Poonam K Sharma | DAV College Jalandhar (original) (raw)

Papers by Poonam K Sharma

ANNALS OF COMMUNICATIONS IN MATHEMATICS, 2024

In this paper, we introduce the concept of tri-quasi hyperideal in Γ-semihyperring generalizing t... more In this paper, we introduce the concept of tri-quasi hyperideal in Γ-semihyperring
generalizing the classical ideal, left ideal, right ideal, bi-ideal, quasi ideal, interior ideal,
bi-interior ideal, weak interior ideal, bi-quasi ideal, tri-ideal, quasi-interior ideal and biquasi-
interior ideal of Γ-semihyperring and semiring. Furthermore, charecterizations of
Γ-semihyperring, regular Γ-semihyperring and simple Γ-semihyperring with relative triquasi
hyperideals are provided discussing the characteristics of Γ-semihyperring of relative
tri-quasi hyperideals.

Annals of Fuzzy Mathematics and Informatics, 2024

This study aims to examine intuitionistic fuzzy congruences and intuitionistic fuzzy submodules o... more This study aims to examine intuitionistic fuzzy congruences
and intuitionistic fuzzy submodules on an R-module (near-ring module).
The relationship between intuitionistic fuzzy congruences and intuitionistic
fuzzy submodules of an R-module is also obtained. Furthermore, the
intuitionistic fuzzy quotient R-module of an R-module over an intuitionistic
fuzzy submodule is defined. The correspondence between intuitionistic
fuzzy congruences on an R-module and intuitionistic fuzzy congruences on
the intuitionistic fuzzy quotient R-module of an R-module over an intuitionistic
fuzzy submodule of an R-module is also obtained.

Notes on Intuitionsitic Fuzzy Sets , 2024

In this paper, we introduce and explore some novel concepts within the frame work of intuitionist... more In this paper, we introduce and explore some novel concepts within the frame work of intuitionistic fuzzy module theory. First, we define the notion of an intuitionistic fuzzy chained module as a generalisation of chained modules, establishing it foundational properties. We then characterise intuitionistic fuzzy chained modules, in terms of its level-cut submodules. In addition to this, we describe an intuitionistic fuzzy chained module in terms of its intuitionistic fuzzy cyclic submodules. Finally, we demonstrate that under specific conditions, the intuitionistic fuzzy multiplication module is an intuitionistic fuzzy chained module.

Notes on Intuitionistic Fuzzy Sets, 2024

In this paper, we define and study the notion of intuitionistic fuzzy classical primary submodule... more In this paper, we define and study the notion of intuitionistic fuzzy classical primary submodules over a unitary R-module M , where R is a commutative ring with unity. This is a generalisation of intuitionistic fuzzy primary ideals and intuitionistic fuzzy classical prime submodules. We further topologize the collection of all intuitionistic fuzzy submodules on an R-module M with a topology having the intuitionistic fuzzy primary Zariski topology on the intuitionistic fuzzy classical primary spectrum IF cp spec(M) as a subspace topology and investigate the properties of this topological space.

Palestine Journal of Mathematics, 2024

In this paper, we introduce the notion of expansion of intuitionistic fuzzy ideals of a commutati... more In this paper, we introduce the notion of expansion of intuitionistic fuzzy ideals of a commutative Γ-ring and by using this concept, we develop the notion of intuitionistic fuzzy f-primary ideals (2-absorbing f-primary ideals) which unify the notion of intuitionistic fuzzy prime ideals (2-absorbing ideals) and intuitionistic fuzzy primary ideals (2-absorbing primary ideals) of Γ-ring. A number of important results about intuitionistic fuzzy prime ideals (2-absorbing ideals) and intuitionistic fuzzy primary ideals (2-absorbing primary ideals) are extended into this general frame work.

