## 2 Robot Reasoning Combined with Its Hedge Algebras
### Robot Reasoning in Dynamic Environments
#### 2.2.2 Applied Hedge Algebra for Robot Sensing in Dynamic Environments  
For the robot, camera vision and linguistics are used in robot sensing to realize cognition in the location process; this process can be used to detect results in an optimal robot decision. The fundamental factors related to a location are both the identification of potential paths and the selection of the optimal decision in the range of appropriate alternative options. Additionally, a robot reasoning can be incorporated in linguistic elements and reasoning things to describe robots in coverage path [16]. While the robot characteristics of linguistic variables and the meaning of hedges in natural language are used to quantify robot sense. Figure 2 shows a robot sensing in dynamic environments. In real-world applications of Turkey and Vietnam, a robotic vacuum cleaner in Big C in experiments can be applied automatically to clean a variety of areas in the supermarket through a vacuum cleaning in dynamic environments, as shown in Figure 2. The robot avoids obstacles consisting of moving or dynamic obstacles. Robot operation is generally based on a simple obstacle avoidance approach, using infrared sensors, while utilizing laser mapping techniques. These sensors and a range finder camera are embedded to hedge algebra for robot sensing in the dirty cleaning and collision avoidance approach. The movement of a robot at the current cell is shown in Figure 3.  
Figure 1: Coverage Path Planning with Spiral Spanning Tree Coverage (STC). Figure 2: A cleaning robot for using Coverage Path Planning in Big C supermarket. Concept of Hedge Algebra (HA)  
(1) _Hedge Algebra (HA)_  
The Hedge Algebra (HA) are defined by formula \(AX=(X,\)\(G,\)\(C,\)\(H,\)\(\leq\)), where, \(G=\{c^{+},\)\(c^{-}\}\) represents primary generators, in which \(c^{+}\) and \(c^{-}\) are, respectively, represents a linguistic variable in positive \(X,\)\(C=\{0,\)\(1,\)\(W\}\) is a constant of sets, consisting of elements in \(X.\)\(H\) which is a set of hedges, \"\(\leq\)\" is semantics in the relation in order on \(X.\) For each \(x\leq X\) in HA, \(H(x)\) is representative of terms \(u\leq X\) generated from \(x\) by applying the hedges of \(H\) and \(u=h_{n},\)\(\ldots,\)\(h_{1}x,\) with \(h_{n},\)\(\ldots,\)\(h_{1}\leq H.\)\(H=H^{+}\leq H^{-},\) in which \(H^{-}\) presents a set of negative hedges, and \(H^{+}\) presents a set of all positive hedges of \(X.\) It is assumed that \(H^{-}=\{h_{-1}<h_{-2}<,\)\(\ldots,\)\(<h_{-q}\}\) and \(H^{+}=\{h_{1}<h_{2}<,\)\(\ldots,\)\(<h_{p}\}\)[15, 20]. (2) _Definition 1_  
Transformation of numerical values to linguistic values in the range of value [0,1]. In function \(IC:Dom\big{(}A_{j}\big{)}\rightarrow[0,1]\) is considered as follows:  
If \(LD_{Ai}=\varnothing\) and \(D_{Ai}\
eq\varnothing\) then \(\forall\omega\in Dom(Ai)\) we have \(IC(\omega)=1-\frac{\psi_{max}-\omega}{\psi_{max}-\psi_{min}},\) with \(Dom(Ai)=\{\psi_{min},\psi_{max}\}\) in domain of language \(Ai.\)  
If \(D_{Ai}\
eq\varnothing,\)\(LD_{Ai}\
eq\varnothing\) then \(\forall\omega\in Dom(Ai)\) we have \(IC(\omega)=\frac{\omega\upsilon(\psi_{max,U})}{\psi_{max}}\) with \(LD_{Ai}=\{\psi_{min,U},\psi_{max,U}\}\) is domain of language \(Ai\)  
(3) _Definition 2_  
Let \(AX\) be a linear algebra with its complete and \(fm\) of a measurement of the opacity \(AX.\) Mapping \(J:X\to P([0,1])\) is called fuzzy based on \(fm\) if it is constructed as inductively with the length \(x\) as follows:  
* \((i)\) Let \(|x|=1\): We construct fuzzy space \(J(c^{-})\) and \(J(c^{+}),\) with \(\big{|}J(x)\big{|}=fm(x),\) so that they form a differential range of [0,1], and are derived from the order of the parts \(c^{-}\) and \(c^{+}\) in which we have \(J(c^{-})\leq J(c^{+}).\)
* \((ii)\) Assume that fuzzy space \(J(x)\) with \(\big{|}J(x)\big{|}=fm(x)\) has been constructed with \(\forall x\in H(G),|x|=n>1\).