Interval Neutrosophic Sets And Topology
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| Author | : Francisco Gallego Lupiáñez |
| Publisher | : Infinite Study |
| Total Pages | : 6 |
| Release | : |
| Genre | : |
| ISBN | : |
In 2005, Smarandache generalized the Atanassov’s intuitionistic fuzzy sets (IFSs) to neutrosophic sets (NS), and other researchers introduced the notion of interval neutrosophic set (INSs), which is an instance of NS, and studied various properties. The notion of neutrosophic topology on the non-standard interval is also due to Smarandache. The purpose of this paper is to study relations between INSs and topology.
| Author | : FRANCISCO GALLEGO LUPIAÑEZ |
| Publisher | : Infinite Study |
| Total Pages | : 9 |
| Release | : |
| Genre | : |
| ISBN | : |
Recently, F.Smarandache generalized the Atanassov's intuitionistic fuzzy sets and other kinds of sets to neutrosophic sets. Also, this author defined the notion of neutrosophic topology on the non-standard interval. One can expect some relation between the intuitionistic fuzzy topology on an IFS and the neutrosophic topology. We show in this work that this is false.
| Author | : Haibin Wang |
| Publisher | : Infinite Study |
| Total Pages | : 99 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 1931233942 |
This book presents the advancements and applications of neutrosophics, which are generalizations of fuzzy logic, fuzzy set, and imprecise probability. The neutrosophic logic, neutrosophic set, neutrosophic probability, and neutrosophic statistics are increasingly used in engineering applications (especially for software and information fusion), medicine, military, cybernetics, physics.In the last chapter a soft semantic Web Services agent framework is proposed to facilitate the registration and discovery of high quality semantic Web Services agent. The intelligent inference engine module of soft semantic Web Services agent is implemented using interval neutrosophic logic.
| Author | : Florentin Smarandache |
| Publisher | : Infinite Study |
| Total Pages | : 18 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In approximation theory, neutrosophic set and logic show an important role. They are generalizations of intuitionistic fuzzy set and logic respectively. Based on neutrosophy, which is a new branch of philosophy, every idea X, has an opposite denoted as anti (X) and their neutral which is denoted as neut (X). These are the main features of neutrosophic set and logic. This chapter is based on the basic concepts of neutrosophic set as well as some of their hybrid structures. In this chapter, we define and study the notion of neutrosophic set and their basic properties. Moreover, interval-valued neutrosophic set are studied with some of their properties. Finally, we define rough neutrosophic sets.
| Author | : Mohammed A. Al Shumrani |
| Publisher | : Infinite Study |
| Total Pages | : 14 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
For the first time we introduce non-standard neutrosophic topology on the extended non-standard analysis space, called non-standard real monad space, which is closed under neutrosophic non-standard infimum and supremum. Many classical topological concepts are extended to the non-standard neutrosophic topology, several theorems and properties about them are proven, and many examples are presented.
| Author | : Dongsik Jo |
| Publisher | : Infinite Study |
| Total Pages | : 30 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property.
| Author | : Dongsik Jo |
| Publisher | : Infinite Study |
| Total Pages | : 29 |
| Release | : |
| Genre | : Mathematics |
| ISBN | : |
In this paper, we introduce the new notion of interval-valued neutrosophic crisp sets providing a tool for approximating undefinable or complex concepts in real world. First, we deal with some of its algebraic structures. We also define an interval-valued neutrosophic crisp (vanishing) point and obtain some of its properties. Next, we define an interval-valued neutrosophic crisp topology, base (subbase), neighborhood, and interior (closure), respectively and investigate some of each property, and give some examples. Finally, we define an interval-valued neutrosophic crisp continuity and quotient topology and study some of each property.
| Author | : Hong-yu Zhang |
| Publisher | : Infinite Study |
| Total Pages | : 16 |
| Release | : |
| Genre | : |
| ISBN | : |
As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world.
| Author | : Wadei Al-Omeri |
| Publisher | : Infinite Study |
| Total Pages | : 21 |
| Release | : |
| Genre | : |
| ISBN | : |
In Geographical information systems (GIS) there is a need to model spatial regions with indeterminate boundary and under indeterminacy.
| Author | : Anjan Mukherjee |
| Publisher | : Infinite Study |
| Total Pages | : 10 |
| Release | : |
| Genre | : |
| ISBN | : |
In this paper we introduce the concept of interval valued neutrosophic soft topological space together with interval valued neutrosophic soft finer and interval valued neutrosophic soft coarser topology.
