Fuzzy Portfolio Diversification with Ordered Fuzzy Numbers

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

“…as compressed fuzzy sets (fuzzy numbers) using aggregation algorithms for different data streams [29,46,47]. It is possible to use a four-step algorithm for "Big Data-fuzzy data" processing of such random streams or consequences using the proposed computational library: (a) Each random stream or consequence of Big Data can be transformed into the compressed fuzzy set (fuzzy number) [1,29,40]. Examples of such random sequences' transformations are presented in References [29,40], where TrFNs "between nine and eleven" and "approximately ten" [29], as well as ordered fuzzy numbers and ordered fuzzy candlesticks [40] This approach for synthesis of the computational library of resulting analytic models for fuzzy maximum of the TrFNs is based on the analysis of the intersection points for the left and right branches of the TRFNs and can be successfully applied for the data processing of fuzzy sets with diverse forms and shapes of the membership functions (Gaussian, bell-shape, exponential, trapezoidal, and others) by construction of the corresponding computational libraries.…”

“…The simulation results confirm the universality and efficiency of the proposed computational library of the horizontal and vertical analytic models for diverse practical applications. The computation library application can be recommended for fuzzy data processing in solving different control and decision-making problems, for example, for choosing the optimal model of the "university-industry" cooperation [48], selection of partners in business, education, sport or culture exchange [49][50][51], route planning and optimization in uncertainty [52][53][54], portfolio selection [40], evaluation of the qualification level of the specialists, control of robots in dynamic environment [55,56], control of industrial processes [13,57] with multi-sensor data processing, and others. Application of the developed computational library (29)-(52) is limited to the usage of the triangular form of FNs.…”

“…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.…”

“…): C = (8,20,25), D = (5,10,40) (53)Data 2018, 3, 59 12 of 19 where parameters of the TrFNs are: c 1 = 8; d 1 = 5; c 0 = 20; d 0 = 10; c 2 = 25; d 2 = 40.…”