# Text Classification Using Intuitionistic Fuzzy Set Measures—An Evaluation Study

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Materials and Methods

#### 3.1. Important Definitions

#### 3.1.1. Fuzzy Sets

#### 3.1.2. Intuitionistic Fuzzy Sets

#### 3.1.3. Distance Measure

**Definition**

**1.**

- C1
- $d(x,y)=0\iff x=y$ (coincidence);
- C2
- $d(x,y)=d(y,x)$ (symmetry);
- C3
- $d(x,z)+d(z,y)\ge d(x,y)$ (triangle inequality).

#### 3.1.4. Similarity Measure

**Definition**

**2.**

- C1
- $S(x,y)=1$ if and only if $x=y$ (coincidence);
- C2
- $S(x,y)=S(y,x)$ (symmetry);
- C3
- $ifx\subseteq y\subseteq z$, then $S(x,z)\le S(x,y)$ and $S(x,z)\le S(y,z)$ (triangle inequality).

#### 3.2. Evaluation Protocol

#### 3.2.1. Bag-of-Words Representation

#### 3.2.2. IFS Representation

#### 3.2.3. IFS Pattern Learning

#### 3.2.4. Document Classification

#### 3.3. Experimental Setup

#### 3.3.1. Distance and Similarity Measures

#### 3.3.2. Datasets

- BBC News: This consists of 2225 articles belonging to 5 topic areas (business, entertainment, politics, sports, and tech) from 2004 and 2005, with a total of 9635 words [50].
- BBC Sports: Similar to the previous one, it contains 737 articles from 5 areas, namely athletics, cricket, football, rugby, and tennis, having a total of 4613 words [50].

#### 3.3.3. Data Preparation

- Documents’ conversion to bag-of-words;
- Word-by-word preprocessing:
- (a)
- Remove escape characters;
- (b)
- Convert to lower case;
- (c)
- Lemmatize word.

- Cut-off words with a document frequency lower than a $0.01$ frequency.

#### 3.3.4. Performance Evaluation

## 4. Results

## 5. Discussion

#### 5.1. BBC News Results

#### 5.2. BBC Sports Results

#### 5.3. Comparison with Standard Machine Learning Approaches

## 6. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Similarity Measure | Expression |
---|---|

${S}_{e}$ | $\sum {w}_{i}\left(1-\left|\frac{(\mu -\nu )-(m-n)}{2}\right|\right)/\sum {w}_{i}$ |

${M}_{H}$ | $\sum {w}_{i}\left(1-\frac{|a\ast {\Delta}_{\mu}+b\ast {\Delta}_{\nu}-c\ast ({\Delta}_{\mu}+{\Delta}_{\nu})|}{a-b}\right)/\sum {w}_{i}$ where $a,b,c\ge 0$ |

${S}_{d}^{p}$ | $1-\frac{1}{\sqrt[\rho ]{N}}\sqrt[\rho ]{{\sum |(\mu +1-\nu )-(m+1-n)|}^{\rho}}$ where $0\le \rho \le +\infty $ |

${S}_{e}^{p}$ | $1-\frac{1}{\sqrt[\rho ]{N}}\sqrt[\rho ]{\sum {\left(\frac{|{\Delta}_{\mu}|+|{\Delta}_{\nu}|}{2}\right)}^{\rho}}$ |

${S}_{s}^{p}$ | $1-\frac{1}{\sqrt[\rho ]{N}}\sqrt[\rho ]{\sum {({\varphi}_{s1}\left(i\right)+{\varphi}_{s2}\left(i\right))}^{\rho}}$ where ${\varphi}_{s1}\left(i\right)=|{m}_{A1}\left(i\right)-{m}_{B1}\left(i\right)|/2$, ${\varphi}_{s2}\left(i\right)=|{m}_{A2}\left(i\right)-{m}_{B2}\left(i\right)|/2$, ${m}_{k1}\left(i\right)=({\mu}_{k}\left(i\right)+{m}_{k}\left(i\right))/2$, ${m}_{k2}\left(i\right)=({m}_{k}\left(i\right)+1-{\nu}_{k}\left(i\right))/2$, ${m}_{k}\left(i\right)=({\mu}_{k}\left(i\right)+1-{\nu}_{k}\left(i\right))/2$ |

${S}_{mod}$ | $\frac{1}{2}\left({S}_{d}^{p}\left(\mu ,m\right)+{S}_{d}^{p}\left(1-\nu ,1-n\right)\right)$ |

${S}_{c}$ | $\frac{1-{d}_{H}(A,B)}{1+{d}_{H}(A,B)}$ |

${S}_{e}$ | $\frac{{e}^{-{d}_{h}(A,B)}-{e}^{-1}}{1-{e}^{-1}}$ |

${S}_{l}$ | $1-{d}_{H}(A,B)$ |

T | $1-\sqrt[\rho ]{\sum {w}_{i}\left[a\ast |{\Delta}_{\mu}{|}^{\rho}+b\ast |{\Delta}_{\nu}{|}^{\rho}+c\ast {\left|{\Delta}_{\pi}\right|}^{\rho}\right]}$ where $1<p<+\infty $, $a,b,c\u03f5[0,1]$ and $a+b+c=1$ |

