Intuitionistic Fuzzy Logic Based Uncertainty Handling of Industrial Grinding Process

Virivinti, Nagajyothi (2017) Intuitionistic Fuzzy Logic Based Uncertainty Handling of Industrial Grinding Process. PhD thesis, Indian Institute of Technology Hyderabad.

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Abstract

Uncertainty in parameters, which are assumed to be known and do not change their values during the course of deterministic optimization, can have a great impact on the outcome of an optimization study (e.g. uncertainty in param eters A, b and c while solving min c x, subject to Ax ≤ b). Investigations on the development and application of optimization approaches that can accommodate such kind of uncertainty in parameters during the course of optimization are, therefore, necessitated. One of the approaches to solve s uch optimization under uncertainty problems (OUU) is to convert the problem into its equivalent deterministic optimization problem (EDOP) and thereafter solve that by well - developed optimization techniques. In this work, assuming the distribution informati on about the uncertain parameters is not available, which is generally difficult to obtain, fuzzy credibility theory based approaches [Fuzzy Expected Value Model (FEVM), Fuzzy Chance Constrained Programming (FCCP) and Fuzzy Robust Optimization (FRO)] are u tilized to serve the aforementioned conversion. To overcome the drawback of fuzzy set theory being not self - dual, generalizations have been performed in terms of intuitionistic fuzzy sets and the fuzzy based approaches (FEVM, FCCP, FRO) have been extended to their intuitionistic fuzzy counterparts i.e. intuitionistic fuzzy based EVM, CCP and RO. Next, an industrial grinding model has been adapted to handle several uncertain parameters, operational as well as model related, and shown how the presence of unce rtainty changes the optimal solutions (compared to the purely deterministic case) and leads to an operating zone of varied risk appetite of a decision maker by defining the entire frontier of the uncertain solution region. The deterministic multi - objective optimization model has been taken from the published work (Mitra and Gopinath, 2004) on which several modifications due to uncertainty in the parameters are carried out. A comparative analysis among these fuzzy approaches is also performed. Unlike two - sta ge stochastic programming (TSSP) approach, a very popular approach to handle uncertainty during optimization, the generic fuzzy and intuitionistic fuzzy approaches do not give rise to the situation of unmanageable explosion in problem size with the increas e in number of uncertain parameters.

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