Proof-of-Concept: Creating "Fuzzy" Sorting Algorithms

Sorting algorithms are common tools for manipulating data and used in both standalone circumstances and within larger more complex algorithms. Thus, it is highly desirable for sorting algorithms to be efficient in terms of storage and computation. By applying the concept of fuzzy logic (an abstract version of Boolean logic) to any well-known algorithm, it generates an abstract version (i.e., fuzzy algorithm) that often results in computational improvements. Although the algorithm may produce a less precise result, this is counteracted by gaining computational efficiency with minimal acceptable trade-offs (e.g., small increase in space requirements, loss of precision). Using an established three-step framework for fuzzification of an algorithm, the resulting new fuzzy algorithm goes beyond a simple conversion of data from raw to fuzzy data by converting the operators and concepts within the algorithm to their abstract equivalents. The purpose of this paper is to demonstrate, as a proof-of-concept, that sorting algorithms can be converted into their corresponding fuzzy sorting algorithms. This paper discusses the preliminary results of: (1) how to apply the general framework by developing the corresponding fuzzy algorithms for a variety of sort algorithms, (2) the success of applying the framework through the development of several fuzzy sort algorithms including fuzzy shell sort, fuzzy strand sort, and fuzzy bucket sort, and (3) the possible applications and benefits of these fuzzy sort algorithms.