intuitionistic logic

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intuitionistic logic

(logic, mathematics)
Brouwer's foundational theory of mathematics which says that you should not count a proof of (There exists x such that P(x)) valid unless the proof actually gives a method of constructing such an x. Similarly, a proof of (A or B) is valid only if it actually exhibits either a proof of A or a proof of B.

In intuitionism, you cannot in general assert the statement (A or not-A) (the principle of the excluded middle); (A or not-A) is not proven unless you have a proof of A or a proof of not-A. If A happens to be undecidable in your system (some things certainly will be), then there will be no proof of (A or not-A).

This is pretty annoying; some kinds of perfectly healthy-looking examples of proof by contradiction just stop working. Of course, excluded middle is a theorem of classical logic (i.e. non-intuitionistic logic).

History.
References in periodicals archive ?
Yildiz: Fixed points in intuitionistic fuzzy metric spaces, Chaos Solitons Fractals, 29(2006), 1073-1078.
Here, we propose an intuitionistic fuzzy regression model and its general form in triangular intuitionistic fuzzy setup is given by
Such uncertainties are usually handled with the help of the topics like probability, fuzzy sets [1], intuitionistic fuzzy sets [2], interval mathematics, rough sets etc.
The concepts of fuzzy sets [8] and intuitionistic fuzzy set [6] were generalized by adding an independent indeterminacy-membership.
In this image fusion method Anathi and Balasubramaiam [2] proposed a novel way to fuse several images using interval-valued intuitionistic fuzzy sets (IVIFSs).
There are some of the authors that being used OWA as aggregation operators such that Xu [29] developed the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator, and the intuitionistic fuzzy hybrid averaging (IFHA) operator.
Their topics include interval-valued intuitionist fuzzy multi-attribute decision making based on satisfactory degree, intuitionistic fuzzy set theory with fair share central processing unit scheduler: a dynamic approach, credibility hypothesis testing of variance of fuzzy normal distribution, appraising the economic values of a logistic handling system under mixed information, and predicting solar and wind energies by fuzzy logic control.
Now a new decision making model based on intuitionistic fuzzy set is introduced.
This paper proposes Multi-Attribute Intuitionistic Fuzzy Group Decision Method (MAIFGDM) using TOPSIS for the selection of the suitable candidate network.
Li (2013) extended AD principles in intuitionistic fuzzy environment for selection of the best knowledge map designs.
Despite controversial nature of fuzzy sets, Atanassov, introduced Intuitionistic fuzzy set [2] which proved to be extremely handy and applicable.