Krishna’s Fuzzy Set Theory | Code – 679 | 7th Editon | 330 +Pages (Mathematics Book 2)

SYLLABUS- FUZZY SET THEORY, Fuzzy Sets: Basic definitions. a-level sets. Convex fuzzy sets. Basic operations on fuzzy

sets. Types of fuzzy sets. Cartesian products. Algebraic products. Bounded sum and

difference. t-norms and t-conorms.

The Extension Principle: The Zadeh’s extension principle. Image and inverse image of

fuzzy sets. Fuzzy numbers. Elements of fuzzy arithmetic.

Fuzzy Relations and Fuzzy Graphs: Fuzzy, relations on fuzzy sets. Composition of

fuzzy relations. Min-Max composition and its properties. Fuzzy equivalence relations.

Fuzzy compatibility relations. Fuzzy relation equations. Fuzzy graphs. Similarity relation.

Possibility Theory: Fuzzy measures. Evidence theory. Necessity measure. Possibility

measure. Possibility distribution. Possibility theory and fuzzy sets. Possibility theory

versus probability theory.

Fuzzy Logic: An overview of classical logic, Multivalued logics. Fuzzy propositions.

Fuzzy quantifiers. Linguistic variables and hedges. Inference from conditional fuzzy

propositions, the compositional rule of inference.

Approximate Reasoning: An overview of fuzzy expert system. Fuzzy implications and

their selection. Multi-conditional approximate reasoning. The role of fuzzy relation

equation.

An Introduction to Fuzzy Control: Fuzzy controllers. Fuzzy rule base. Fuzzy inference

engine. Fuzzification. Defuzzification and the various defuzzification methods (the

centre of area, the centre of maxima, and the mean of maxima methods).

Decision Making in Fuzzy Environment: Individual decision making. Multiperson

decision making. Multicriteria decision making. Multistage decision making. Fuzzy

ranking methods. Fuzzy linear programming.