# Set Theory and Logic

## 1411 Submissions

[4] **viXra:1411.0529 [pdf]**
*submitted on 2014-11-21 07:00:54*

### New Techniques to Analyse the Prediction of Fuzzy Models

**Authors:** W. B. Vasantha Kandasamy, Florentin Smarandache, Ilanthenral K.

**Comments:** 242 Pages.

In this book the authors for the first time have ventured to study, analyse and investigate fuzzy and neutrosophic models and the experts opinion. To make such a study, innovative techniques and defined and developed. Several important conclusions about these models are derived using these new techniques. Open problems are suggested in this book.

**Category:** Set Theory and Logic

[3] **viXra:1411.0528 [pdf]**
*submitted on 2014-11-21 07:02:15*

### Pseudo Lattice Graphs and their Applications to Fuzzy and Neutrosophic Models

**Authors:** Vasantha Kandasamy, Florentin Smarandache, Ilanthenral K.

**Comments:** 275 Pages.

In this book the authors for the first time have merged vertices and edges of lattices to get a new structure which may or may not be a lattice but is always a graph. This merging is done for graph too which will be used in the merging of fuzzy models. Further merging of graphs leads to the merging of matrices; both these concepts play a vital role in merging the fuzzy and neutrosophic models.
Several open conjectures are suggested.

**Category:** Set Theory and Logic

[2] **viXra:1411.0051 [pdf]**
*submitted on 2014-11-07 05:57:21*

### A Unified Complexity Theory. Annex VII

**Authors:** Ricardo Alvira

**Comments:** 5 Pages.

It reviewes the difference between cocnepts involving Certainty/Uncertainty.

**Category:** Set Theory and Logic

[1] **viXra:1411.0009 [pdf]**
*submitted on 2014-11-01 23:51:59*

### A Rigorous Procedure for Generating a Well-Ordered Set of Reals Without Use of Axiom of Choice / Well-Ordering Theorem

**Authors:** Karan Doshi

**Comments:** 8 Pages.

Well-ordering of the Reals@@ presents a major challenge in Set theory. Under the standard Zermelo Fraenkel Set theory (ZF) with the Axiom of Choice (ZFC), a well-ordering of the Reals is indeed possible. However the Axiom of Choice (AC) had to be introduced to the original ZF theory which is then shown equivalent to the well-ordering theorem. Despite the result however, no way has still been found of actually constructing a well-ordered Set of Reals. In this paper the author attempts to generate a well ordered Set of Reals without using the AC i.e. under ZF theory itself using the Axiom of the Power Set as the guiding principle.

**Category:** Set Theory and Logic