The aim of this thesis is to develop the fuzzy relational calculus. To develop this calculus, we study four algebraic formalisations of fuzzy relations which are called fuzzy relation algebras, Zadeh categories, relation algebras and Dedekind categories, and we strive to arrive at their representation theorems. The calculus of relations has been investigated since the middle of the nineteenth c...

We present empirical measures of wealth inequality and its intergenerational transmission among four horticulturalist populations. Wealth is construed broadly as embodied somatic and neural capital, including body size, fertility and cultural knowledge, material capital such as land and household wealth, and relational capital in the form of coalitional support and field labor. Wealth inequalit...

In most statistical analysis, inequality or extent of variation in income isrepresented in terms of certain summary measures. But some authors arguedthat the concept of inequality is vague and thus cannot be measured as anexact concept. Therefore, fuzzy set theory provides naturally a useful toolfor such circumstances. In this paper we have introduced a real-valued fuzzymethod of illustrating t...

in the present paper we define the notion of fuzzy inner productand study the properties of the corresponding fuzzy norm. in particular, it isshown that the cauchy-schwarz inequality holds. moreover, it is proved thatevery such fuzzy inner product space can be imbedded in a complete one andthat every subspace of a fuzzy hilbert space has a complementary subspace.finally, the notions of fuzzy bo...

Fuzzy Databases have been a fertile research area that has produced a wide variety of remarkable solutions for the storage and manipulation of imperfect information. Proposals can be found in the three most relevant data models: relational, object-oriented, and object-relational. Query capabilities have been especially studied in the context of the relational data model, while in object models ...

Successes with kernel-based classification methods have spawned many recent efforts to kernelize clustering algorithms for object data. We extend this idea to the relational data case by proposing kernelized forms of the non-Euclidean relational fuzzy (NERF) and hard (NERH) c-means algorithms. We show that these relational forms are dual to kernelized forms of fuzzy and hard c-means (FCM, HCM) ...

In this paper it has been studied the sequence of membership functions and of join spaces (see [7]), determined by a class of 1–hypergroups which are not complete (see [2]).

We provide a self contained survey of the state of art of the fuzzy binary relations and some of their applications.

This paper studies a fuzzy graph rewriting with single pushout approach from a viewpoint of fuzzy relational calculus. Two possible kinds of matchings for fuzzy graph rewritings are given, namely, a rigorous matching which just generalizes matchings for crisp (or ordinary) graph rewritings, and an "-matching which represents rather ambiguous or fuzzy one. Finally the pullback structure of fuzzy...

In a previous work, we have explored a proximity-based approach for relaxing queries involving fuzzy predicates. This proximity was defined in a relative way. In this paper we consider an absolute proximity and we show how it can be used for the purpose of query weakening. The main features of the weakening mechanism resulting from the use of this kind of proximity are investigated as well. Las...