Difference between revisions of "Fuzzy logic language/en"

To mathematically represent this degree of belonging is the function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> called '<nowiki/>'''Membership Function''''. The function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> is a continuous function defined in the interval <math>[0;1]</math>where it is:

*<math>\mu_ {\tilde {A}}(x) = 1\rightarrow </math>   if <math>x</math> is totally contained in <math>A</math> (these points are called 'nucleus', they indicate <u>plausible</u> predicate values).

*<math>\mu_ {\tilde {A}}(x) = 0\rightarrow </math> if <math>x</math> is not contained in <math>A</math>

The graphical representation of the function <math>\mu_{\displaystyle {\tilde {A}}}(x)</math> it can be varied; from those with linear lines (triangular, trapezoidal) to those in the shape of bells or 'S' (sigmoidal) as depicted in Figure 1, which contains the whole graphic concept of the function of belonging.<ref>{{Cite book  

If <math>{A}</math> represented a set in the ordinary sense of the term or classical language logic previously described, its membership function could assume only the values <math>1</math> or <math>0</math>, <math>\mu_{\displaystyle {{A}}}(x)= 1 \; \lor \;\mu_{\displaystyle {{A}}}(x)= 0</math> depending on whether the element <math>x</math> whether or not it belongs to the whole, as considered. Figure 2 shows a graphic representation of the crisp (rigidly defined) or fuzzy concept of membership, which clearly recalls Smuts's considerations.<ref name=":0">•SMUTS J.C. 1926, [[wikipedia:Holism_and_Evolution|Holism and Evolution]], London: Macmillan.</ref>  

*'''Classical Logic''' in the Dental Context <math>{A}</math> in which only a logical process that gives as results <math>\mu_{\displaystyle {{A}}}(x)= 1 </math> it will be possible, or <math>\mu_{\displaystyle {{A}}}(x)= 0 </math> being the range of data <math>D=\{\delta_1,\dots,\delta_4\}</math>reduced to basic knowledge <math>KB</math> in the set <math>{A}</math>. This means that outside the dental world there is a void and that term of set theory, it is written precisely <math>\mu_{\displaystyle {{A}}}(x)= 0 </math> and which is synonymous with a high range of:

  </math> and a result <math>0<\mu_ {\tilde {A}}(x) < 1</math> because of basic knowledge <math>KB</math> which at this point is represented by the union of <math>KB_c</math>  dental and neurological contexts. The result of this scientific-clinical implementation of dentistry would allow a:{{q2|Reduction of differential diagnostic error|}}

Topics that could distract the reader’s attention—was, in fact, essential for demonstrating the message. Normally, in fact, when any more or less brilliant mind allows itself to throw a stone into the pond of Science, a shockwave is generated, typical of the period of Kuhn’s extraordinary science, against which most of the members of the international scientific community row. With good faith, we can say that this phenomenon—as regards the topics we are addressing here—is well represented in the premise at the beginning of the chapter.

In these chapters, in fact, a fundamental topic for science has been approached: the re-evaluation, the specific weight that has always been given to <math>P-value</math>, awareness of scientific / clinical contexts <math>KB_c</math>, having undertaken a more elastic path of Fuzzy Logic than the Classical one, realizing the extreme importance of <math>KB</math> and ultimately the union of contexts <math>KB_c</math> to increase its diagnostic capacity.<ref>Mehrdad Farzandipour, Ehsan Nabovati, Soheila Saeedi, Esmaeil Fakharian. [https://pubmed.ncbi.nlm.nih.gov/30119845/ Fuzzy decision support systems to diagnose musculoskeletal disorders: A systematic literature review] . Comput Methods Programs Biomed. 2018 Sep;163:101-109. doi: 10.1016/j.cmpb.2018.06.002. Epub 2018 Jun 6.</ref><ref>Long Huang, Shaohua Xu, Kun Liu, Ruiping Yang, Lu Wu. [https://pubmed.ncbi.nlm.nih.gov/34257635/ A Fuzzy Radial Basis Adaptive Inference Network and Its Application to Time-Varying Signal Classification] . Comput Intell Neurosci, 2021 Jun 23;2021:5528291.

doi: 10.1155/2021/5528291.eCollection 2021.</ref>

In the next chapter we will be ready to undertake an equally fascinating path that will leads us to the context of a System Language logic and will allow us to deepen our knowledge no longer only in clinical semeiotics but in the understanding of system functions as recently it is approaching in neuromotor disciplines for Parkinson's disease.<ref>Mehrbakhsh Nilashi, Othman Ibrahim, Ali Ahani. [https://pubmed.ncbi.nlm.nih.gov/27686748/ Accuracy Improvement for Predicting Parkinson's Disease Progression.] Sci Rep. 2016 Sep 30;6:34181.

doi: 10.1038/srep34181.</ref> In Masticationpedia, of course, we will report the topic 'System Inference' in the field of the masticatory  system as we could read in the next chapter entitled 'System logic'.