Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets 9 (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey 10 relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure 11 domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, 12 we apply ...

In this paper, two sets of sufficient conditions are obtained to ensure the existence and stability of a unique equilibrium point of unforced first-order fuzzy relational dynamical systems by using two different approaches which are both based on the fuzzy relational matrix of the model.In the first approach, the equilibrium point of the system is one of the centers of the related membership fu...

Medoids-based fuzzy relational clustering generates clusters of objects based on relational data, which records pairwise similarity or dissimilarities among objects. Compared with single-medoid based approaches, multiple-weighted medoids has shown superior performance in clustering. In this paper, we present a new version of fuzzy relational clustering in this family called fuzzy clustering wit...

This paper comprises two parts, the first deals with the conception of a class of Hybrid Granular Min-Max Fuzzy-Neuro Relational Learners, for which a learning scheme was devised that uses an exhaustive search over the fuzzy partitions of involved variables, automatic fuzzy hypotheses generation, formulation and testing, and successive approximation procedure of Min-Max relational equations. Th...

One of the famous mathematical inequalities is Minkowski’s inequality. It is an important inequality from both mathematical and application points of view. In this paper, a Minkowski type inequality for fuzzy integrals is studied. The established results are based on the classical Minkowski inequality for integrals. Moreover, a generalized Minkowski type inequality for fuzzy integrals is sugges...

Fuzzy relational identi"cation builds a relational model describing a system's behaviour by a nonlinear mapping between its variables. In this paper, we propose a new fuzzy relational algorithm based on the simpli"ed max}min relational equation. The algorithm presents an adaptation method applied to the gravity-centre of each fuzzy set based on the error integral value between the measured and ...

Recently, Flores-Franulič et al. [A note on fuzzy integral inequality of Stolarsky type, Applied Mathematics and Computation 208 (2008) 55-59] proved the Stolarsky’s inequality for the Sugeno integral on the special class of continuous and strictly monotone functions. This result can be generalized to a general class of fuzzy convex functions in this paper. We also give a fuzzy integral inequal...

Transformations of credit in 16th-century England illustrate how interpersonal transactions cause changes in inequality. Despite the efforts of such outstanding scholars as Eric Wolf, Don Kalb, and Timothy Earle, inequality has lost the prominent position it once occupied among anthropological concerns. As a result, anthropologists are missing the opportunity to intervene in important debates a...

Fuzzy relational identification builds a relational model describing system’s behaviour by a nonlinear mapping between its variables. In this paper, we propose a new fuzzy relational algorithm based on simplified max-min relational equation. The algorithm presents an adaptation method applied to gravity-center of each fuzzy set based on error integral value between measured and predicted system...

The aim of this thesis is to extend the fuzzy relational product calculations from binary to ternary relations, and apply the ternary fuzzy relational product calculations to processing of the URBS data. It is demonstrated that, by ternary fuzzy relational product calculations, the respondents with the similar cognitive structures can be clustered into groups and cognitive structures of those g...