Analysis Commons^™

New Techniques To Analyse The Prediction Of Fuzzy Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Ilanthenral

Branch Mathematics and Statistics Faculty and Staff Publications

For the first time authors have ventured to study, analyse and investigate the properties of the fuzzy models, the experts opinion and so on. Here the concept of merged Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps are carried out, which are based on merged graphs and merged matrices. This concept is better than the usual combined Fuzzy Cognitive Maps. Further by this new technique we are able to give equal importance to all the experts who work with the problem. Here the new concept of New Average Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps is defined and described. This new …

Eccentricity, Space Bending, Dimension, Florentin Smarandache, Marian Nitu, Mircea Eugen Selariu

Branch Mathematics and Statistics Faculty and Staff Publications

The main goal of this paper is to present new transformations, previously non-existent in traditional mathematics, that we call centric mathematics (CM) but that became possible due to the new born eccentric mathematics, and, implicitly, to the supermathematics (SM).

As shown in this work, the new geometric transformations, namely conversion or transfiguration, wipe the boundaries between discrete and continuous geometric forms, showing that the first ones are also continuous, being just apparently discontinuous.

Algebraic Structures On The Fuzzy Interval [0, 1), Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce several algebraic structures on the special fuzzy interval [0, 1). This study is different from that of the algebraic structures using the interval [0, n) n ≠ 1, as these structures on [0, 1) has no idempotents or zero divisors under ×. Further [0, 1) under product × is only a semigroup. However by defining min(or max) operation in [0, 1); [0, 1) is made into a semigroup. The semigroup under × has no finite subsemigroups but under min or max we have subsemigroups of order one, two and so on. [0, 1) under + …

Algebraic Structures On Finite Complex Modulo Integer Interval C([0, N)), Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book authors introduce the notion of finite complex modulo integer intervals. Finite complex modulo integers was introduced by the authors in 2011. Now using this finite complex modulo integer intervals several algebraic structures are built. Further the concept of finite complex modulo integers itself happens to be new and innovative for in case of finite complex modulo integers the square value of the finite complex number varies with varying n of Zn. In case of finite complex modulo integer intervals also we can have only pseudo ring as the distributive law is not true, in general in C([0, …

New Results Of Intuitionistic Fuzzy Soft Set, Florentin Smarandache, Said Broumi, Mamoni Dhar, Pinaki Majumdar

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, three new operations are introduced on intuitionistic fuzzy soft sets .They are based on concentration, dilatation and normalization of intuitionistic fuzzy sets. Some examples of these operations were given and a few important properties were also studied.

Special Pseudo Linear Algebras Using [0,N), Florentin Smarandache, W.B. Vasantha Kandasamy

Branch Mathematics and Statistics Faculty and Staff Publications

In this book we introduce some special type of linear algebras called pseudo special linear algebras using the interval [0, n). These new types of special pseudo interval linear algebras has several interesting properties. Special pseudo interval linear algebras are built over the subfields in Zn where Zn is a S-ring. We study the substructures of them. The notion of Smarandache special interval pseudo linear algebras and Smarandache strong special pseudo interval linear algebras are introduced. The former Sspecial interval pseudo linear algebras are built over the Sring itself. Study in this direction has yielded several interesting results. S-strong special …

Further Generalization Of N-D Distance And N-D Dependent Function In Extenics, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Prof. Cai Wen [1] defined the 1-D Distance and 1-D Dependent Function in 1983. F. Smarandache [6] generalized them to n-D Distance and n-D Dependent Function respectively in 2012 during his postdoc research at Guangdong University of Technology in Guangzhou. O. I. Şandru [7] extended the last results in 2013. Now [2015], as a further generalization, we unify all these results into a single formula for the n-D Distance and respectively for the n-D Dependent Function.

Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces, A. A. Salama, Florentin Smarandache, Valeri Kroumov

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we generalize the crisp topological space to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.

Single Valued Neutrosophic Information Systems Based On Rough Set Theory, Said Broumi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

The theory of rough sets was firstly proposed by Pawlak. Later on, Smarandache introduced the concept of neutrosophic (NS) sets in 1998. In this paper based on the concept of rough neutrosohic set, we define the concept of single valued neutrosophic information systems. In addition, we will discuss the knowledge reduction and extension of the single valued neutrosophic information systems.