[18] **viXra:1808.0281 [pdf]**
*submitted on 2018-08-20 04:47:04*

**Authors:** Vasantha KandasamyW.B., Ilanthenral Kandasamy, Florentin Smarandache

**Comments:** 8 Pages.

Fuzzy set theory was introduced by Zadeh and was generalized to the Intuitionistic Fuzzy Set (IFS) by Atanassov. Real-world, uncertain, incomplete, indeterminate, and inconsistent data were presented philosophically as a neutrosophic set by Smarandache [3], who also studied the notion
of neutralities that exist in all problems.

**Category:** General Mathematics

[17] **viXra:1808.0280 [pdf]**
*submitted on 2018-08-20 04:48:40*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Florentin Smarandache, Yongquan Zhou

**Comments:** 11 Pages.

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision
makers are only approximate, which gives rise of neutrosophic critical path problem.

**Category:** General Mathematics

[16] **viXra:1808.0279 [pdf]**
*submitted on 2018-08-20 04:50:13*

**Authors:** Mai Mohamed, Mohamed Abdel-Baset, Florentin Smarandache, Yongquan Zhou

**Comments:** 8 Pages.

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision
makers are only approximate, which gives rise of neutrosophic critical path problem.

**Category:** General Mathematics

[15] **viXra:1808.0278 [pdf]**
*submitted on 2018-08-20 04:51:20*

**Authors:** Jack Allen, Housila P. Singh

**Comments:** 15 Pages.

This paper proposes a family of estimators of population mean using information on several auxiliary variables and analyzes its properties in the presence of measurement errors.

**Category:** General Mathematics

[14] **viXra:1808.0277 [pdf]**
*submitted on 2018-08-20 04:52:46*

**Authors:** Mohamed Abdel-Basset, Mai Mohamed, Florentin Smarandache

**Comments:** 21 Pages.

One of the most significant competitive strategies for organizations is sustainable supply chain management (SSCM). The vital part in the administration of a sustainable supply chain is the sustainable supplier selection, which is a multi-criteria decision-making issue, including many conflicting criteria.

**Category:** General Mathematics

[13] **viXra:1808.0272 [pdf]**
*submitted on 2018-08-20 05:12:26*

**Authors:** Arindam Dey, Said Broumi, Le Hoang Son, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 7 Pages.

In this paper, we discuss the minimum spanning tree (MST) problem of an undirected neutrosophic weighted connected graph in which a single-valued neutrosophic number, instead of a real number/fuzzy number, is assigned to each arc as its arc length.We define this type of MST as neutrosophic minimum spanning tree (NMST).

**Category:** General Mathematics

[12] **viXra:1808.0271 [pdf]**
*submitted on 2018-08-20 05:15:45*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache, Kishore Kumar P K

**Comments:** 16 Pages.

In this chapter, we introduce a new algorithm for finding a minimum spanning tree (MST) of an undirected neutrosophic weighted connected graph whose edge weights are represented by an interval valued neutrosophic number. In addition, we compute the cost of MST and compare the de- neutrosophied value with an equivalent MST having the detereministic weights. Finally, a numerical example is provided.

**Category:** General Mathematics

[11] **viXra:1808.0269 [pdf]**
*submitted on 2018-08-20 05:18:04*

**Authors:** Ganeshsree Selvachandran, Shio Gai Quek, Florentin Smarandache, Said Broumi

**Comments:** 17 Pages.

A single-valued neutrosophic set (SVNS) is a special case of a neutrosophic set which is
characterized by a truth, indeterminacy, and falsity membership function, each of which lies in the standard interval of [0, 1]. This paper presents a modified Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) with maximizing deviation method based on the single-valued neutrosophic set (SVNS) model.

**Category:** General Mathematics

[10] **viXra:1808.0267 [pdf]**
*submitted on 2018-08-20 05:20:59*

**Authors:** Mohamed Abdel-Basset, Mai Mohamed, Florentin Smarandache

**Comments:** 18 Pages.

Every organization seeks to set strategies for its development and growth and to do this, it must take into account the factors that affect its success or failure. The most widely used
technique in strategic planning is SWOT analysis. SWOT examines strengths (S), weaknesses (W),opportunities (O) and threats (T), to select and implement the best strategy to achieve organizational goals.

**Category:** General Mathematics

[9] **viXra:1808.0266 [pdf]**
*submitted on 2018-08-20 05:22:13*

**Authors:** Said Broumi, Assia Bakali, Mohamed Talea, Florentin Smarandache

**Comments:** 7 Pages.

In this research paper, we propose the graph of the bipolar single-valued neutrosophic set (BSVNS) model. This graph generalized the graphs of single-valued neutrosophic set models.

**Category:** General Mathematics

[8] **viXra:1808.0265 [pdf]**
*submitted on 2018-08-20 05:23:23*

**Authors:** V Christianto, F Smarandache, Y Umniyati

**Comments:** 3 Pages.

It has been known for long time that the cosmic sound wave was there since the early epoch of the Universe. Signatures of its existence are abound. However, such a sound wave model of cosmology is rarely developed fully into a complete framework.

**Category:** General Mathematics

[7] **viXra:1808.0226 [pdf]**
*submitted on 2018-08-17 00:25:54*

**Authors:** Toshiro Takami

**Comments:** 19 Pages.

I found a prime number theorem. All prime numbers except 2 and 3 are /sqrt(24a-23)=t .
(a =positive integer, t =prime number)
As an exception, 77 which is not a prime number comes up, but it seems to be treated as the only exception.

**Category:** General Mathematics

[6] **viXra:1808.0191 [pdf]**
*submitted on 2018-08-14 07:38:32*

**Authors:** Edgar Valdebenito

**Comments:** 3 Pages.

This note presents an image related with the function f(z)=ln(2z+tan z).

**Category:** General Mathematics

[5] **viXra:1808.0174 [pdf]**
*submitted on 2018-08-13 06:51:14*

**Authors:** Saikat Sarkar

**Comments:** 8 Pages.

Here i am representing some basic graphs of some known functions and their behaviour.

**Category:** General Mathematics

[4] **viXra:1808.0158 [pdf]**
*submitted on 2018-08-12 11:45:22*

**Authors:** Radomir Majkic

**Comments:** 4 Pages.

There is no cuboid with all integer edges and face diagonals.

**Category:** General Mathematics

[3] **viXra:1808.0105 [pdf]**
*submitted on 2018-08-08 20:22:13*

**Authors:** Travis Keraly

**Comments:** 1 Page. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Using a simple pattern, a linear chromatic scale is revealed, beginning and ending with a perfect octave.

**Category:** General Mathematics

[2] **viXra:1808.0092 [pdf]**
*submitted on 2018-08-07 10:53:42*

**Authors:** Colin James III

**Comments:** 1 Page. Copyright © 2018 by Colin James III All rights reserved. Respond to this author's email address: info@ersatz-systems dot com. (We instruct troll Mikko at Disqus to read the entire article twice before she starts typing.)

In superposition calculus, the property of translation invariance for A < B → XAY < XBY for all words A,B,X,Y as TCTT TCTT TCTT TTTT is not tautologous and hence refuted.

**Category:** General Mathematics

[1] **viXra:1808.0005 [pdf]**
*submitted on 2018-08-01 01:53:32*

**Authors:** Janne Hakkarainen

**Comments:** 2 Pages.

Magic squares have interested (recreational) mathematicians for hundreds, if not thousands, of years. But what would happen if the grid of a magic square would be infinite?

**Category:** General Mathematics