S | $1-\frac{1}{2N}\sum \left(\right|{\delta}_{A}-{\delta}_{B}|+|{\alpha}_{A}-{\alpha}_{B}\left|\right)$ where ${\delta}_{k}={\mu}_{k}+(1-{\mu}_{k}-{\nu}_{k}){\mu}_{k}$, ${\alpha}_{k}={\nu}_{k}+(1-{\mu}_{k}-{\nu}_{k}){\nu}_{k}$, with $k=\{A,B\}$ |

${S}_{p}^{c}$ | $\frac{\sqrt[\rho ]{2}-{L}_{p}(A,B)}{\sqrt[\rho ]{2}(1+{L}_{p}(A,B))}$ where ${L}_{p}=\frac{1}{N}\sum \left(\right|{\Delta}_{\mu}{|}^{\rho}+|{\Delta}_{\nu}{\left|\right)}^{\rho}$ |

${S}_{p}^{e}$ | $\frac{{e}^{-{L}_{p}(A,B)}-{e}^{-\sqrt[\rho ]{2}}}{1-{e}^{-\sqrt[\rho ]{2}}}$ |

${S}_{p}^{l}$ | $\frac{\sqrt[\rho ]{2}-{L}_{p}(A,B)}{\sqrt[\rho ]{2}}$ |

Similarity Measure | Expression |
---|---|

${S}_{gw}^{p}$ | $1-\sqrt[\rho ]{\sum {w}_{i}{\left(\frac{|{\Delta}_{\mu}|+|{\Delta}_{\nu}|+|{\Delta}_{\pi}|}{2}\right)}^{\rho}}$ where $0\le \rho \le +\infty $ |

${S}_{new2}$ | $1-\frac{1-exp\left(1-\frac{1}{2}\sum \left(|\sqrt{\mu}-\sqrt{m}|+|\sqrt{\nu}-\sqrt{n}|\right)\right)}{1-{e}^{-n}}$ |

${S}_{pk1}$ | $\frac{\sum min(\mu ,m)+min(\nu ,n)}{\sum max(\mu ,m)+max(\nu ,n)}$ |

${S}_{pk2}$ | $1-\frac{1}{2}\left(ma{x}_{i}\left(\right|{\Delta}_{\mu}\left|\right)+ma{x}_{i}\left(\right|{\Delta}_{\nu}\left|\right)\right)$ |

${S}_{pk3}$ | $1-\frac{\sum \left(\right|{\Delta}_{\mu}|+|{\Delta}_{\nu}\left|\right)}{\sum \left(\right|\mu +m|+|\nu ,n\left|\right)}$ |

${S}_{w1}$ | $\frac{1}{N}\frac{\sum min(\mu ,m)+min(\nu ,n)}{\sum max(\mu ,m)+max(\nu ,n)}$ |

${S}_{w2}$ | $\frac{1}{N}\sum \left(1-\frac{1}{N}\left(\right|{\Delta}_{\mu}|+|{\Delta}_{\nu}\left|\right)\right)$ |

${S}_{a}^{c}$ | $\frac{U\left(a\right)-{J}_{a}(A,B)}{(1+{J}_{a}(A,B))U\left(a\right)}$ where $U\left(a\right)=$$\left\{\begin{array}{cc}\mathrm{ln}2\hfill & a=1\hfill \\ \frac{1}{a-1}\left(1-\frac{1}{{2}^{a-1}}\right)\hfill & a\ne 1,a>0\hfill \end{array}\right.$, ${J}_{a}(A,B)=\frac{1}{N}\sum {j}_{a}({A}_{i},{B}_{i})$, ${j}_{a}(A,B)=$$\left\{\begin{array}{cc}\frac{-1}{a-1}{T}_{AB}^{\mu a}{T}_{AB}^{\nu a}{T}_{AB}^{\pi a}\hfill & a\ne 1,a>0\hfill \\ \frac{-1}{2}{L}_{AB}^{\mu}{L}_{AB}^{\nu}{L}_{AB}^{\pi}\hfill & a=1\hfill \end{array}\right.$ ${T}_{AB}^{qa}={\left(\frac{{q}_{A}+{q}_{B}}{2}\right)}^{a}-\frac{1}{2}({q}_{A}^{a}+{q}_{B}^{a})$ ${L}_{AB}^{q}=({q}_{A}+{q}_{B})ln\left(\frac{{q}_{A}+{q}_{B}}{2}\right)-{q}_{A}ln{q}_{A}-{q}_{B}ln{q}_{B}$, with $q=\{\mu ,\nu ,\pi \}$ |

${S}_{a}^{e}$ | $\frac{{e}^{-{J}_{a}(A,B)}-{e}^{-U\left(a\right)}}{1-{e}^{-U\left(a\right)}}$ |

