Decision fusion using fuzzy logic

Fuzzy logic based systems are known for performing tasks to certain predefined precision level. These kinds of systems perform approximate reasoning in similar fashion as we do. The accuracy of reasoning process mainly depends upon the rules defined by designer of relevant domain. In the past few decades, Fuzzy logic (FL) based techniques have been used in varieties of applications such as i) imageanalysis - detection of edges, feature extraction, classification, and clustering, ii) parameter estimation of unknown dynamic systems – aircraft, iii) home appliances – washing machine, air conditioning systems, and iv) decision fusion – situation and threat assessment. Each and every ingredient, e.g. membership functions, rule base, implication methods, aggregation and de-fuzzification methods etc, of Fuzzy logic that helps in developing such applications plays a very crucial role towards the success of final product. In this thesis, FL concepts, fuzzy sets and their properties, FL operators, hedges, fuzzy proposition and rule-based systems, fuzzy maps and inference engine, and defuzzification methods are investigated. The relationships, interconnectivities and contradistinction between various operations/operators, using numerical simulations and examples are also brought out. Some efforts have been made to incorporate Fuzzy logic in estimation theory to estimate the unknown states of a dynamic system by processing the sensor data having uncertainties due to measurement noise. The algorithms are developed by considering the combination of Fuzzy logic and KF that have traditionally been considered to be radically different. The former is considered heuristic and the latter as statistical filtering. Two schemes such as KF and Fuzzy Kalman filter (FKF) are applied for target tracking application and their performances evaluated. Also the concept of Fuzzy logic is extended to state level data fusion for similar sensors. The performances of Fuzzy logic based fusion methods are compared with conventional fusion method that is state vector fusion (SVF) to track manoeuvring target. An attempt has been made to extend the Fuzzy logic concepts in decision fusion where the main objective of decision fusion is to take final course of action in entire surveillance volume at any instant of time using outputs from different levels, e.g. level 1 – object refinement and level 2 – situation refinement, of Multi Sensor Data Fusion (MSDF) system. The accuracy of outputs from decision fusion depends not only on the architectures/algorithms involved in it but also on the different fusion levels. Towards the development of decision fusion based expert systems, various levels of MSDF system and methods available for implementing expert systems are studied. This thesis covers a few examples of developing decision making systems as an aid to the pilots of fighter aircraft engaged in air combat situations such as: airto- air attack, air-to-ground or ground-to-air attacks, etc. It is well known that the core part of any FL based system is Fuzzy inference engine where the rules are processed using Fuzzy implication methods to get output Fuzzy sets. It will not be wrong to say that the implication method plays a critical role to get the desired response from the system. Hence, it becomes necessary to select an appropriate implication method from the existing methods. However, if any new implication method is found then it should satisfy some of the intuitive criteria of Generalized Modus Ponens and Generalized Modus Tollens so that it can be fitted into the process of system development using FL. In this thesis, a procedure/methodology that helps to find out that any of the existing implication methods matches with given set of intuitive criteria of GMP and GMT is developed. In order to realize the scheme, MATLAB® and graphics are used to develop a user interactive package to evaluate the implication methods w.r. t. these criteria. Some new fuzzy implication functons are also proposed and evaluated using the MATLAB/GUI tool developed in this thesis.