Fuzzy Preference Modelling and Multicriteria Decision Support

Frontmatter

Chapter 1. Fuzzy logical connectives

Abstract

In order to be able to work with valued concepts (especially, relations in subsequent chapters) we provide a rather complete and up to date survey of connectives used in fuzzy set theory. This approach to the foundations is only one possible way (for others see Höhle and Stout (1991)).

János Fodor, Marc Roubens

Chapter 2. Valued binary relations

Abstract

Binary relations play a central role in various fields of mathematics. Especially, equivalence relations and different kinds of ordering relations are employed in basic mathematical models. Typical areas are decision making and measurement theory. In addition, applications of binary relations appear naturally in social sciences.

János Fodor, Marc Roubens

Chapter 3. Valued preference modelling

Abstract

Preference modelling is a fundamental part of several applied fields but at the same time it has its own interesting theoretical problems. Our aim in this chapter is to propose an axiomatic approach to the definition of valued strict preference, indifference and incomparability associated with a valued (weak) preference relation so that most of the relationships (corresponding to the classical connections) among these valued relations are preserved.

János Fodor, Marc Roubens

Chapter 4. Similarity relations and valued orders

Abstract

In the classical theory of binary relations probably the two most important and most frequently applied classes consist of equivalence relations (with associated partitions) and different kinds of orders.

János Fodor, Marc Roubens

Chapter 5. Aggregation operations

Abstract

We consider m valued relations R ₁,..., R _m , 0 ≤ R _i ≤ 1, and we are willing to substitute to the vector (R ₁,..., R _m ) one simple valued relation R using the aggregation operator M :

$$\bigcup\limits_{m = 1}^\infty {{{\left[ {0,1} \right]}^m}} \to \left[ {0,1} \right]suchthat0R = M\left( {{R_{1,}} \ldots ,{R_m}} \right)1$$

.

János Fodor, Marc Roubens

Chapter 6. Ranking procedures

Abstract

The problem of ranking deals with the definition of a preorder on a finite set of alternatives A based on a given valued preference relation R: A ² → [0,1].

János Fodor, Marc Roubens

Chapter 7. Multiple criteria decision making

Abstract

In this Chapter, we imagine a decision maker (or a group of experts) trying to establish or examine fair procedures to combine opinions about alternatives related to different points of view.

János Fodor, Marc Roubens

Chapter 8. Summary, perspectives and open problems

Abstract

In this chapter we reformulate some results included in the book from a more practical point of view. This may help non-specialists to catch the main points and go into details (if they need any) in the corresponding Sections. Some unsolved theoretical problems are also presented.

János Fodor, Marc Roubens

Backmatter