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Issue:Intuitionistic fuzzy interpretations of Conway's game of life. Part 2: Modal and extended modal transformations of the game field

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Title of paper: Intuitionistic fuzzy interpretations of Conway's game of life. Part 2: Modal and extended modal transformations of the game field
Author(s):
Lilija Atanassova
Institute of Information Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 2, Sofia-1113, Bulgaria
l.c.atanassova@gmail.com
Krassimir Atanassov
CLBME, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Bl. 105, Sofia-1113, Bulgaria
krat@bas.bg
Presented at: 11th IWGN, Sofia, 5 December 2010
Published in: Conference proceedings, pages 83—88
Download: Download-icon.png PDF (163  Kb, Info)
Abstract: Intuitionistic fuzzy sets (IFSs) are an extension of Zadeh's fuzzy sets, which introduce a degree of membership and a degree of non-membership whose sum is equal to or less than 1 and the complement to 1 is called a degree of uncertainty. Conway's Game of Life is a popular heuristic zero-player game, devised by John Horton Conway in 1970. Its "universe" is an infinite two-dimensional orthogonal grid of square cells, each of which is in one of two possible states, alive or dead. Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. In a stepwise manner, the state of each cell in the grid preserves or alternates with respect to a given list of rules.

In a previous authors' research, for each cell its IF estimation was defined as a pair consisting of the degrees lp and la, namely degrees of presence and absence of life, where lp + la ≤ 1.

The article proposes intuitionistic fuzzy approaches to modifying of the Game of Life cells' states. These approaches are based on the IF modal and extended modal operators.

Keywords: Conway's Game of Life, Intuitionistic fuzzy sets.
References:
  1. http://en.wikipedia.org/wiki/Conway's_Game_of_Life
  2. Atanassov K. Intuitionistic Fuzzy Sets, Heidelberg, Springer, 1999.
  3. Atanassov K., L. Atanassova, A game method for modelling. Third International School "Automation and Scientific Innstrumentation" (Ed. L. Antonov) Varna, 1984, 229-232.
  4. Atanassov K., On a combinatorial game-method for modelling, Advances in Modelling & Analysis, AMSE Press, Vol. 19, 1994, No. 2, 41-47.
  5. Atanassov K., Atanassova L., Sasselov D., On the combinatorial game-method for modelling in astronomy, Comptes Rendus de l'Academie bulgare des Sciences, Tome 47, 1994, No. 9, 5-7.
  6. Atanassova, L., K. Atanassov. Intuitionistic fuzzy interpretations of Conway's game of life. Part 1. Lecture Notes in Computer Science, No. 6046, Springer, 2011 (in press).
  7. Feys, R., Modal logics, Gauthier, Paris, 1965.
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