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 ?
The concept of intuitionistic fuzzy set was introduced are studied by Atanassov [1] and many works by the same author and his colleagues appeared in the literature [[2],[3],[4]].
Intuitionistic fuzzy C-means (IFCM) algorithm, as a successful extension and variant of FCM, has attracted extensive attention and has been widely used in many fields such as image processing and pattern recognition [8].
This paper presents new axiomatic definitions of entropy measure using concept of probability and distance for interval-valued intuitionistic fuzzy sets (IvIFSs) by considering degree of hesitancy which is consistent with the definition of entropy given by De Luca and Termini.
Atanassov [1] extends the fuzzy set characterized by a membership function to the intuitionistic fuzzy set (IFS), which is characterized by a membership function, a non-membership function, and a hesitancy function.
An intuitionistic fuzzy set offers a better way to deal with uncertain multi-attribute problems (Mehlawat & Grover, 2018; Rodriguez, Ortega, & Concepcion, 2017; Ren, Xu, & Wang, 2017; Khemiri, Elbedouimaktouf, Grabot, & Zouari, 2017; Ye, 2017).
To this end, an extension of CODAS (Combinative Distance-based Assessment) method with Interval-Valued Intuitionistic Fuzzy Sets (IVIF) is designed and the CODAS-IVIF procedure is provided.
By including a fuzzy set the degree of nonmembership, Atanassov [6] in 1986 suggested the intuitionistic fuzzy set (IFS), which seems more precise for provides opportunities and uncertainty quantification to accurately model a problem based on existing knowledge and monitoring.
Szmidt [12] and Vlachos [13] introduced some entropy measures for intuitionistic fuzzy sets (IFSs) and discussed their applications in pattern recognition.
Therefore, this paper focuses on a dynamic multiattribute decision-making method with interval-valued triangular fuzzy number intuitionistic fuzzy that considers interaction between attributes.
Among them, some similarity measures of intuitionistic fuzzy sets (IFSs) have been proposed.
Since Atanassov (1986) proposed the concept of intuitionistic fuzziness, it has been widely used in pattern recognition, market forecasting, etc.
The concepts of fuzzy sets [8] and intuitionistic fuzzy set [6] were generalized by adding an independent indeterminacy-membership.