The problem of embedding incomplete into complete relations has been an important topic of research in the context of crisp relations and their applications. Several variations of the acclaimed Szpilrajn’s theorem have been provided, inclusive of the case when some order conditions between elements are imposed on the extension. We extend the analysis of that topic by Alcantud to the fuzzy case....

We present a framework of L-fuzzy modifiers for L being a complete lattice. They are used to model linguistic hedges that act on linguistic terms represented by L-fuzzy sets. In the modelling process the context is taken into account by means of L-fuzzy relations, endowing the L-fuzzy modifiers with a clear inherent semantics. To our knowledge, these L-fuzzy modifiers are the first ones propose...

Equivalence relations and orderings are key concepts of mathematics. For both types of relations, formulations within the framework of fuzzy relations have been proposed already in the early days of fuzzy set theory. While similarity (indistinguishability) relations have turned out to be very useful tools, e.g. for the interpretation of fuzzy partitions and fuzzy controllers, the utilization of...

In decision making, consistency in fuzzy preference relations is associated with the study of transitivity property. While using additive consistency property to complete incomplete preference relations, the preference values found may lie outside the interval [0, 1] or the resultant relation may itself be inconsistent. This paper proposes a method that avoids inconsistency and completes an inc...

In this study, an outsourcer evaluation and management system is developed for a manufacturing company by use of Fuzzy goal programming (FGP). A first phase of the methodology evaluation criteria for outsources and the objectives of the company are determined. Considering the fuzziness in the decision data, linguistic variables that can be expressed in generalized fuzzy number are used. The pro...

Inspired by the idea of multiplicative intuitionistic preference relation (Xia MM et al. Preference relations based on intuitionistic multiplicative information, IEEE Transactions on Fuzzy Systems, 2013, 21(1): 113-133), in this paper, a new preference relation called the interval-valued multiplicative intuitionistic preference relation is developed. It is analyzed the basic operations for inte...

The purpose of this paper is to present a classiication method of alternatives for multiple preference ordering criteria based on the concept of fuzzy majority. The fuzzy majority is represented by a fuzzy quantiier, and applied in the aggregation by means of an OWA operator whose weights are calculated by the fuzzy quantiier. For every preference ordering criterion we derive a preference order...

We revisit the notion of fuzzy revealed preference, with the intention of using it in decision making. A decision making agent manages resources that are priced, and it has a certain wealth. We review proposed fuzzifications of preference relations. Although they are well founded, they cannot deal well with decision making under fuzzy constraints. We introduce the fuzzy budget set as a general ...