[Tex/LaTex] Designing a new tuple of Algebra Operators

Question

It's neccessary to have at least two extra tuples of Albera Operators.

A minimal tuple is a triple (to_be_subset_eq, meet_operator, join_operator).

There are some ideas how to make 2 extra tupes. However I need help with their implementation. For examples, as follows:

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amssymb}

\usepackage{soul}
\setul{1pt}{0.5pt} %depth, thikness

\usepackage[normalem]{ulem}
\renewcommand{\ULthickness}{0.5pt}
\renewcommand{\ULdepth}{1pt}

\usepackage{accents}

\def\uSubsetOne{\mbox{\bfseries\b{$\Subset$}}}
\def\uSubsetTwo{\mbox{\ul{$\Subset$}}} %soul package
\def\uSubsetThree{\mbox{\uline{$\Subset$}}} %ulem pakcage
\newcommand{\uSubsetFour}[1]{\underline{#1\mkern-4mu}\mkern4mu } %\underline hacking 

the \underline hacking is from here

\def\uSubsetFive{\mathbf{\underaccent{\bar}{\Subset}}} %accent package

\begin{document}

1. In the First triple  $(\sqsubseteq,\sqcap,\sqcup)$ we need to increase the thickness.

2. Possible variants of $\Subset$ upgrading.

2.1. $(\uSubsetOne,\Cap,\Cup)$ --- the line should be at the right corner.

2.2. $(\uSubsetTwo,\Cap,\Cup)$ ---  the width of the line is too large, soul package. 

2.3. $(\uSubsetThree,\Cap,\Cup)$ ---  the width of the line is too large, ulem package.

2.4. $(\uSubsetFour{\Subset},\Cap,\Cup)$ --- lack of thickness, problems with depth and positioning, width is too large. 

2.5. $(\uSubsetFive,\Cap,\Cup)$ --- the line should be at the right corner, accents package.

\end{document}

The result of compilation:

Here are some useful links:
to design a New Large Math Symbol

to design a New Arrow-like relation symbol – this variant is aslo applicable in case of implementing \multimapdot instead of an arrow in a triple (\sqsubseteq,\sqcap,\sqcup).

to design a New fuzzy logic symbol

to design a New Box-like symbol

Can anyone please help me?

Answer 1

Is this more what you are looking for? I have used the stackengine package for setting things vertically relative. The thicker square operators were created by laying two copies in close proximity (.2pt vertical and horizontal offset). The underlined subset placed a \rule under the \Subset.

\documentclass{article}
\usepackage[T1]{fontenc}
\usepackage{amssymb}
\usepackage{stackengine}
\stackMath
\def\Sqsubseteq{\def\stacktype{L}\mathrel{\stackon[.2pt]{\sqsubseteq}{\kern.2pt\sqsubseteq}}}
\def\Sqcap{\def\stacktype{L}\mathrel{\stackon[.2pt]{\sqcap}{\kern.2pt\sqcap}}}
\def\Sqcup{\def\stacktype{L}\mathrel{\stackon[.2pt]{\sqcup}{\kern.2pt\sqcup}}}
\def\uSubset{\mathrel{\stackunder[1pt]{\Subset}{\rule{1.35ex}{.45pt}}}}
\begin{document}
1. In the First triple  $(\sqsubseteq,\sqcap,\sqcup)$ we need to increase the thickness.\par
1. Try $(\Sqsubseteq,\Sqcap,\Sqcup)$\par
2. Possible variants of $\Subset$ upgrading.\par
Try $(\uSubset,\Cap,\Cup)$ 
\end{document}