Synthesis of Analytic Models for Subtraction of Fuzzy Numbers with Various Membership Function’s Shapes

Real-Time Fuzzy Data Processing Based on a Computational Library of Analytic Models

“…These techniques for data analysis rely, for example, on the usage of such flexible soft computing components as (a) non-parametrized and parametrized operators of t-norm and s-norm [29], t-concepts [31], fuzzy signatures and signatures trees [32], vector quantization and fuzzy S-tree [33], (b) different fuzzy inference engines (Mamdani, Sugeno, etc. [13,29]), (c) as well as different fuzzy approaches for implementation of fuzzy arithmetic operations with fuzzy numbers (FNs), including FNs-minimum, FNs-maximum, FNs-subtraction, FNs-multiplication, FNs-division, and FNs-addition [29,30,[34][35][36][37][38][39].…”

“…Special attention should be paid to the formation of the resulting analytic models for fuzzy arithmetic because of their capacity to increase the accuracy and speed of the Big Data processing [30,34]. In some practical cases, it is possible to transform the big volume of information to corresponding fuzzy numbers [29,40] with further implementation of the resulting MFs for corresponding arithmetic operations with FNs.…”

“…One of the efficient approaches for the synthesis of the resulting MFs' analytic models is using  -cuts [29,34,41], in particular, for construction of the horizontal (inverse) and vertical (direct) models of the resulting membership functions. However, in some cases, the necessity to form such resulting models is time consuming and leads to the decrease in data processing speed and lower quality of the real-time control and decision-making processes [1,34,42,43].…”

“…One of the efficient approaches for the synthesis of the resulting MFs' analytic models is using  -cuts [29,34,41], in particular, for construction of the horizontal (inverse) and vertical (direct) models of the resulting membership functions. However, in some cases, the necessity to form such resulting models is time consuming and leads to the decrease in data processing speed and lower quality of the real-time control and decision-making processes [1,34,42,43]. Successful examples of fuzzy technique application for finding efficient solutions under uncertainty in various fields of human activity include automation of the different technological processes, optimization of transport routes and logistics planning, evaluation of the investment and perspective research project proposals, decision making in medical diagnostics and medical image retrieval, management of banking and finances, etc.…”

“…One of the efficient approaches for the synthesis of the resulting MFs' analytic models is using α-cuts [29,34,41], in particular, for construction of the horizontal (inverse) and vertical (direct) models of the resulting membership functions. However, in some cases, the necessity to form such resulting models is time consuming and leads to the decrease in data processing speed and lower quality of the real-time control and decision-making processes [1,34,42,43]. Another approach deals with usage of Zadeh's extension principle [29,[43][44][45] or algorithm of Max-Min convolution [30], which requires a transformation of each initial fuzzy set (involved in fuzzy data processing) to discrete form using a discreteness step ∆y = y max −y min K = const for determining y i+1 = y i + ∆y, (i = 0, 1, 2, .…”