Pradip Kumar Sharma

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For any intuitionistic fuzzy set A = { < x ,  A (x) ,  A (x) > : x X} of a set X , the crisp subset C  ,  (A) = { x X :  A (x)   ,  A (x)   } of X called the (, ) – cut of A is studied by the authors [5] and [9].The purpose of this paper is to study the intuitionistic fuzzy modules with the help of their ( ,)-cut sets. Further some results(More)
The author have already introduced the notion of -fuzzy set, -anti fuzzy set and (, )-fuzzy set in a group and studied their properties in [5], [6] and [7] respectively. In this paper, we introduced the notion of (, )-anti fuzzy set and subsequently study (, )-anti fuzzy subgroup (normal subgroup) and their related properties. We have also obtained(More)
In this paper, the notion of t-intuitionistic fuzzy set and t-intuitionistic fuzzy subgroup (normal subgroup) are defined and discussed. The homomorphic behavior of t-intuitionistic fuzzy subgroup (normal subgroup) and their inverse homomorprhic images has been obtained. Some related result have been derived. Keywords: Intuitionistic fuzzy (IFS) ,(More)
Recently in the connected digital world, targeted attack has become one of the most serious threats to conventional computing systems. Advanced persistent threat (APT) is currently one of the most important threats considering the information security concept. APT persistently collects data from a specific target by exploiting vulnerabilities using diverse(More)
On the basis of fuzzy sets introduced by L.A. Zadeh, we first gave the definition of -fuzzy set and then defined -fuzzy subgroups and -fuzzy normal subgroups and finally, defined quotient group of the -fuzzy cosets of an -fuzzy normal subgroup. This paper proves a necessary and sufficient condition of -fuzzy subgroup (normal subgroup) to be fuzzy(More)
In this paper, the notion of t-intuitionistic fuzzy cosets of a Intuitionistic fuzzy submodule and t-intuitionistic fuzzy quotient modules are defined and discussed. A homomorphism from a given module onto the set of all t-intuitionistic fuzzy quotient module is established. Some related results has been derived.
In this paper an attempt has been made to define the notion of intuitionistic fuzzy order of an element in intuitionistic fuzzy subgroup. Here we prove that every element of a group and its inverse have the same intuitionistic fuzzy order. We also define the order of intuitionistic fuzzy subgroup and prove the Lagrange's Theorem in the intuitionistic fuzzy(More)