Notes on Intuitionistic Fuzzy Sets, 2024

As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitioni... more As a generalization of the concepts of an intuitionistic fuzzy prime ideal and a prime intuitionistic fuzzy ideal, the concepts of an intuitionistic fuzzy 2-absorbing ideal and a 2-absorbing intuitionistic fuzzy ideal of a lattice are introduced. Some results on such intuitionistic fuzzy ideals are proved. It is shown that the radical of an intuitionistic fuzzy ideal of L is a 2-absorbing intuitionistic fuzzy ideal if and only if it is a 2-absorbing primary intuitionistic fuzzy ideal of L. We also introduce and study these concepts in the product of lattices.

Advances in Fuzzy Sets and Systems, 2024

In this paper, we study the properties of intuitionistic fuzzy modules from the categorical point... more In this paper, we study the properties of intuitionistic fuzzy modules
from the categorical point of view by proving that the category
CR-IFM of intuitionistic fuzzy modules has products, coproducts,
equalizers and coequalizers. Then, we show that every intuitionistic
fuzzy coretraction (retraction) is an intuitionistic fuzzy equalizer (coequalizer). Further, categorical goodness of intuitionistic fuzzy
modules is illustrated by proving that the category of intuitionistic
fuzzy modules CR IFM is complete and co-complete.

CREAT.MATH.INFORM., 2024

In this paper, we establish the intuitionistic fuzzy version of the Lasker-Noether theorem for a ... more In this paper, we establish the intuitionistic fuzzy version of the Lasker-Noether theorem for a commutative Γ-ring. We show that in a commutative Noetherian Γ-ring, every intuitionistic fuzzy ideal A can be decomposed as the intersection of a finite number of intuitionistic fuzzy irreducible ideals (primary ideals). This decomposition is called an intuitionistic fuzzy primary decomposition. Further, we show that in case of a minimal intuitionistic fuzzy primary decomposition of A, the set of all intuitionistic fuzzy associated prime ideals of A is independent of the particular decomposition. We also discuss some other fundamental results pertaining to this concept.

Notes on Intuitionistic Fuzzy Sets, 2023

The aim of this paper is to introduce two special type of morphisms, namely Retraction and Coretr... more The aim of this paper is to introduce two special type of morphisms, namely Retraction and Coretraction in the category (C R-IFM) of intuitionistic fuzzy modules. We obtain the condition under which a morphism in C R-IFM , that is an intuitionistic fuzzy R-homomorphism, to be a retraction or a coretraction. Then, we acquire some equivalent statements for these two morphisms. Further, we study free, projective and injective objects in C R-IFM and establish their relation with morphism in C R-IFM and retraction, coretraction.

South East Asian J. of Mathematics and Mathematical Sciences, 2023

In this paper, we introduce the notion of F-closure of intuitionistic fuzzy submodules of a modul... more In this paper, we introduce the notion of F-closure of intuitionistic fuzzy submodules of a module M. Our attempt is to investigate various characteristics of such an F-closure. If F is a non-empty set of intuitionistic fuzzy ideals of a commutative ring R and A is an intuitionistic fuzzy submodule of M , then the F-closure of A is denoted by Cl M F (A). If F is weak closed under intersection, then (1) F-closure of A exhibits the submodule character, and (2) the intersection of F-closure of two intuitionistic fuzzy submodules equals the F-closure of intersection of the intuitionistic fuzzy submodules. If F is weak closed under intersection, then the submodule property of F-closure implies that F is closed. Moreover, if F is inductive, then F is a topological filter if and only if Cl M F (A) is an intuitionistic fuzzy submodule for any intuitionistic fuzzy submodule A of M .

Notes on Intuitionistic Fuzzy Sets, 2023

The aim of this paper is to present some characterizations of almost prime ideals and almost prim... more The aim of this paper is to present some characterizations of almost prime ideals and almost prime submodules in the intuitionistic fuzzy environment. We investigate various properties of these concepts and achieve many results.