${S}_{a}^{l}$ | $\frac{U\left(a\right)-{J}_{a}(A,B)}{U\left(a\right)}$ |

${C}_{IFS}$ | $\frac{1}{N}\sum \frac{+p}{\sqrt{{\mu}_{A}^{2}\left(i\right)+{\nu}_{A}^{2}\left(i\right)}\sqrt{{\mu}_{B}^{2}\left(i\right)+{\nu}_{B}^{2}\left(i\right)}}$ |

${S}_{IFS}$ | $\frac{1}{3}({C}_{IFS}+{C}_{IFS}^{*}+{C}_{IFS}^{**})$ where ${C}_{IFS}^{*}=\frac{1}{N}\sum \frac{{\varphi}_{A}{\varphi}_{B}+\nu n}{\sqrt{{\varphi}_{A}^{2}{\nu}^{2}}\sqrt{{\varphi}_{B}^{2}{n}^{2}}}$, ${C}_{IFS}^{**}=\frac{1}{N}\sum \frac{(1-\mu )(1-m)+(1-\nu )(1-n)}{\sqrt{{(1-\mu )}^{2}+{(1-\nu )}^{2}}\sqrt{{(1-m)}^{2}+{(1-n)}^{2}}}$ with ${\varphi}_{k}=\frac{1+{\mu}_{k}-{\nu}_{k}}{2}$ |

${S}_{new,p}$ | $1-\sqrt[\rho ]{\sum {w}_{i}\left(\right|{\Delta}_{\mu}{\left|\right)}^{\rho}}-\sqrt[\rho ]{\sum {w}_{i}\left(\right|{\Delta}_{\nu}{\left|\right)}^{\rho}}$ where ${w}_{i}0$, $\rho 1$ |

${\tilde{S}}_{1}$ | $\frac{N+\sum (T(\mu ,m)+T(\nu ,n)-{\nu}_{A}-{\nu}_{B}}{N+max\{\sum (\mu -m),\sum (\nu -p\left)\right\}}$ ${T}_{\lambda}(x,y)=$$\left\{\begin{array}{cc}min(x,y)\hfill & if\lambda =0\hfill \\ x\ast y\hfill & if\lambda =1\hfill \\ max(0,x+y-1)\hfill & if\lambda =\infty \hfill \\ {log}_{\lambda}(1+\frac{({\lambda}^{x}-1)({\lambda}^{y}-1)}{\lambda -1})\hfill & otherwise\hfill \end{array}\right.$ |

${\tilde{S}}_{5}$ | $\frac{N+\sum (T(\mu ,m)+T(\nu ,n)-{\nu}_{A}-{\nu}_{B})}{n-\mu +m-T(\mu ,m)-T(\nu ,n)\}}$ |

${\tilde{S}}_{2}$ | $\frac{2N+\sum \left(2T\right(\mu ,m)+2T(\nu ,n)-\mu -m-\nu -n)}{2N+\sum \left(T\right(\mu ,m)+T(\nu ,n\left)\right)-min\{\sum (\mu +p,\sum (m+\nu )\}}$ |

${\tilde{S}}_{6}$ | $\frac{2N+\sum \left(2T\right(\mu ,m)+2T(\nu ,n)-\mu -m-\nu -n)}{2N}$ |

${\tilde{S}}_{2}^{\prime}$ | $\frac{\sum (\mu +m+\nu +n-2T(\mu ,n)-2T(m,\nu \left)\right)}{N-\sum \left(T\right(\mu ,n)+T(m,\nu \left)\right)+max\{\sum (\mu +n),\sum (m+\nu \left)\right\}}$ |

${\tilde{S}}_{6}^{\prime}$ | $\frac{\sum (\mu +m+\nu +n-2T(\mu ,n)-2T(m,\nu \left)\right)}{2N}$ |

${\tilde{S}}_{1}^{c}$ | $\frac{N+\sum \left(T\right(\mu ,m)+T(\nu ,n)-\mu -m}{N-min\{\sum (\mu ,\nu ),\sum (m,n\left)\right\}}$ |

${\tilde{S}}_{5}^{c}$ | $\frac{N+\sum \left(T\right(\mu ,m)+T(\nu ,n)-\nu -n}{N-\sum (\nu +n-T(\mu ,m)-T(\nu ,n\left)\right)}$ |

Similarity Measure | Expression |
---|---|

${L}_{5}$ | $1-\sqrt[\rho ]{\frac{\sum {\left(\frac{{\Delta}_{\mu}+{\Delta}_{\nu}}{\mu \vee m+\nu \vee n}\right)}^{\rho}}{N}}$ |

${N}_{6}$ | $1-\sqrt[\rho ]{\frac{\sum {\left(\frac{{\Delta}_{\mu}+{\Delta}_{\nu}}{2}\right)}^{\rho}}{N}}$ |

${F}_{5}$ | $\frac{{e}^{2-\sqrt[\rho ]{\frac{\sum {\left({\Delta}_{\mu}\right)}^{\rho}}{N}}\sqrt[\rho ]{\frac{\sum {\left({\Delta}_{\nu}\right)}^{\rho}}{N}}}-1}{{e}^{2}-1}$ |

