scholarly journals Soft rational line integral

2021 ◽  
Vol 31 (4) ◽  
pp. 578-596
Author(s):  
S. Acharjee ◽  
D.A. Molodtsov
Keyword(s):  
Computer Science ◽  
Set Theory ◽  
Soft Set ◽  
Theoretical Development ◽  
Classical Analysis ◽  
Computing Systems ◽  
Line Integral ◽  
Fundamental Properties ◽  
Necessary And Sufficient ◽  
Rational Line

Soft set theory is a new area of mathematics that deals with uncertainties. Applications of soft set theory are widely spread in various areas of science and social science viz. decision making, computer science, pattern recognition, artificial intelligence, etc. The importance of soft set-theoretical versions of mathematical analysis has been felt in several areas of computer science. This paper suggests some concepts of a soft gradient of a function and a soft integral, an analogue of a line integral in classical analysis. The fundamental properties of soft gradients are established. A necessary and sufficient condition is found so that a set can be a subset of the soft gradient of some function. The inclusion of a soft gradient in a soft integral is proved. Semi-additivity and positive uniformity of a soft integral are established. Estimates are obtained for a soft integral and the size of its segment. Semi-additivity with respect to the upper limit of integration is proved. Moreover, this paper enriches the theoretical development of a soft rational line integral and associated areas for better functionality in terms of computing systems.

On Soft Graphs and Chained Soft Graphs

2018 ◽  
Vol 7 (2) ◽  
pp. 85-102
Author(s):  
K. P. Ratheesh
Keyword(s):  
Computer Science ◽  
Set Theory ◽  
Equivalence Relation ◽  
Medical Science ◽  
Soft Set ◽  
Fuzzy Graph

Soft set theory has a rich potential for application in many scientific areas such as medical science, engineering and computer science. This theory can deal uncertainties in nature by parametrization process. In this article, the authors explore the concepts of soft relation on a soft set, soft equivalence relation on a soft set, soft graphs using soft relation, vertex chained soft graphs and edge chained soft graphs and investigate various types of operations on soft graphs such as union, join and complement. Also, it is established that every fuzzy graph is an edge chained soft graph.

scholarly journals Belief and Possibility Belief Interval-Valued N-Soft Set and Their Applications in Multi-Attribute Decision-Making Problems

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1498
Author(s):  
Shahbaz Ali ◽  
Muneeba Kousar ◽  
Qin Xin ◽  
Dragan Pamučar ◽  
Muhammad Shazib Hameed ◽  
...  
Keyword(s):  
Decision Making ◽  
Set Theory ◽  
Soft Set ◽  
Mathematical Tool ◽  
Soft Sets ◽  
Fundamental Properties ◽  
Research Article ◽  
Multi Attribute Decision Making ◽  
Algebraic Operations ◽  
Interval Valued

In this research article, we motivate and introduce the concept of possibility belief interval-valued N-soft sets. It has a great significance for enhancing the performance of decision-making procedures in many theories of uncertainty. The N-soft set theory is arising as an effective mathematical tool for dealing with precision and uncertainties more than the soft set theory. In this regard, we extend the concept of belief interval-valued soft set to possibility belief interval-valued N-soft set (by accumulating possibility and belief interval with N-soft set), and we also explain its practical calculations. To this objective, we defined related theoretical notions, for example, belief interval-valued N-soft set, possibility belief interval-valued N-soft set, their algebraic operations, and examined some of their fundamental properties. Furthermore, we developed two algorithms by using max-AND and min-OR operations of possibility belief interval-valued N-soft set for decision-making problems and also justify its applicability with numerical examples.

Semi-invariant submanifolds of a normal almost paracontact manifold

Filomat ◽  
2017 ◽  
Vol 31 (15) ◽  
pp. 4875-4887 ◽  
Author(s):  
Mehmet Atçeken ◽  
Siraj Uddin
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Fundamental Properties ◽  
Invariant Submanifolds ◽  
Normal Almost Paracontact Manifold ◽  
Necessary And Sufficient

In this paper, we introduce the notion of semi-invariant submanifolds of a normal almost paracontact manifold. We study their fundamental properties and the particular cases. The necessary and sufficient conditions are given for a submanifold to be invariant or anti-invariant. Also, we give some results for semi-invariant submanifolds of a normal almost paracontact manifold with constant c and we construct an example.

scholarly journals Coleman integration for even-degree models of hyperelliptic curves

2015 ◽  
Vol 18 (1) ◽  
pp. 258-265 ◽  
Author(s):  
Jennifer S. Balakrishnan
Keyword(s):  
Number Theory ◽  
Computer Science ◽  
Hyperelliptic Curves ◽  
Open Book ◽  
Line Integral ◽  
Book Series ◽  
Numerical Examples ◽  
Lecture Notes ◽  
Integration Algorithms ◽  
Mathematical Sciences

The Coleman integral is a $p$-adic line integral that encapsulates various quantities of number theoretic interest. Building on the work of Harrison [J. Symbolic Comput. 47 (2012) no. 1, 89–101], we extend the Coleman integration algorithms in Balakrishnan et al. [Algorithmic number theory, Lecture Notes in Computer Science 6197 (Springer, 2010) 16–31] and Balakrishnan [ANTS-X: Proceedings of the Tenth Algorithmic Number Theory Symposium, Open Book Series 1 (Mathematical Sciences Publishers, 2013) 41–61] to even-degree models of hyperelliptic curves. We illustrate our methods with numerical examples computed in Sage.