Bulletin of the Korean Mathematical Society, 2014

Let E be a free product of a finite number of cyclic groups, and S a normal subgroup of E such t... more Let E be a free product of a finite number of cyclic groups,
and S a normal subgroup of E such that E/S ∼= G is finite. For a prime
p, Sˆ = S/S′Sp may be regarded as an FpG-module via conjugation in
E. The aim of this article is to prove that Sˆ is decomposable into two
indecomposable modules for finite elementary abelian p-groups G.

Notes on Intuitionistic Fuzzy Sets, 2023

Let L be a complete lattice. We introduce and characterise intuitionistic L-fuzzy classical prime... more Let L be a complete lattice. We introduce and characterise intuitionistic L-fuzzy classical prime submodule and intuitionistic L-fuzzy 2-absorbing submodules of a unitary module M over a commutative ring R with identity. We compare both of these submodules with intuitionistic L-fuzzy prime submodules. It is proven that in the case of the multiplication module M , the two notions of intuitionistic L-fuzzy classical prime submodules and intuitionistic L-fuzzy prime submodules coincide. Many other related results concerning these notions are obtained.

Let N be a proper submodule of M. Then, N is said to be a prime (primary) submodule of M provided... more Let N be a proper submodule of M. Then, N is said to be a prime (primary) submodule of M provided that whenever a ∈ R and m ∈ M, with am ∈ N ⇒ m ∈ N or a ∈ (N : M) (or m ∈ N or a n ∈ (N : M) for some n ∈ N). Definition (2-absorbing submodule) Let N be a proper submodule of M. Then, N is said to be a 2-absorbing submodule of M provided that whenever a, b ∈ R and m ∈ M, with abm ∈ N ⇒ ab ∈ (N : M) or am ∈ N or bm ∈ N. Definition (Classical prime submodule) A proper submodule N of an R-module M is called classical prime, if for any elements a, b ∈ R and x ∈ M, the condition abx ∈ N ⇒ ax ∈ N or bx ∈ N.

In this paper we try to study the intuitionistic-fuzzy aspects of socle of modules over rings. We... more In this paper we try to study the intuitionistic-fuzzy aspects of socle of modules over rings. We demonstrate some properties of a socle of intuitionistic-fuzzy submodules and their relations with intuitionistic-fuzzy essential submodules and a family of intuitionistic-fuzzy complemented submodules of a module. Some related results are also established.

International Journal of Research in Academic World

In this paper, we study relative ordered (m, n)-hyperideals in ordered semihypergroups. We also s... more In this paper, we study relative ordered (m, n)-hyperideals in ordered semihypergroups. We also study relative (m, 0)-hyperideals and relative (0, n)-hyperideals as well as characterize regular ordered semihypergroups, and obtain some results based on these relative hyperideals. We prove that the intersection of all relative ordered (m, n)-hyperideals of S containing s is a relative ordered (m, n)-hyperideal of S containing s. Suppose that (S,•,≤) is an ordered semihypergroup, A ⊆ S and m,n are positive integers. We prove that if R(m,0) and L(0,n) be the set of all relative ordered (m,0)-hyperideals and the set of all relative ordered (0,n)-hyperideals of S, respectively. Then the following assertions are true: i) S is relative (m,0)-regular if and only if for all R ∈ R(m,0), R = (Rm •A]A. ii) S is relative (0,n)-regular if and only if for all L ∈ R(0,n), L = (A•Ln]A. Furthermore, suppose that (S, •, ≤) is an ordered semihypergroup and m, n are non-negative integers. Let A ⊆ S. Suppose that A(m,n) is the set of all relative ordered (m, n)-hyperideals of S. Then, we have the following: S is (m,n)-regular ⇐⇒ ∀A ∈ A(m,n),A = (Am •A•An]A.

