Comparison of Defuzzification Operators on Geographic Data of Ratio Scale

Fuzzy logic is a contemporary theory that has found numerous applications in Geographic Information Systems (GIS). Fuzzy logic allows for the representation of uncertainty and imprecision in spatial data, making it a valuable tool for dealing with the inherent ambiguity present in many geographic datasets. To solve a problem using a knowledge-based fuzzy system, the description and processing of the influencing factors or variables in fuzzy terms is required. The key components of a knowledge-based fuzzy system within the context of GIS are: Fuzzification, definition of the knowledge base, processing of the rules and finally defuzzification. Defuzzification is an important aspect of fuzzy logic and fuzzy set theory, as it helps convert fuzzy linguistic terms or fuzzy sets into crisp values that can be used in decision-making or analysis. Moreover, this might seem contradictory to the primary objective of fuzzy set theory, which is to model and work with uncertainty and imprecision. The aim of this paper is, first, to review defuzzification operators that are suitable for handling geographic data of ratio scale and second to compare these defuzzification operators by applying them to actual geographic data sets. For this reason, a case study based on pollution data of the municipality of Athens, Greece, was carried out to estimate pollution produced by SO2. The results of the application of defuzzification operators for the above geographic data set are compared and final conclusions are presented.

On Methodology of Fuzzy Systems

Fuzziness is one of the general characteristics of human thinking and objective things.Fuzzy systems are efficient tools to simulate human thinking and execute fuzzy information processing. This paper discusses several fundamental problems on methodology of fuzzy systems briefly,including generalized fuzzy entropy, generalized defuzzification strategies and fuzzy consistent relation.

Electrical Load Forecasting Using Fuzzy System

To cope with the demand and supply of electrical load of an interconnected power system of a country, we need to forecast its demand in advance. In this paper, we use a fuzzy system to forecast electrical load on short-term basis. Here, we consider temperature, humidity, seasons of a year and time segments of a day as the parameters, which govern the demand of electrical load. For each of the parameter, we use several membership functions (MFs) and then apply the Mamdani rule on MFs and the output is determined by using the centroid method. Finally, the surface plot reveals the real scenario of the load demand. The difference between actual load and the output of the fuzzy system is found as +1.65% to -13.76%. The concept of the paper can be applied in interconnected power system of Bangladesh to reduce power loss, especially when generation is higher than the demand.

New Decision-Making Technique Based on Hurwicz Criteria for Fuzzy Ranking

Efficient decision-making remains an open challenge in the research community,and many researchers are working to improve accuracy through the use of various computational techniques.In this case,the fuzzification and defuzzification processes can be very useful.Defuzzification is an effective process to get a single number from the output of a fuzzy set.Considering defuzzification as a center point of this research paper,to analyze and understand the effect of different types of vehicles according to their performance.In this paper,the multi-criteria decision-making(MCDM)process under uncertainty and defuzzification is discussed by using the center of the area(COA)or centroidmethod.Further,to find the best solution,Hurwicz criteria are used on the defuzzified data.Anewdecision-making technique is proposed using Hurwicz criteria for triangular and trapezoidal fuzzy numbers.The proposed technique considers all types of decision makers’perspectives such as optimistic,neutral,and pessimistic which is crucial in solving decisionmaking problems.A simple case study is used to demonstrate and discuss the Centroid Method and Hurwicz Criteria for measuring risk attitudes among decision-makers.The significance of the proposed defuzzification method is demonstrated by comparing it to previous defuzzification procedures with its application.

A Similarity Based Fuzzy System as a Function Approximator

In this paper, an attempt is made to prove that some similarity based fuzzy systems can be found to behave as function approximators. A typical similarity based fuzzy system is proposed and its behaviour is shown to have the said property. It elucidates the connection between similarity relation and similarity measure of fuzzy sets to fuzzy inference methodology. The concept of similarity relation is used in fuzzification of crisp input values. Similarity index is used in measuring approximate equality of fuzzy sets over a given universe of discourse of a linguistic variable. The similarity between the observation(s) and the antecedent of a rule is used in selecting rule(s) for possible firing and also in modifying the relation between the antecedent and consequent of the rule based on the specific observation. Inference is drawn through the usual composition and subsequently by projecting the modified fuzzy restriction acting on the variables of interest on the universe of the linguistic variable in the consequent of the rule. A specificity based defuzzification scheme is proposed for multiple-rule firing. It has been proved systematically that such a similarity based fuzzy system can uniformly approximate continuous functions to any desired degree of accuracy on a closed and bounded interval. Simulation results are presented for the well-known dc-motor problem. A comparative study is made to establish the validity and efficiency of the proposed similarity based fuzzy system.

The Use of Fuzzy Logic in Predicting Percentage (%) Dilution of Weld during Tig Welding Process

Welding operation of metals, gives rise to high temperature that results in melting of mating parts. The final composition of the joints formed in terms of its microstructure and properties at the fusion zone depends greatly on the degree of dilution of the weld. With an expert prediction technique, it may be possible to predict even before weld, the integrity of weld joint from the proposed process parameter. The aim of this study is to predict the percentage dilution (%D) of TIG mild steel welds using fuzzy logic. In this study, the weld specimen was produced using the TIG welding process guided by the central composite experimental design and thereafter percentage dilution (%D) was measured and fed to the fuzzy logic software. The process parameters include the voltage, current, gas flow rate and welding speed. The results obtained showed that the fuzzy logic tool is a good predictive tool and the model developed has proven to be very efficient in handling works of this nature, thereby saving time, energy and money wasted in pre-welding procedures. It would be encouraging to compare other quality parameters with process parameters to see how it can further help in quality improvement.

A Modification to the Fuzzy Regression Discontinuity Model to Settings with Fuzzy Variables

Despite the fact that fuzzy regression discontinuity designs are growing in popularity, a lot of research takes into account treatment non-compliance difficulties, specifically the fuzziness of the treatment impact. This paper took into account independent and dependent fuzzy factors when creating these designs. Additionally we took into account treatment non-compliance difficulties, specifically the fuzziness of the treatment impact, as other research does. The modified Fuzzy Regression Discontinuity model is preferable for modeling fuzzy data. It enables us to draw improved causal effects accommodating fuzzy variables, not just the fuzziness of the treatment effect as in Fuzzy Regression Discontinuity models. A fuzzy dataset is converted into crisp data by the Centroid method of defuzzification. Once the data is crisp, the traditional least squares methods of approximation are used to estimate the parameters in the model since these parameters are considered crisp whilst the error terms are fuzzy. The Alcohol Use Disorders Identification Test score(AUDIT score) can be used as a cutoff to initiate treatment in this case and can be used to predict the progression of HIV disease and/or AIDS. Counseling helps to lower the use of alcohol in people living with HIV/AIDS (PLWHA) as a result, improving the participants’ CD4 counts.