${F}_{6}$ | $1-\frac{{\left(\sqrt[\rho ]{\frac{\sum {\left({\Delta}_{\mu}\right)}^{\rho}}{N}}\right)}^{u}+{\left(\sqrt[\rho ]{\frac{\sum {\left({\Delta}_{\nu}\right)}^{\rho}}{N}}\right)}^{v}}{2},(u,v>0)$ |

${F}_{7}$ | $1-\frac{sin\frac{{\pi}_{3.14}}{2}\left(\sqrt[\rho ]{\frac{\sum {\left({\Delta}_{\mu}\right)}^{\rho}}{N}}\right)+\left(sin\frac{{\pi}_{3.14}}{2}\sqrt[\rho ]{\frac{\sum {\left({\Delta}_{\nu}\right)}^{\rho}}{N}}\right)}{2}$ |

${S}_{WY}$ | $\frac{1}{2}\sum {w}_{i}\left(\sqrt{\mu \ast m}+2\sqrt{\nu \ast n}+\sqrt{\pi \ast p}+\sqrt{(1-\nu )(1-n)}\right)$ |

${S}_{CCL}$ | $\sum \left({w}_{i}\left(1-\frac{\left|2\right(\mu -m)-(\nu -n\left)\right|}{3}\left(1-\frac{\pi +p}{2}\right)-\frac{\left|2\right(\nu -n)-(\mu -m\left)\right|}{3}\left(\frac{\pi +p}{2}\right)\right)\right)$ |

${W}_{IFSSs}$ | $\frac{\sum {w}_{i}\left((\mu \ast m)+(\nu \ast n)\right)}{\sum \left(({\mu}^{2}\vee {m}^{2})+{(\nu \vee n)}^{2}\right)}\left(\sum {w}_{i}\right)$ |

Distance Measure | Expression |
---|---|

${d}_{e}$ | $\sqrt{\frac{1}{2}\sum _{i=1}^{n}\left[{\Delta}_{\mu}^{2}+{\Delta}_{\nu}^{2}\right]}$ |

${d}_{h}$ | $\frac{1}{2}\sum _{i=1}^{n}\left[|{\Delta}_{\mu}|+|{\Delta}_{\nu}|\right]$ |

${d}_{ne}$ | $\sqrt{\frac{1}{2n}\sum _{i=1}^{n}\left[{\Delta}_{\mu}^{2}+{\Delta}_{\nu}^{2}\right]}$ |

${d}_{nh}$ | $\frac{1}{2n}\sum _{i=1}^{n}\left[|{\Delta}_{\mu}|+|{\Delta}_{\nu}|\right]$ |

${d}_{IFS}^{1}$ | $\sqrt{\frac{1}{2}\sum _{i=1}^{n}\left[{\Delta}_{\mu}^{2}+{\Delta}_{\nu}^{2}+{\Delta}_{\pi}^{2}\right]}$ |

${e}_{IFS}^{1}$ | $\frac{1}{2}\sum _{i=1}^{n}\left[\right|{\Delta}_{\mu}|+|{\Delta}_{\nu}|+|{\Delta}_{\pi}\left|\right]$ |

${l}_{IFS}^{1}$ | $\sqrt{\frac{1}{2n}\sum _{i=1}^{n}\left[{\Delta}_{\mu}^{2}+{\Delta}_{\nu}^{2}+{\Delta}_{\pi}^{2}\right]}$ |

${q}_{IFS}^{1}$ | $\frac{1}{2n}\sum _{i=1}^{n}\left[|{\Delta}_{\mu}|+|{\Delta}_{\nu}|+|{\Delta}_{\pi}|\right]$ |

${d}_{h2}$ | $\sum max\left\{\right|{\Delta}_{\mu}|,|{\Delta}_{\nu}\left|\right\}$ |

${e}_{h}$ | $\frac{1}{N}\sum max\left\{\right|{\Delta}_{\mu}|,|{\Delta}_{\nu}\left|\right\}$ |

${l}_{h}$ | $\sqrt{\sum max\{{\Delta}_{\mu}^{2},{\Delta}_{\nu}^{2}\}}$ |

${q}_{h}$ | $\sqrt{\frac{1}{N}\sum max\{{\Delta}_{\mu}^{2},{\Delta}_{\nu}^{2}\}}$ |

${d}_{1}$ | $\sum _{i=1}^{n}{w}_{i}\left[\frac{|{\Delta}_{\mu}|+|{\Delta}_{\nu}|}{4}+\frac{max\left\{\right|{\Delta}_{\mu}|,|{\Delta}_{\nu}\left|\right\}}{2}\right]/\sum _{i=1}^{n}{w}_{i}$ |

${d}_{2}^{p}$ | $\frac{1}{\sqrt[\rho ]{n}}\sqrt[\rho ]{\sum _{i=1}^{n}{\left(\frac{|{\Delta}_{\mu}|+|{\Delta}_{\nu}|}{2}\right)}^{\rho}}$ |

