In this paper we generalize some classical factorizations of a fuzzy relation into a symmetric component (indifference) and an asymmetric and regular component (regular fuzzy strict preference). From the above notions, we establish two properties of any regular fuzzy strict preference of a max-∗-transitive fuzzy relation, which are then used to obtain new fuzzy versions of Gibbard’s oligarchy t...

Looking at decisiveness as crucial, we discuss the existence of an order-preserving function for the nontotal crisp preference relation naturally associated to a nontotal fuzzy preference relation. We further present conditions for the existence of an upper semicontinuous order-preserving function for a fuzzy binary relation on a crisp topological space.

We study the transitivity of fuzzy preference relations, often considered as a fundamental property providing coherence to a decision process. We consider the transitivity of fuzzy relations w.r.t. conjunctors, a general class of binary operations on the unit interval encompassing the class of triangular norms usually considered for this purpose. Having fixed the transitivity of a large prefere...

This paper introduces a new approach to classification which combines pairwise decomposition techniques from machine learning with ideas and tools from fuzzy preference modeling. The approach, called fuzzy relational classification, effectively reduces the problem of classification to a problem of decision making based on a fuzzy preference relation. It will be shown that, by decomposing such a...

Intuitionistic fuzzy preference relation has turned out to be a powerful structure in representing the decision makers’ preference information especially when the decision makers are not able to express their preferences accurately due to the unquantifiable information, incomplete information, unobtainable information, partial ignorance, and so forth. The aim of this paper is to develop some te...

In fuzzy decision problems, the ordering of fuzzy numbers is the basic problem. The fuzzy preference relation is the reasonable representation of preference relations by a fuzzy membership function. This paper studies Nakamura’s and Kołodziejczyk’s preference relations. Eight cases, each representing different levels of overlap between two triangular fuzzy numbers are considered. We analyze the...

Intuitionistic fuzzy sets theory which is the generalisation of fuzzy sets theory is more suitable tool for dealing with imprecise information. The information provided by the decision maker is imprecise in many situations. So, intuitionistic fuzzy preference relation is a suitable tool for such cases. The estimation of the priority vector of the intuitionistic fuzzy preference relation is an i...

We generalize the solution of a multicriterial optimization problem which has been given in [5]. They have used a comparison of the criterion fuzzy preference relations and the general fuzzy preference relation. Based on this comparison they have constructed the ordering of criteria. Our modification builds on pairwise similarity of criterion related fuzzy preference relations. We illustrate ou...

This paper investigates the multiple attribute decision making problem with preference information on alternatives, in which multiple decision makers give their preference information in three forms, i.e., preference orderings, utility values and fuzzy preference relation. A new approach is presented to make use of both the decision makers' social fuzzy preference relation on alternatives and d...

The aim of this paper is to propose a procedure to estimate missing preference values when dealing with incomplete fuzzy linguistic preference relations assessed using a 2–tuple fuzzy linguistic approach. This procedure attempts to estimate the missing information in an individual incomplete fuzzy linguistic preference relation using only the preference values provided by the respective expert....