The main goal of this paper is to count subgroups which are isomorphic to cyclic p-group, interna... more The main goal of this paper is to count subgroups which are isomorphic to cyclic p-group, internal direct product of two cyclic p-group or semi direct product of two cyclic p-group of the non-Abelian p-group Zpn o Zp, n ≥ 2 where p may be even or odd prime, by using simple-theoretical approach. AMS Subject Classification: Primary 20D60; Secondary 20D15

Creative Mathematics and Informatics, 2023

In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionisti... more In this paper, we introduced the notion of intuitionistic fuzzy prime radical of an intuitionistic fuzzy ideal in Γ-rings. We also characterise intuitionistic fuzzy primary ideal of Γ-rings. We also analyse homomorphic behaviour of intuitionistic fuzzy primary ideal and intuitionistic fuzzy prime radical of Γ-rings.

Notes on Intuitionistic Fuzzy Sets, 2022

In this paper, we initiate the study of a generalization of intuitionistic fuzzy primary ideals i... more In this paper, we initiate the study of a generalization of intuitionistic fuzzy primary ideals in Γ-ring by introducing intuitionistic fuzzy 2-absorbing primary ideals. We investigate the structural characteristics of intuitionistic fuzzy 2-absorbing primary ideals and study their properties.

Pan-American Journal of Mathematics, 2022

The purpose of this paper is to introduce and investigate primary ideal and P-primary ideal in th... more The purpose of this paper is to introduce and investigate primary ideal and P-primary ideal in the intuitionistic fuzzy environment and lay down the foundation for the primary decomposition theorem in the intuitionistic fuzzy setting. Also a suitable characterization of intuitionistic fuzzy P-primary ideal will be discussed.

ANNALS OF COMMUNICATIONS IN MATHEMATICS, 2024

Annals of Fuzzy Mathematics and Informatics, 2024

Notes on Intuitionsitic Fuzzy Sets , 2024

Notes on Intuitionistic Fuzzy Sets, 2024

Palestine Journal of Mathematics, 2024

Notes on Intuitionistic Fuzzy Sets, 2024

Advances in Fuzzy Sets and Systems, 2024

CREAT.MATH.INFORM., 2024

Notes on Intuitionistic Fuzzy Sets, 2023

South East Asian J. of Mathematics and Mathematical Sciences, 2023

Notes on Intuitionistic Fuzzy Sets, 2023

Bulletin of the Korean Mathematical Society, 2014

Notes on Intuitionistic Fuzzy Sets, 2023

International Journal of Research in Academic World

Creative Mathematics and Informatics, 2023

Notes on Intuitionistic Fuzzy Sets, 2022

Pan-American Journal of Mathematics, 2022

The emerging approach to computing is refer to Soft computing which is placed parallel to the ... more The emerging approach to computing is refer to Soft computing which is placed parallel to the remarkable ability of the human mind to reason and learn in a environment of uncertainty and imprecision.

Some of it’s principle components includes:
Neural Network(NN)
Genetic Algorithm(GA)
Machine Learning (ML)
Probabilistic Reasoning(PR)
Fuzzy Logic(FL)

These methodologies (techniques) form the core of soft computing.
The main goal of soft computing is to develop intelligent machines to provide solutions to real world problems, which are not modeled, or too difficult to model mathematically.
It’s aim is to exploit the tolerance for Approximation, Uncertainty, Imprecision, and Partial Truth in order to achieve close resemblance with human like decision making.

8TH INT. IFS AND CONTEMPORARY MATHEMATICS CONFERENCE TURKEY, 2022

In this talk we introduce the notion of intuitionistic fuzzy polynomial ideal Ax of a polynomial ... more In this talk we introduce the notion of intuitionistic fuzzy
polynomial ideal Ax of a polynomial ring R[x] induced by an
intuitionistic fuzzy ideal A of a ring R. Then many properties of Ax
will be discussed. We shall also establish an isomorphism theorem
of a ring of intuitionistic fuzzy cosets of Ax . It will be shown that an
intuitionistic fuzzy ideal A of a ring R is an intuitionistic fuzzy prime
if and only if Ax is an intuitionistic fuzzy prime ideal of R[x].
However, if Ax is an intuitionistic fuzzy maximal ideal of R[x], then
A is an intuitionistic fuzzy maximal ideal of R, but converse is not
true. We will also investigate the nil radical structure of Ax . The
homomorphic image and inverse image of an intuitionistic fuzzy
polynomial ideal Ax and nil radical of Ax when A is an intuitionistic
fuzzy prime ideal of a ring R will also be discussed.

