# On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

## 3. Definitions

#### 3.1. Groupoid Space

#### 3.2. Distributed Monoid Space

#### 3.3. Topological Distributed Monoid (DM)

#### 3.4. Topological Translation

#### 3.5. Fuzzy Topological Measure

#### 3.6. Local Isomorphism

#### 3.7. Local Homeomorphism

## 4. Analytical Properties

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Lemma.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Theorem**

**4.**

**Proof.**

**Theorem**

**5.**

**Proof.**

**Theorem**

**6.**

**Proof.**

**Theorem**

**7.**

**Proof.**

**Theorem**

**8.**

**Proof.**

**Theorem**

**9.**

**Proof.**

**Theorem**

**10.**

**Proof.**

**Theorem**

**11.**

**Proof.**

**Theorem**

**12.**

**Proof.**

## 5. Computational Evaluations

## 6. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**MDPI and ACS Style**

Bagchi, S.
On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces. *Symmetry* **2019**, *11*, 9.
https://doi.org/10.3390/sym11010009

**AMA Style**

Bagchi S.
On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces. *Symmetry*. 2019; 11(1):9.
https://doi.org/10.3390/sym11010009

**Chicago/Turabian Style**

Bagchi, Susmit.
2019. "On the Analysis and Computation of Topological Fuzzy Measure in Distributed Monoid Spaces" *Symmetry* 11, no. 1: 9.
https://doi.org/10.3390/sym11010009