scholarly journals Hybrid structures applied to ideals in near-rings

2021 ◽  
Author(s):  
B. Elavarasan ◽  
G. Muhiuddin ◽  
K. Porselvi ◽  
Y. B. Jun
Keyword(s):  
Set Theory ◽  
Fuzzy Set ◽  
Real World ◽  
Rough Set Theory ◽  
Wide Spectrum ◽  
Hybrid Structure ◽  
Soft Set ◽  
Hybrid Structures ◽  
Classical Mathematics ◽  
Classical Means

AbstractHuman endeavours span a wide spectrum of activities which includes solving fascinating problems in the realms of engineering, arts, sciences, medical sciences, social sciences, economics and environment. To solve these problems, classical mathematics methods are insufficient. The real-world problems involve many uncertainties making them difficult to solve by classical means. The researchers world over have established new mathematical theories such as fuzzy set theory and rough set theory in order to model the uncertainties that appear in various fields mentioned above. In the recent days, soft set theory has been developed which offers a novel way of solving real world issues as the issue of setting the membership function does not arise. This comes handy in solving numerous problems and many advancements are being made now-a-days. Jun introduced hybrid structure utilizing the ideas of a fuzzy set and a soft set. It is to be noted that hybrid structures are a speculation of soft set and fuzzy set. In the present work, the notion of hybrid ideals of a near-ring is introduced. Significant work has been carried out to investigate a portion of their significant properties. These notions are characterized and their relations are established furthermore. For a hybrid left (resp., right) ideal, different left (resp., right) ideal structures of near-rings are constructed. Efforts have been undertaken to display the relations between the hybrid product and hybrid intersection. Finally, results based on homomorphic hybrid preimage of a hybrid left (resp., right) ideals are proved.

On soft set-valued maps and integral inclusions

2021 ◽  
pp. 1-15
Author(s):  
Monairah Alansari ◽  
Shehu Shagari Mohammed ◽  
Akbar Azam
Keyword(s):  
Fixed Point ◽  
Set Theory ◽  
Fuzzy Set Theory ◽  
Fixed Point Theorems ◽  
Soft Set ◽  
Mathematical Tool ◽  
Multivalued Maps ◽  
Soft Sets ◽  
Special Cases ◽  
New Development

As an improvement of fuzzy set theory, the notion of soft set was initiated as a general mathematical tool for handling phenomena with nonstatistical uncertainties. Recently, a novel idea of set-valued maps whose range set lies in a family of soft sets was inaugurated as a significant refinement of fuzzy mappings and classical multifunctions as well as their corresponding fixed point theorems. Following this new development, in this paper, the concepts of e-continuity and E-continuity of soft set-valued maps and αe-admissibility for a pair of such maps are introduced. Thereafter, we present some generalized quasi-contractions and prove the existence of e-soft fixed points of a pair of the newly defined non-crisp multivalued maps. The hypotheses and usability of these results are supported by nontrivial examples and applications to a system of integral inclusions. The established concepts herein complement several fixed point theorems in the framework of point-to-set-valued maps in the comparable literature. A few of these special cases of our results are highlighted and discussed.

scholarly journals A New Extended Soft Intersection Set toM,N-SIImplicative Fitters ofBL-Algebras

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jianming Zhan ◽  
Qi Liu ◽  
Hee Sik Kim
Keyword(s):  
Set Theory ◽  
Soft Set ◽  
Mathematical Framework ◽  
Boolean Filters

Molodtsov’s soft set theory provides a general mathematical framework for dealing with uncertainty. The concepts of(M,N)-SIimplicative (Boolean) filters ofBL-algebras are introduced. Some good examples are explored. The relationships between(M,N)-SIfilters and(M,N)-SIimplicative filters are discussed. Some properties of(M,N)-SIimplicative (Boolean) filters are investigated. In particular, we show that(M,N)-SIimplicative filters and(M,N)-SIBoolean filters are equivalent.

Soft Set-Based Switching Faults Decision Making in DTC Induction Motor Drives

2014 ◽  
Vol 24 (02) ◽  
pp. 1550021 ◽  
Author(s):  
Veli Türkmenoğlu ◽  
Mustafa Aktaş ◽  
Serkan Karataş ◽  
Halil İbrahim Okumuş
Keyword(s):  
Decision Making ◽  
Fault Detection ◽  
Induction Motor ◽  
Set Theory ◽  
Wavelet Decomposition ◽  
Motor Drives ◽  
Soft Set ◽  
Fault Detection And Diagnosis ◽  
Induction Motor Drives ◽  
Detection Mechanism

This paper introduces a method for detection and identification of IGBT-based drive open-circuit fault of DTC induction motor drives. The detection mechanism is based on soft set theory and wavelet decomposition, if it is detailed, ⊼-product decision making method and sym2 wavelet decomposition have been used in the detection mechanism. In this method, the stator currents have been used as an input to the system. The stator current has been used for the detection of the fault. The signal analysis has been performed up to the six level details wavelets decomposition. Faulty switch is detected by applying soft set theory to sixth level wavelets transformation. This is the first time applied to inverter in induction motor drives fault detection. The results demonstrate that the proposed fault detection and diagnosis system has very good capabilities.

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