraic properties.
Abstract: The first step towards near-rings was an axiomatic research done by Dickson in 1905. In 1936, it was Zassenhaus who used the name near-ring. Many parts of the well established theory of rings are transferred to near-rings and new specific features of near-rings have been discovered. To deal with the idea of near-rings using ternary product Warud Nakkhasen and Bundit Pibaljommee have applied the concept of ternary semiring to define left ternary near- rings, ternary subnearrings and their ideals and investigated some properties of Lfuzzy ternary near subrings in 2012. In this paper, we consider right ternary near-rings and their ideals and apply fuzzy soft set technology initiated by Maji et al in 2001 to introduce fuzzy soft right ternary near-rings, fuzzy soft ideals and study their basic algebraic properties.
4 citations
TL;DR: The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information as discussed by the authors .
Abstract: The use of a single-valued neutrosophic set (svns) makes it much easier to manage situations in which one must deal with incorrect, unexpected, susceptible, faulty, vulnerable, and complicated information. This is a result of the fact that the specific forms of material being discussed here are more likely to include errors. This new theory has directly contributed to the expansion of both the concept of fuzzy sets and intuitionistic fuzzy sets, both of which have experienced additional development as a direct consequence of the creation of this new theory. In svns, indeterminacy is correctly assessed in a way that is both subtle and unambiguous. Furthermore, membership in the truth, indeterminacy, and falsity are all completely independent of one another. In the context of algebraic analysis, certain binary operations may be regarded as interacting with algebraic modules. These modules have pervasive and complicated designs. Modules may be put to use in a wide variety of different applications. Modules have applications in a diverse range of industries and market subsets due to their adaptability and versatility. Under the umbrella of the triplet (μ,ν,ω) structure, we investigate the concept of svns and establish a relationship between it and the single-valued neutrosophic module and the single-valued neutrosophic submodule, respectively. The purpose of this study is to gain an understanding of the algebraic structures of single-valued neutrosophic submodules under the triplet structure of a classical module and to improve the validity of this method by analyzing a variety of important facets. In this article, numerous symmetrical features of modules are also investigated, which demonstrates the usefulness and practicality of these qualities. The results of this research will allow for the successful completion of both of these objectives. The tactics that we have devised for use in this article are more applicable to a wide variety of situations than those that have been used in the past. Fuzzy sets, intuitionistic fuzzy sets, and neutrosophic sets are some of the tactics that fall under this category.
2 citations
01 Jan 2014
TL;DR: In this paper, some characterizations of a near-ring in terms of Q-fuzzy quotient near- ring and Q- fuzzy ideal are proved and some of there properties are investigated.
Abstract: In this paper, we shall study Q-fuzzy ideal and Q-fuzzy quotient near-ring and investigate some of there properties and we prove some characterizations of a near-ring in terms of Q-fuzzy quotient near-ring and Q-fuzzy ideal.
2 citations
01 Jan 2017
TL;DR: The important concept of fuzzy set has been introduced by L.A. Zadeh in 1965 and then fuzzy subsets have been applied to various branches of mathematics and in this direction the fuzzy ideals of partially ordered near-rings are studied.
Abstract: The important concept of fuzzy set has been introduced by L.A. Zadeh [14] in 1965. Since then many papers on fuzzy sets appeared showing its importance in the field of mathematics. The notion of a fuzzy subset was introduced by Zadeh [14] and then fuzzy subsets have been applied to various branches of mathematics. Near-rings are one of the generalized structures of rings. W.J. Liu [3] has studied fuzzy invariant subgroups and fuzzy ideals. In1998 S. D. Kim and H. S. kim [2] has been introduced analogue of fuzzy ideals of near-rings. G. Pilz [9] introduced near-rings and in 1971 Rosenfeld [11] initiated the study of fuzzy subgroups. In [4] M. Muralikrishna Rao studied T-fuzzy ideal in ordered T-semi rings. In [10] A. Radha Krishna and M. Bandari defined the partially ordered (P.O) near-ring. M. Akram[l] introduced the notion of fuzzy ideals in near-rings with respect to a tnorm T. In [12] Bh. Satyanarayana introduced -near-rings. T. Srinivas and T. Nagaiah [13] introduced the notion of T-fuzzy ideals of near-rings and investigated some of their properties. After that T. Nagaiah et al. [5, 6, 7] studied fuzzy ideals of partially ordered -semi groups and anti fuzzy ideals in near-ring. In [8] T. Nagaiah and L. Bhaskar introduced the notion of T-fuzzy ideal of PON. In this direction we study the fuzzy ideals of partially ordered near-rings.
2 citations
References
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"On T-fuzzy ideals in nearrings" refers methods in this paper
...Triangular norms were introduced by Schweizer and Sklar [10, 11] to model the distances in probabilistic metric spaces....
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365 citations
TL;DR: The aim of this paper is to introduce the notion of a fuzzy subnear-ring, to study fuzzy ideals of a near-ring and to give some properties of fuzzy prime ideals ofA near- ring.
153 citations
"On T-fuzzy ideals in nearrings" refers background in this paper
...Abou-Zaid [13] introduced the notion of a fuzzy subnearring and studied fuzzy left (right) ideals of a nearring, and gave some properties of fuzzy prime ideals of a nearring....
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31 Dec 1992
TL;DR: This book discusses the formation of families and the role of language in the development of families in the rapidly changing environment.
Abstract: CHAPTER 1: INTRODUCTION TO NEARRINGS CHAPTER 2: PLANAR NEARRINGS CHAPTER 3: THE GREAT UNIFIER CHAPTER 4: SOME FIRST FAMILIES OF NEARRINGS AND SOME OF THEIR IDEALS CHAPTER 5: SOME STRUCTURE OF GROUPS OF UNITS CHAPTER 6: AVANT-GARDE FAMILIES OF NEARRINGS
123 citations