Poonam K Sharma
Dr. P.K. Sharma completed his master degree in Mathematics from D.A.V. College, Jalandhar in 1988. He further pursued his Ph.D degree in Modern Algebra from Jamia Millia Islamia University, New Delhi which he completed in 1993. His first appointment as lecturer in Mathematics was at D.A.V. College, Chandigarh in 1993. After serving for one year he joined D.A.V. College, Jalandhar in 1994. Till date he is serving at D.A.V. College, Jalandhar.
Publications:
He has published 171 research papers in National and International Journals and has written 4 books for post-graduation namely Topology, Modern Algebra, Real Analysis and Discrete Mathematics and one research book, Algebra: Relative relation modules of finite groups, published from Lambert Academia Publication Germany. His field of interest is Topology, Algebra and Fuzzy Mathematics.
Others Achievements:
Dr. P.K. Sharma is a member of editorial boards of 5 International Journals namely (i) International Journal of Fuzzy Mathematics and Systems (ii) Journal of Intelligent and Fuzzy System (iii) Neural Computing and Application (iv) Journal of the Egyptian Mathematical Society (v) Annals of Fuzzy Mathematics and Informatics (AFMI). He is a life member of 4 different Mathematical Societies namely (i) Ramanujan Mathematical Society (ii) Indian Mathematical Society (iii) Jammu Mathematical Society and (iv) Indian Society of Information Theory and Applications.
He has participated in 25 National and 20 International conferences and has chaired many sessions in Nationals and International conferences.
He has also organized three U.G.C. sponsored National conferences and one Teacher’s Enrichment Workshop at D.A.V. College, Jalandhar and has delivered nearly 25 extension lectures on various topics of mathematics in different colleges of Punjab.
He has visited U.S.A. in 2013 and Bulgaria in 2016 under the travel grant scheme of U.G.C. for presenting his research papers in the International Conference on scientific computing and Intuitionistic fuzzy sets and its Applications.
Project:
Dr. Sharma had completed one Major Research Project “ A study on Intuitionistic Fuzzy G-Modules” sponsored by U.G.C., in 2017 and four students have completed their Ph.D degree and two students are doing Ph.D under his guidance . Dr. Sharma has guided 25 students for their M.Phil. Dissertations
Honors and awards
• Extracts from the “Register of Copyright” of the Project titled “Characterization of Some Intuitionistic Fuzzy Ideals in Gamma-rings”, was registered with registration number L-1150063/2024, Diary No. 15851/2024-CO/L Government of India on 27/06/2024. https://copyright.gov.in/frmStatusGenUser.aspx
• Honorary D.Sc. (Doctrin de Science Award Honoris Causa) in Mathematics, Reference No.: H- 456306092023PKS by International Agency for Standards and Ratings on 6th Sept. 2023.
• Awarded Lifetime achievement Award by VDGOOD Professional Association, in the International Scientist Award on Engineering, Science and Medicine, held at Salem, India on 08 & 09 Jan. 2021.
• Nominated in who’s who in the world for 2015
Supervisors: Dr. P.K. Sharma supervised four Ph.D. scholars and two scholars are still working under his supervision.
Phone: 09872006365
Address: D.A.V. College, Jalandhar, Punjab, India.
Publications:
He has published 171 research papers in National and International Journals and has written 4 books for post-graduation namely Topology, Modern Algebra, Real Analysis and Discrete Mathematics and one research book, Algebra: Relative relation modules of finite groups, published from Lambert Academia Publication Germany. His field of interest is Topology, Algebra and Fuzzy Mathematics.
Others Achievements:
Dr. P.K. Sharma is a member of editorial boards of 5 International Journals namely (i) International Journal of Fuzzy Mathematics and Systems (ii) Journal of Intelligent and Fuzzy System (iii) Neural Computing and Application (iv) Journal of the Egyptian Mathematical Society (v) Annals of Fuzzy Mathematics and Informatics (AFMI). He is a life member of 4 different Mathematical Societies namely (i) Ramanujan Mathematical Society (ii) Indian Mathematical Society (iii) Jammu Mathematical Society and (iv) Indian Society of Information Theory and Applications.
He has participated in 25 National and 20 International conferences and has chaired many sessions in Nationals and International conferences.
He has also organized three U.G.C. sponsored National conferences and one Teacher’s Enrichment Workshop at D.A.V. College, Jalandhar and has delivered nearly 25 extension lectures on various topics of mathematics in different colleges of Punjab.
He has visited U.S.A. in 2013 and Bulgaria in 2016 under the travel grant scheme of U.G.C. for presenting his research papers in the International Conference on scientific computing and Intuitionistic fuzzy sets and its Applications.
Project:
Dr. Sharma had completed one Major Research Project “ A study on Intuitionistic Fuzzy G-Modules” sponsored by U.G.C., in 2017 and four students have completed their Ph.D degree and two students are doing Ph.D under his guidance . Dr. Sharma has guided 25 students for their M.Phil. Dissertations
Honors and awards
• Extracts from the “Register of Copyright” of the Project titled “Characterization of Some Intuitionistic Fuzzy Ideals in Gamma-rings”, was registered with registration number L-1150063/2024, Diary No. 15851/2024-CO/L Government of India on 27/06/2024. https://copyright.gov.in/frmStatusGenUser.aspx
• Honorary D.Sc. (Doctrin de Science Award Honoris Causa) in Mathematics, Reference No.: H- 456306092023PKS by International Agency for Standards and Ratings on 6th Sept. 2023.
• Awarded Lifetime achievement Award by VDGOOD Professional Association, in the International Scientist Award on Engineering, Science and Medicine, held at Salem, India on 08 & 09 Jan. 2021.
• Nominated in who’s who in the world for 2015
Supervisors: Dr. P.K. Sharma supervised four Ph.D. scholars and two scholars are still working under his supervision.
Phone: 09872006365
Address: D.A.V. College, Jalandhar, Punjab, India.
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Papers by Poonam K Sharma
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.
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.
to intuitionistic fuzzy semiprime submodules. Also we introduce and study new properties of
intuitionistic fuzzy semiprime submodules. Many related results are obtained.
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.
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.
to intuitionistic fuzzy semiprime submodules. Also we introduce and study new properties of
intuitionistic fuzzy semiprime submodules. Many related results are obtained.
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.
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.
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.
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.
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.