${d}_{eh}$ | $\sum _{i=1}^{n}max\left\{\right|{\Delta}_{\mu}|,|{\Delta}_{\nu}|,|{\Delta}_{\pi}\left|\right\}$ |

${l}_{eh}$ | $\frac{1}{N}\sum _{i=1}^{n}max\left\{\right|{\Delta}_{\mu}|,|{\Delta}_{\nu}|,|{\Delta}_{\pi}\left|\right\}$ |

${l}_{eh}$ | $\sqrt{\sum max\{{\Delta}_{\mu}^{2},{\Delta}_{\nu}^{2},{\Delta}_{\pi}^{2}\}}$ |

${q}_{eh}$ | $\sqrt{\frac{1}{N}\sum max\{{\Delta}_{\mu}^{2},{\Delta}_{\nu}^{2},{\Delta}_{\pi}^{2}\}}$ |

${D}_{IFS}$ | ${I}_{IFS}(A,B)+{I}_{IFS}(B,A)$, where ${I}_{IFS}(A,B)=\sum \left[\mu ln\frac{\mu}{\frac{1}{2}(\mu +m)}+\nu ln\frac{\nu}{\frac{1}{2}(\nu +n)}\right]$ |

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**Figure 2.**Class distribution and mean of word count per sample text for (

**a**) BBC News and (

**b**) BBC Sports datasets.

**Figure 3.**Confusion matrices of (

**a**) Decision Tree and (

**b**) ${S}_{p}^{c}$ during the validation process.

Authors Names | Parameters | Measure Name | Reference |
---|---|---|---|

S. M. Chen | weights, a, b, c | ${S}_{e}$ | [30] |

D.H. Hong, C. Kim | weights, a, b, c | ${M}_{H}$ | [31] |

L. Dengfeng, C. Chuntian | p, weights | ${S}_{d}^{p}$ | [24] |

Z. Liang, P. Shi | p, weights | ${S}_{e}^{p}$, ${S}_{s}^{p}$ | [32] |

H.B. Mitchell | p, weights | ${S}_{mod}$ | [25] |

W.L. Hung, M.S. Yang | weights | ${S}_{c}$, ${S}_{e}$, ${S}_{l}$ | [26] |

H.W. Liu | p, weights, a, b, c | T | [33] |

C. Zhang, H. Fu | - | S | [34] |

W.L. Hung, M.S. Yang | a | ${S}_{p}^{c}$, ${S}_{p}^{e}$, ${S}_{p}^{l}$ | [35] |

S. Park, Y.C. Kwun, K.M. Lim | p, weights | ${S}_{gw}^{p}$ | [36] |

W.L. Hung, M.S. Yang | - | ${S}_{new2}$, ${S}_{pk1}$, ${S}_{pk2}$, ${S}_{pk3}$, ${S}_{w1}$, ${S}_{w2}$ | [37] |

W.L. Hung, M.S. Yang | p | ${S}_{a}^{c}$, ${S}_{a}^{e}$, ${S}_{a}^{l}$ | [38] |

J. Ye | weights | ${C}_{IFS}$ | [39] |

C.M. Hwang, M.S. Yang | - | ${S}_{IFS}$ | [40] |

P. Julian, K.C. Hung, S. Lin | p, weights | ${S}_{new,p}$ | [41] |

I. Iancu | lamda | ${\tilde{S}}_{1}$, ${\tilde{S}}_{5}$, ${\tilde{S}}_{2}$, ${\tilde{S}}_{6}$, ${\tilde{S}}_{2}^{\prime}$, ${\tilde{S}}_{6}^{\prime}$, ${\tilde{S}}_{1}^{c}$, ${\tilde{S}}_{5}^{c}$ | [42] |

G. Deng, Y. Jiang, J. Fu | weights, p, u, v | ${L}_{5}$, ${N}_{6}$, ${F}_{5}$, ${F}_{6}$, ${F}_{7}$ | [43] |

Y. Song, X. Wang, L. Lei, A. Xue | weights | ${S}_{WY}$ | [44] |

S.M. Chen, S. Cheng, T.C. Lan | weights | ${S}_{CCL}$ | [45] |

P. Muthukumar, G.S.S. Krishnan | weights | ${W}_{IFSSs}$ | [46] |

Authors Names | Parameters | Measure Name | Reference |
---|---|---|---|

K.T. Atanassov | - | ${d}_{e}$, ${d}_{h}$, ${d}_{ne}$, ${d}_{nh}$ | [22] |

E. Szmidt, A. Kacprzyk | - | ${d}_{IFS}^{1}$, ${e}_{IFS}^{1}$, ${l}_{IFS}^{1}$, ${q}_{IFS}^{1}$ | [23] |

P. Grzegorzewski | - | ${d}_{h2}$, ${e}_{h}$, ${l}_{h}$, ${q}_{h}$ | [29] |

W. Wang, X. Xin | weights, p | ${d}_{1}$, ${d}_{2}^{p}$ | [20] |

Y. Yang, F. Chiclana | - | ${d}_{eh}$, ${l}_{eh}$, ${e}_{eh}$, ${q}_{eh}$ | [47] |

I.K. Vlachos, G.D. Sergiadis | - | ${D}_{IFS}$ | [48] |

Distance Measures | Parameters | Weights (${\mathit{r}}_{{\mathit{j}}_{1}}$, ${\mathit{r}}_{{\mathit{j}}_{1}}^{*}$) | Accuracy % | Precision % | Recall % | F1 % | DoC |
---|---|---|---|---|---|---|---|

