MOD Natural Neutrosophic Subset Topological Spaces and Kakutani’s Theorem

MOD Natural Neutrosophic Subset Topological Spaces and Kakutani’s Theorem
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
Total Pages: 278
Release:
Genre:
ISBN: 1599734907

In this book authors for the first time develop the notion of MOD natural neutrosophic subset special type of topological spaces using MOD natural neutrosophic dual numbers or MOD natural neutrosophic finite complex number or MOD natural neutrosophic-neutrosophic numbers and so on to build their respective MOD semigroups. Later they extend this concept to MOD interval subset semigroups and MOD interval neutrosophic subset semigroups. Using these MOD interval semigroups and MOD interval natural neutrosophic subset semigroups special type of subset topological spaces are built. Further using these MOD subsets we build MOD interval subset matrix semigroups and MOD interval subset matrix special type of matrix topological spaces. Likewise using MOD interval natural neutrosophic subsets matrices semigroups we can build MOD interval natural neutrosophic matrix subset special type of topological spaces. We also do build MOD subset coefficient polynomial special type of topological spaces. The final chapter mainly proposes several open conjectures about the validity of the Kakutani’s fixed point theorem for all MOD special type of subset topological spaces.

Special Subset Linguistic Topological Spaces

Special Subset Linguistic Topological Spaces
Author: W. B. Vasantha Kandasamy
Publisher: Infinite Study
Total Pages: 259
Release:
Genre: Mathematics
ISBN:

In this book, authors, for the first time, introduce the new notion of special subset linguistic topological spaces using linguistic square matrices. This book is organized into three chapters. Chapter One supplies the reader with the concept of ling set, ling variable, ling continuum, etc. Specific basic linguistic algebraic structures, like linguistic semigroup linguistic monoid, are introduced. Also, algebraic structures to linguistic square matrices are defined and described with examples. For the first time, non-commutative linguistic topological spaces are introduced. The notion of a linguistic special subset of doubly non-commutative topological spaces of linguistic topological spaces is introduced in this book.

Neutrosophy

Neutrosophy
Author: Florentin Smarandache
Publisher:
Total Pages: 110
Release: 1998
Genre: Mathematics
ISBN:

Neutrosophic Topological Spaces

Neutrosophic Topological Spaces
Author: Murad Arar
Publisher: Infinite Study
Total Pages: 16
Release: 2020-12-01
Genre: Mathematics
ISBN:

In this paper, the concept of neutrosophic topological spaces is introduced. We define and study the properties of neutrosophic open sets, closed sets, interior and closure. The set of all generalize neutrosophic pre-closed sets GNPC and the set of all neutrosophic open sets in a neutrosophic topological space can be considered as examples of generalized neutrosophic topological spaces.

Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov

Nonsmooth Optimization in Honor of the 60th Birthday of Adil M. Bagirov
Author: Napsu Karmitsa
Publisher: MDPI
Total Pages: 116
Release: 2020-12-18
Genre: Science
ISBN: 3039438352

The aim of this book was to collect the most recent methods developed for NSO and its practical applications. The book contains seven papers: The first is the foreword by the Guest Editors giving a brief review of NSO and its real-life applications and acknowledging the outstanding contributions of Professor Adil Bagirov to both the theoretical and practical aspects of NSO. The second paper introduces a new and very efficient algorithm for solving uncertain unit-commitment (UC) problems. The third paper proposes a new nonsmooth version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems. In the fourth paper, the abs-linear representation of piecewise linear functions is extended to yield simultaneously their DC decomposition as well as the pair of generalized gradients. The fifth paper presents the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and nonsmooth optimization problems in many practical applications. In the sixth paper, a problem concerning the scheduling of nuclear waste disposal is modeled as a nonsmooth multiobjective mixed-integer nonlinear optimization problem, and a novel method using the two-slope parameterized achievement scalarizing functions is introduced. Finally, the last paper considers binary classification of a multiple instance learning problem and formulates the learning problem as a nonconvex nonsmooth unconstrained optimization problem with a DC objective function.

On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces

On Generalized Closed Sets and Generalized Pre-Closed Sets in Neutrosophic Topological Spaces
Author: Wadei Al-Omeri
Publisher: Infinite Study
Total Pages: 12
Release:
Genre: Mathematics
ISBN:

In this paper, the concept of generalized neutrosophic pre-closed sets and generalized neutrosophic pre-open sets are introduced. We also study relations and various properties between the other existing neutrosophic open and closed sets. In addition, we discuss some applications of generalized neutrosophic pre-closed sets, namely neutrosophic pT12 space and neutrosophic gpT12 space. The concepts of generalized neutrosophic connected spaces, generalized neutrosophic compact spaces and generalized neutrosophic extremally disconnected spaces are established. Some interesting properties are investigated in addition to giving some examples.

Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set

Neutrosophic Set - A Generalization of The Intuitionistic Fuzzy Set
Author: Florentin Smarandache
Publisher: Infinite Study
Total Pages: 10
Release: 2010-08-23
Genre: Mathematics
ISBN:

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

Neutrosophic Semi-Continuous Multifunctions

Neutrosophic Semi-Continuous Multifunctions
Author: R. Dhavaseelan
Publisher: Infinite Study
Total Pages: 10
Release:
Genre:
ISBN:

In this paper we introduce the concepts of neutrosophic upper and neutrosophic lower semi-continuous multifunctions and study some of their basic properties.

ON I-OPEN SETS AND I-CONTINUOUS FUNCTIONS IN IDEAL BITOPOLOGICAL SPACES

ON I-OPEN SETS AND I-CONTINUOUS FUNCTIONS IN IDEAL BITOPOLOGICAL SPACES
Author: M. CALDAS
Publisher: Infinite Study
Total Pages: 13
Release:
Genre: Mathematics
ISBN:

The concept of ideals in topological spaces has been introduced and studied by Kuratowski [19] and Vaidyanathasamy [24]. Hamlett and Jankovic (see [12], [13], [17] and [18]) used topological ideals to generalize many notions and properties in general topology.

RETRACT NEUTROSOPHIC CRISP SYSTEM FOR GRAY SCALE IMAGE

RETRACT NEUTROSOPHIC CRISP SYSTEM FOR GRAY SCALE IMAGE
Author: A. A. SALAMA
Publisher: Infinite Study
Total Pages: 14
Release:
Genre:
ISBN:

In this paper, we aim to develop a new type of neutrosophic crisp set called the retract neutrosophic crisp set and shows a grayscale image in a 2D Cartesian domain with neutrosophic crisp components in the neutrosophic domain.