involutive negation
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Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2389
Author(s):  
Ildar Z. Batyrshin

A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently the class of pd-independent linear negators has been introduced and characterized using Yager’s negator. The open problem was how to introduce involutive negators generating involutive negations of pd. To solve this problem, we extend the concepts of contracting and involutive negations studied in fuzzy logic on probability distributions. First, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. Then, we show that any pd-independent negator is non-involutive, and any non-trivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pd-dependent negators. It generates an involutive negation of probability distributions.


2021 ◽  
Vol 405 ◽  
pp. 88-105
Author(s):  
Nicolás Madrid ◽  
Manuel Ojeda-Aciego
Keyword(s):  

2010 ◽  
Vol 161 (3) ◽  
pp. 390-411 ◽  
Author(s):  
Petr Cintula ◽  
Erich Peter Klement ◽  
Radko Mesiar ◽  
Mirko Navara

2006 ◽  
Vol 157 (24) ◽  
pp. 3125-3144 ◽  
Author(s):  
Tommaso Flaminio ◽  
Enrico Marchioni
Keyword(s):  

2006 ◽  
Vol 52 (3) ◽  
pp. 269-282 ◽  
Author(s):  
Petr Cintula ◽  
Erich Peter Klement ◽  
Radko Mesiar ◽  
Mirko Navara

2000 ◽  
Vol 39 (2) ◽  
pp. 103-124 ◽  
Author(s):  
Francesc Esteva ◽  
Lluís Godo ◽  
Petr Hájek ◽  
Mirko Navara

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