${d}_{e}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0903 |

${d}_{h}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 3.9711 |

${d}_{ne}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${d}_{nh}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${d}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0903 |

${e}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 3.9711 |

${l}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${q}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${d}_{h}$ | $p=7.00$ | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${e}_{h}$ | $p=7.00$ | ($0.1$, $0.1$) | 88.94 | 90.45 | 88.98 | 88.63 | 0.0031 |

${l}_{h}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0903 |

${q}_{h}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 3.9711 |

${d}_{1}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${d}_{2}^{p}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${d}_{eh}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0903 |

${l}_{eh}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 3.9711 |

${e}_{eh}$ | - | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${q}_{eh}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${D}_{IFS}$ | - | ($0.1$, $1.0$) | 94.25 | 94.10 | 93.98 | 94.02 | 5.5846 |

Similarity Measures | Parameters | Weights (${\mathit{r}}_{{\mathit{j}}_{1}}$, ${\mathit{r}}_{{\mathit{j}}_{1}}^{*}$) | Accuracy % | Precision % | Recall % | F1 % | DoC |
---|---|---|---|---|---|---|---|

${S}_{e}$ | $a=6.00$, $b=-4.00$, $c=7.00$ | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${M}_{H}$ | $a=6.00$, $b=-4.00$, $c=7.00$ | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${S}_{d}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${S}_{e}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${S}_{s}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${S}_{mod}$ | $p=7.00$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${S}_{c}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${S}_{e}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0025 |

${S}_{l}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0031 |

T | $a=0.34$, $b=0.47$, $c=0.42$, $p=9.00$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

S | - | ($0.1$, $1.0$) | 50.65 | 61.21 | 49.05 | 39.49 | 0.0091 |

${S}_{p}^{c}$ | $a=6.00$ | ($1.0$, $0.1$) | 94.83 | 94.67 | 94.62 | 94.63 | 0.0019 |

${S}_{p}^{e}$ | $a=6.00$ | ($1.0$, $0.1$) | 94.83 | 94.67 | 94.62 | 94.63 | 0.0021 |

${S}_{p}^{l}$ | $a=6.00$ | ($1.0$, $0.1$) | 94.83 | 94.67 | 94.62 | 94.63 | 0.0022 |

${S}_{gw}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0025 |

${S}_{new2}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0023 |

${S}_{pk1}$ | - | ($1.0$, $0.1$) | 50.47 | 60.86 | 48.9 | 39.26 | 0.0293 |

${S}_{pk2}$ | - | ($1.0$, $0.1$) | 75.06 | 77.75 | 74.99 | 74.56 | 0.0418 |

${S}_{pk3}$ | - | ($1.0$, $0.1$) | 50.47 | 60.86 | 48.9 | 39.26 | 0.0157 |

${S}_{w1}$ | - | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0017 |

${S}_{w2}$ | - | ($0.1$, $0.1$) | 49.17 | 39.46 | 47.68 | 37.84 | 0 |

${S}_{a}^{c}$ | $p=7.00$ | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0026 |

${S}_{a}^{e}$ | $p=7.00$ | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0033 |

${S}_{a}^{l}$ | $a=6.00$, $b=-4.00$, $c=7.00$ | ($0.1$, $0.1$) | 49.66 | 61.04 | 48.18 | 38.51 | 0.0016 |

${C}_{IFS}$ | - | ($0.1$, $0.325$) | 94.74 | 94.67 | 94.57 | 94.56 | 0.0033 |

${S}_{IFS}$ | - | ($0.55$, $0.325$) | 93.71 | 93.44 | 93.47 | 93.44 | 0.0019 |

${S}_{new,p}$ | $p=7.00$ | ($0.325$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0040 |

${\tilde{S}}_{1}$ | - | ($0.1$, $1.0$) | 71.91 | 80.40 | 73.01 | 73.03 | 0.0097 |

${\tilde{S}}_{5}$ | - | ($1.0$, $0.1$) | 59.78 | 75.68 | 60.60 | 61.30 | 0.0112 |

${\tilde{S}}_{2}$ | - | ($0.55$, $0.1$) | 75.55 | 84.69 | 74.10 | 73.14 | 0.0007 |

${\tilde{S}}_{6}$ | - | ($0.1$, $0.55$) | 91.69 | 92.20 | 91.84 | 91.49 | 0.0006 |

${\tilde{S}}_{2}^{\prime}$ | - | ($1.0$, $1.0$) | 55.33 | 58.77 | 56.51 | 55.42 | 0.0091 |

