A WABL-Based Two-Dimensional Representative of Fuzzy Numbers

Defuzzificationmethods have an important place in fuzzy logic and fuzzy set theory. Normally,the defuzzified value of a fuzzy number gives the average numerical equivalentof this number. However, the WABL operator, which is a more universaldefuzzification operator, carries more information within itself. In thisstudy, the defuzzified value of the fuzzy number is discussed within theframework of a two-dimensional plane and new concepts of WABL AreaRepresentative (WABL_AR) and Area Center of Gravity (ACOG) are proposed forfuzzy numbers. The properties of these concepts have been examinedtheoretically and suitable theorems for triangular fuzzy numbers have beenproven. A numerical example is given for calculating the ACOG.</p

Determination of the Location Valuation Index based on Public Transportation in Big Cities

Inthe countries’ economy, the housing acquisition and rental market has animportant economic role. On the other hand, housing prices change quite rapidlydue to effects such as inflation and earthquakes. Due to these rapid changes,it becomes difficult to stabilize and objectively evaluate housing prices. Inevaluating houses, in addition to the characteristics of the house itself, thelocation where this house is located also has an important effect.In this study, the Location Valuation Index (LVI)was created to evaluate any location based on the ease of transportation fromthis location to other points of the city based on public transportationnetwork. For this purpose, cost values ​​between stops were used. The proposedmodel was run on data from İzmir, Turkey’s third largest city, and a map of LVIvalues ​​of the city was created.</p

Communications in Computer and Information Science

Defuzzification methods have an important place in fuzzy logic and fuzzy set theory. There are various defuzzification methods in the literature, such as Center of Gravity (COG), Mean of the Maxima (MOM), Bisector of Area (BOA), Weighted Average Based on Levels (WABL), etc. Normally, the defuzzified value of a fuzzy number gives the average numerical representative of this fuzzy number according to the membership degrees of components. However, the WABL operator, which is a more universal defuzzification operator, carries more information within itself. In this study, the defuzzified value of the fuzzy number is discussed within the framework of a two-dimensional plane. This approach includes information about the defuzzified numerical representative as well as the quality of this representative. New concepts of WABL Area Representative (WABL_AR) and Area Center of Gravity (ACOG) are proposed for fuzzy numbers. The properties of these concepts have been examined theoretically and suitable theorems for triangular fuzzy numbers have been proven. A numerical example is given for calculating the WABL_AR and ACOG values.</p