论文信息 - Constructing Examples of Fuzzy Implications within the Mizar Mathematical Library

Constructing Examples of Fuzzy Implications within the Mizar Mathematical Library

The aim of our work is to show, by means of the Mizar system, how we can cope with the formalization of fundamental properties of fuzzy implications; we construct basic nine examples of these operators. This is the continuation of the formal approach to fuzzy sets within the Mizar Mathematical Library, with fuzzy numbers, fuzzy relations, triangular norms and conorms as building blocks of the theory.

Adam Grabowski

[1] Adam Naumowicz,et al. Mizar: State-of-the-art and Beyond , 2015, CICM.

[2] Jesse Alama,et al. Tarski Geometry Axioms , 2014, Formaliz. Math..

[3] Didier Dubois,et al. Fuzzy sets and systems ' . Theory and applications , 2007 .

[4] Adam Grabowski. Formal Introduction to Fuzzy Implications , 2017, Formaliz. Math..

[5] Philippe Smets,et al. Implication in fuzzy logic , 1987, Int. J. Approx. Reason..

[6] Adam Naumowicz,et al. The Role of the Mizar Mathematical Library for Interactive Proof Development in Mizar , 2017, Journal of Automated Reasoning.

[7] Adam Grabowski,et al. Extending Formal Fuzzy Sets with Triangular Norms and Conorms , 2017, EUSFLAT/IWIFSGN.

[8] Adam Grabowski,et al. Initial Comparison of Formal Approaches to Fuzzy and Rough Sets , 2015, ICAISC.

[9] Adam Grabowski. Fundamental Properties of Fuzzy Implications , 2018, Formaliz. Math..

[10] Adam Grabowski,et al. Basic Formal Properties of Triangular Norms and Conorms , 2017, Formaliz. Math..

[11] Adam Naumowicz,et al. Four Decades of Mizar , 2015, Journal of Automated Reasoning.

[12] Takashi Mitsuishi. The Concept of Fuzzy Set and Membership Function and Basic Properties of Fuzzy Set Operation , 2004 .

[13] Robert LIN,et al. NOTE ON FUZZY SETS , 2014 .

[14] Adam Grabowski,et al. On the computer certification of fuzzy numbers , 2013, 2013 Federated Conference on Computer Science and Information Systems.