${\tilde{S}}_{6}^{\prime}$ | - | ($0.775$, $0.325$) | 93.48 | 93.36 | 93.45 | 93.29 | 0.0012 |

${\tilde{S}}_{1}^{c}$ | - | ($1.0$, $0.325$) | 64.9 | 76.35 | 65.71 | 66.39 | 0.0056 |

${\tilde{S}}_{5}^{c}$ | - | ($0.1$, $0.1$) | 90.25 | 91.11 | 89.72 | 89.72 | 0 |

${L}_{5}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.775$, $0.55$) | 94.29 | 94.24 | 94.09 | 94.10 | 0.0289 |

${N}_{6}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0018 |

${F}_{5}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0006 |

${F}_{6}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0 |

${F}_{7}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 93.17 | 93.19 | 92.76 | 92.86 | 0.0028 |

${S}_{WY}$ | - | ($0.1$, $0.325$) | 94.47 | 94.26 | 94.23 | 94.24 | 0.0005 |

${S}_{CCL}$ | - | ($0.1$, $1.0$) | 49.93 | 60.98 | 48.42 | 38.74 | 0.0083 |

${W}_{IFSSs}$ | - | ($1.0$, $0.1$) | 65.75 | 81.88 | 63.86 | 59.92 | 0.0285 |

Similarity Measures | Parameters | Weights (${\mathit{r}}_{{\mathit{j}}_{1}}$, ${\mathit{r}}_{{\mathit{j}}_{1}}^{*}$) | Accuracy % | Precision % | Recall % | F1 % | DoC |
---|---|---|---|---|---|---|---|

${S}_{e}$ | $a=6.00$, $b=-4.00$, $c=7.00$ | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0014 |

${M}_{H}$ | $a=6.00$, $b=-4.00$, $c=7.00$ | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0014 |

${S}_{d}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0028 |

${S}_{e}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0028 |

${S}_{s}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0028 |

${S}_{mod}$ | $p=7.00$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0028 |

${S}_{c}$ | - | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0014 |

${S}_{e}$ | - | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0023 |

${S}_{l}$ | - | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0028 |

T | $a=0.34$, $b=0.47$, $c=0.42$, $p=9.00$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0028 |

S | - | ($0.1$, $1.0$) | 28.49 | 83.19 | 36.36 | 29.31 | 0.0081 |

${S}_{p}^{c}$ | $a=6.00$ | ($0.1$, $0.1$) | 96.47 | 96.69 | 96.78 | 96.72 | 0 |

${S}_{p}^{e}$ | $a=6.00$ | ($0.1$, $0.1$) | 96.47 | 96.69 | 96.78 | 96.72 | 0 |

${S}_{p}^{l}$ | $a=6.00$ | ($0.1$, $0.1$) | 96.47 | 96.69 | 96.78 | 96.72 | 0 |

${S}_{gw}^{p}$ | $p=7.00$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0045 |

${S}_{new2}$ | - | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0021 |

${S}_{pk1}$ | - | ($0.775$, $0.1$) | 26.46 | 83.12 | 35.38 | 27.44 | 0.0269 |

${S}_{pk2}$ | - | ($0.775$, $0.325$) | 79.65 | 81.51 | 77.73 | 78.79 | 0.0489 |

${S}_{pk3}$ | - | ($0.775$, $0.1$) | 26.46 | 83.12 | 35.38 | 27.44 | 0.0144 |

${S}_{w1}$ | - | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.002 |

${S}_{w2}$ | - | ($0.1$, $0.1$) | 24.42 | 81.04 | 33.44 | 24.17 | 0 |

${S}_{a}^{c}$ | $p=7.00$ | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0024 |

${S}_{a}^{e}$ | $p=7.00$ | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.003 |

${S}_{a}^{l}$ | $a=6.00$, $b=-4.00$, $c=7.00$ | ($0.1$, $0.1$) | 25.10 | 83.07 | 33.90 | 25.50 | 0.0014 |

${C}_{IFS}$ | - | ($0.1$, $0.55$) | 96.47 | 96.99 | 96.71 | 96.84 | 0.0023 |

${S}_{IFS}$ | - | ($1.0$, $0.775$) | 95.93 | 96.54 | 96.11 | 96.31 | 0.0067 |

${S}_{new,p}$ | $p=7.00$ | ($0.325$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0064 |

${\tilde{S}}_{1}$ | - | ($0.1$, $1.0$) | 69.61 | 76.86 | 72.68 | 71.01 | 0.0072 |

${\tilde{S}}_{5}$ | - | ($1.0$, $0.1$) | 50.47 | 78.02 | 54.83 | 54.77 | 0.0096 |

${\tilde{S}}_{2}$ | - | ($0.775$, $0.1$) | 82.36 | 86.95 | 87.83 | 84.91 | 0.0012 |

${\tilde{S}}_{6}$ | - | ($0.1$, $0.55$) | 94.44 | 93.89 | 95.63 | 94.61 | 0.0006 |

${\tilde{S}}_{2}^{\prime}$ | - | ($1.0$, $1.0$) | 40.30 | 58.81 | 47.36 | 43.41 | 0.0072 |

