کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
397033 | 1438459 | 2014 | 17 صفحه PDF | دانلود رایگان |
• Proposed a new concept of imaginary extreme numbers.
• Resolved the division-by-zero problem in sweeping and Gaussian elimination operations.
• Applied imaginary numbers to representing linear models in knowledge-based systems.
• Established a new method for solving linear equations via combining belief functions.
• Reduced exponential complexity into polynomial-time for linear models-based inferences.
This paper proposes the concept of imaginary extreme numbers, which are like traditional imaginary number a+bia+bi with i=−1 being replaced by e=1/0e=1/0, along with the usual operations on these numbers including addition, subtraction, and division. It then applies the concept to representing linear equations in knowledge-based systems. It proves that the combination of linear equations via Dempsterʼs rule is equivalent to solving a system of simultaneous equations or finding a least-squares estimate when they are overdetermined.
Journal: International Journal of Approximate Reasoning - Volume 55, Issue 1, Part 3, January 2014, Pages 294–310