7th Int. IFS and Contemporary Mathematics Conference at Turkey, 2021

In this talk, we study the concept of residual quotient of IF subsets of ring and module and deve... more In this talk, we study the concept of residual quotient of IF subsets of ring
and module and develop many properties out of these. Using the concept
of residual quotient, we investigate some important characterization of
annihilator of IF submodules, IF prime(primary) submodules and IF
prime(primary) decomposition.

In this power point presentation, I try to explain the contribution of mathematics in our life an... more In this power point presentation, I try to explain the contribution of mathematics in our life and how it make our life easy and beautiful.

The notion of fuzzy set was introduced by L.A. Zadeh as a generalization of the notion of classic... more The notion of fuzzy set was introduced by L.A. Zadeh as a generalization of the notion of classical set or crisp set. Fuzzy topological spaces were introduced by C.L. Chang and studied by many eminent authors like R. Lowen and C.K. Wong. A. Rosenfeld applied the notion of fuzzy set to algebra and introduced fuzzy subgroup of a group. Shaoquan Sun introduced the notion of fuzzy Boolean subalgebra in a Boolean algebra. In this talk, we will discuss fuzzy topology by involving the Boolean algebraic structure on it and introduce the notion of Boolean algebraic fuzzy topological spaces. We will examine many properties of these spaces and obtain many results.

Result concerning various ideals in near rings (as defined by Yakabe, Chelvam and Ganesan, Kim an... more Result concerning various ideals in near rings (as defined by Yakabe, Chelvam and
Ganesan, Kim and Zhan and Xueling as well as some generalization thereof) that have been
established over the past three decays, will be discussed. These include the fuzzy ideals, fuzzy
quasi ideals and fuzzy bi-ideals in near rings. In this talk, we extend these notion to intuitionistic
fuzzy ideals, intuitionistic fuzzy quasi-ideals, intuitionistic fuzzy bi-ideals in near-rings. A relationship between various types of ideals has been established.

The Concept of a module over a ring is a generalization of the notion of vector space, where in t... more The Concept of a module over a ring is a generalization of the notion of vector space, where in the corresponding scalars are allowed to lie in an arbitrary ring. Modules also generalize the notion of abelian groups, which are modules over the ring of integers. Thus a module like a vector space, is an additive abelian group, a product is defined between the elements of a ring and the elements of the module, and this multiplication is associative (when used with multiplication in the ring) and distributive. Modules are very closely related to the representation theory of groups. They are also one of the central notions of commutative algebra and homological algebra, and are widely used in algebraic geometry and algebraic topology.

In this talk , author differentiate between the ordinary or classical set theory given by George ... more In this talk , author differentiate between the ordinary or classical set theory given by George Cantor in 1876 and the Fuzzy Set Theory given by L.A.Zadeh in 1965 with the Intuitionistic fuzzy set theory given by K,T. Atanssov in 1983. Author has given a detail work done in the intuitionistic fuzzy subgroups and discuss some of their importance.

Here in this talk, author give a detail about the fuzzy set theory. He also show by citing many e... more Here in this talk, author give a detail about the fuzzy set theory. He also show by citing many examples the usefulness of this theory in the development of technology . He outline the various step of this fuzzy logic used in washing machine .

In this article, we have given an explicit recursive formula for the number of intuitionistic fuz... more In this article, we have given an explicit recursive formula for the number of intuitionistic fuzzy subgroups of a finite cyclic group are distinct prime numbers. A method for constructing an intuitionistic fuzzy subgroup of a given group in terms of double pinned flags is also proposed.