${\tilde{S}}_{6}^{\prime}$ | - | ($1.0$, $0.1$) | 94.30 | 93.71 | 95.61 | 94.50 | 0.0018 |

${\tilde{S}}_{1}^{c}$ | - | ($1.0$, $0.325$) | 63.50 | 73.42 | 66.40 | 65.26 | 0.004 |

${\tilde{S}}_{5}^{c}$ | - | ($0.1$, $0.1$) | 90.09 | 89.41 | 91.95 | 89.84 | 0 |

${L}_{5}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($1.0$, $0.775$) | 96.20 | 96.46 | 96.34 | 96.37 | 0.0371 |

${N}_{6}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0028 |

${F}_{5}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0009 |

${F}_{6}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($1.0$, $0.775$) | 96.20 | 96.36 | 96.40 | 96.35 | 0 |

${F}_{7}$ | $p=7.00$, $u=4.43$, $v=7.22$ | ($0.1$, $0.1$) | 96.34 | 96.54 | 96.47 | 96.48 | 0.0045 |

${S}_{WY}$ | - | ($0.1$, $0.325$) | 95.93 | 97.33 | 95.64 | 96.42 | 0.0006 |

${S}_{CCL}$ | - | ($0.1$, $1.0$) | 25.78 | 83.09 | 34.40 | 26.22 | 0.0075 |

${W}_{IFSSs}$ | - | ($1.0$, $0.1$) | 62.82 | 84.04 | 65.53 | 64.82 | 0.0261 |

Distance Measures | Parameters | Weights (${\mathit{r}}_{{\mathit{j}}_{1}}$, ${\mathit{r}}_{{\mathit{j}}_{1}}^{*}$) | Accuracy % | Precision % | Recall % | F1 % | DoC |
---|---|---|---|---|---|---|---|

${d}_{e}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.1001 |

${d}_{h}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 3.423 |

${d}_{ne}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.002 |

${d}_{nh}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 0.0014 |

${d}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.1001 |

${e}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 3.423 |

${l}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.002 |

${q}_{IFS}^{1}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 0.0014 |

${d}_{h}$ | $p=7.00$ | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 0.0014 |

${e}_{h}$ | $p=7.00$ | ($0.1$, $0.1$) | 95.66 | 95.54 | 96.15 | 95.77 | 0.0034 |

${l}_{h}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.1001 |

${q}_{h}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 3.423 |

${d}_{1}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.002 |

${d}_{2}^{p}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 0.0014 |

${d}_{eh}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.1001 |

${l}_{eh}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 3.423 |

${e}_{eh}$ | - | ($0.1$, $0.1$) | 93.62 | 96.32 | 92.79 | 94.28 | 0.002 |

${q}_{eh}$ | - | ($0.1$, $0.1$) | 25.1 | 83.07 | 33.9 | 25.5 | 0.0014 |

${D}_{IFS}$ | - | ($0.1$, $0.55$) | 95.39 | 97.07 | 95.02 | 95.94 | 3.6342 |

BBC News | BBC Sports | |||||||
---|---|---|---|---|---|---|---|---|

Model/Measure | Accuracy(%) | Precision(%) | Recall(%) | F1(%) | Accuracy(%) | Precision(%) | Recall(%) | F1(%) |

Decision Tree | 81.61 | 81.85 | 81.04 | 81.31 | 88.19 | 88.14 | 87.87 | 87.96 |

KNN | 82.69 | 86.47 | 81.63 | 82.79 | 88.46 | 92.96 | 87.42 | 89.16 |

${S}_{p}^{c}$ | 94.83 | 94.67 | 94.62 | 94.63 | 96.47 | 96.69 | 96.78 | 96.72 |

${C}_{IFS}$ | 94.74 | 94.67 | 94.57 | 94.56 | 96.47 | 96.99 | 96.71 | 96.84 |

${D}_{IFS}$ | 94.25 | 94.10 | 93.98 | 94.02 | 95.39 | 97.07 | 95.02 | 95.94 |

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## Share and Cite

**MDPI and ACS Style**

Sidiropoulos, G.K.; Diamianos, N.; Apostolidis, K.D.; Papakostas, G.A.
Text Classification Using Intuitionistic Fuzzy Set Measures—An Evaluation Study. *Information* **2022**, *13*, 235.
https://doi.org/10.3390/info13050235

**AMA Style**

Sidiropoulos GK, Diamianos N, Apostolidis KD, Papakostas GA.
Text Classification Using Intuitionistic Fuzzy Set Measures—An Evaluation Study. *Information*. 2022; 13(5):235.
https://doi.org/10.3390/info13050235

**Chicago/Turabian Style**

Sidiropoulos, George K., Nikolaos Diamianos, Kyriakos D. Apostolidis, and George A. Papakostas.
2022. "Text Classification Using Intuitionistic Fuzzy Set Measures—An Evaluation Study" *Information* 13, no. 5: 235.
https://doi.org/10.3390/info13050235