In the social decision making context, a manipulator attempts to change the social choice in his favor by misrepresenting his preferences. Gibbard and Satterthwaite [7,10] established independently that a strategic manipulation can be observed when using any non-dictatorial voting choice procedure. In this paper, we are interested in the manipulation of the social choice when individuals reveal...

The notion of fuzzy function based on many-valued equivalence relations (many-valued similarity relations (equalities) [17, 18, 19], fuzzy equivalence relations [4, 6, 7, 21, 22, 26], similarity relations [1, 2, 3, 15, 28], indistinguishability operators [27], etc.) has been introduced by several authors, and applied to category theory [5], approximate reasoning and fuzzy control theory [8, 10,...

A T-fuzzy equivalence relation is a fuzzy binary relation on a set X which is reflexive, symmetric and T-transitive for a t-norm T. Recently, Mesiar et al. [R. Mesiar, B. Reusch, H. Thiele, Fuzzy equivalence relations and fuzzy partitions, J. Multi-Valued Logic Soft Comput. 12 (2006) 167–181] have generalised the t-norm T to any general conjunctor C and investigated the minimal assumptions requ...

the concept of  -semihypergroups is a generalization of semigroups, a generalization of semihypergroups and a generalization of  -semigroups. in this paper, we study the concept of semiprime ideals in a  -semihypergroup and prove some results. also, we introduce the notion of  -hypergroups and closed  -subhypergroups. finally, we study the concept of  -semihypergroups associated to binary...

we study the problem of reconstructing binary images from four projections data in a fuzzy environment. given the uncertainly projections,w e want to find a binary image that respects as best as possible these projections. we provide an iterative algorithm based on fuzzy integer programming and linear membership functions.

Fuzzy relation equations (FRE) are associated with the composition of binary fuzzy relations. In the present work FRE are used as a tool for studying the process of learning a new subject matter by a student class. A classroom application and other suitable examples connected to the student learning of the derivative are also presented illustrating our results and useful conclusions are obtained.

This paper introduces a new approach to classification which combines pairwise decomposition techniques with ideas and tools from fuzzy preference modeling. More specifically, our approach first decomposes a polychotomous classification problem involving m classes into an ensemble of binary problems, one for each ordered pair of classes. The corresponding classifiers are trained on the relevant...

Rough set theory is a suitable tool for dealing with the imprecision, uncertainty, incompleteness, and vagueness of knowledge. In this paper, new lower and upper approximation operators for generalized fuzzy rough sets are constructed, and their definitions are expanded to the interval-valued environment. Furthermore, the properties of this type of rough sets are analyzed. These operators are s...

Classical classification and clustering based on equivalence relations are very important tools in decision-making. An equivalence relation is usually determined by properties of objects in a given domain. When making decision, anything that can be spoken about in the subject position of a natural sentence is an object, properties of which are fundamental elements of the knowledge of the given ...

FCA is a mathematical formalism having many applications in data mining and knowledge discovery. Originally it deals with binary data tables. However, there is a number of extensions that enrich standard FCA. In this paper we consider two important extensions: fuzzy FCA and pattern structures, and discuss the relation between them. In particular we introduce a scaling procedure that enables rep...