: Fuzzy Sets were introduced by L.A. Zadeh in 1965. One generalization of the notion of fuzzy se... more : Fuzzy Sets were introduced by L.A. Zadeh in 1965. One generalization of the notion of fuzzy sets was proposed by K. Atanassov in the beginning of 1983 and presented before the Seventh Scientific Session of ITKR, Sofia, June 1983. In addition to the degree of membership known from the fuzzy sets, here a new degree is introduced, called the degree of non-membership, with the requirement that their sum be less than or equal to 1. The complement of the sum of two degrees to 1 is regarded as a degree of uncertainty. This new extension of the fuzzy sets was named intuitionistic fuzzy set (IFS). The name of intuitionistic fuzzy sets is due George Gargov, with the motivation that their fuzzification denies the law of the excluded middle - one of the main ideas of intuitionism. Later in 1983 it turned out that the new sets allow for the definition of operators which are generalizations of the modal operators of necessity and possibility, which was the first serious result connecting IFS with classical logic and set theory.
Some of the area’s where the IFS Theory has found its important place:
Operations and relations over IFS. Algebraic research in the frame of the IFS theory ( IF groups, IF rings and Ideals , IF modules, IF fields , IF vector spaces etc. )
IF geometry, IF Analysis and IF Topology (IF numbers, IF Topology)
IF Logics (IF propositional and predicate calculus, IF modal and temporal logics, Connection between IF logics and other logical systems)
IF Approach to Artificial Intelligence(Decision making and machine learning, Neutral networks and pattern recognition, Expert system, logical programming )
IF Generalized Nets
IF Graphs
Applications of IFSs (Medicine, optimization, chemical engineering, economics, computer hardware, astronomy, sociology, biology)
Here, in this talk, I will discuss the algebraic research in the frame of the IFS theory and in particular, will introduce intuitionistic fuzzy group and explore some of their properties. Some latest development in this area will also be highlighted.

George Cantor, in 1870's gave the concept of set theory which is of great importance not only in ... more George Cantor, in 1870's gave the concept of set theory which is of great importance not only in mathematics but in other disciplines also. Fuzzy Set Theory was formalized by Prof. Lotfi Asker Zadeh at the University of California in 1965 to generalize classical set theory. Zadeh was almost single handedly responsible for the early development in this field. A fuzzy set is defined in terms of a membership function which is a mapping from the universal set X to the interval [0,1]. i.e. The mapping  A : X  [0,1] is a fuzzy subset of X (or fuzzy set A). A characteristic function is a special case of a membership function and a crisp set is a special case of a fuzzy set. A fuzzy set A is generally denoted by In 1971, A. Rosenfeld applied the notion of fuzzy sets to algebra and introduced fuzzy subgroups of a group. In 1979, Anthony and Sherwood redefined fuzzy subgroup. In 1981, P.S. Das introduced the idea of level subsets which in turn was used by Mukherjee and Bhattacharya in 1985, to show that almost all the global notions of fuzzy subgroup can be characterized by its level subgroups. Later on the concept of product and homomorphism was also established. Besides this, the idea of fuzzy subrings and ideals was introduced by Wang Jin-Liu in 1983, which was extended by many authors and various concepts and results of the ring theory were established in fuzzy settings. R. Kumar, S. K. Bhambri, P. Kumar , in 1995, set the notion of product of fuzzy ideals and fuzzy submodules. In 2004, Shery Fernandez introduced and studied the notion of fuzzy G-modules.

As an abstraction of the geometric notion of translation, author in [8] has introduced two operat... more As an abstraction of the geometric notion of translation, author in [8] has introduced two operators T + and T -called the fuzzy translation operators on the fuzzy set and studied their properties and also investigated the action of these operators on the (Anti) fuzzy subgroups of a group in [8] and (Anti) fuzzy subring and ideal of a ring in . The notion of anti fuzzy submodule of a module has also been introduced by the author in . In this paper, we investigate the action of these two operators on (Anti) fuzzy submodules of a module and prove that they are invariant under these translations. But converse of this is not true. We also obtain the conditions, when the converse is also true.