In this article, we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent, which indicates that they have the same number of elements. The concepts of fuzzy sets and fuzzy classes in the class of all countable sets are introduced, and several standard relations and constructions, such as the fuzzy power set and exponentiation, are defi...

The fuzzy measure can highlight important information in analyzing component features, patterns, and trends. However, fuzzy densities and interaction effects are usually unknown or uncertain for implications thus making the fuzzy measure limited in applications. This research proposes an extended fuzzy measure to derive the conditional fuzzy densities from dominance-based rough set approach (DR...

Fuzzy formal logics were introduced in or-der to handle graded truth values insteadof only ‘true’ and ‘false’. A wide range ofsuch logics were introduced successfully, likeMonoidal T-norm based Logic, Basic Logic,Gödel Logic, Lukasiewicz Logic etc. How-ever, in general, fuzzy set theory is not onlyconcerned with vagueness, but also with un-certainty. A possible s...

this paper investigates the stability analysis of fuzzy relational dynamic systems. a new approach is introduced and a set of sufficient conditions is derived which sustains the unique globally asymptotically stable equilibrium point in a first-order fuzzy relational dynamic system with sumproduct fuzzy composition. this approach is also investigated for other types of fuzzy relational composit...

this study is an investigation of fuzzy linear regression model for crisp/fuzzy input and fuzzy output data. a least absolutes deviations approach to construct such a model is developed by introducing and applying a new metric on the space of fuzzy numbers. the proposed approach, which can deal with both symmetric and non-symmetric fuzzy observations, is compared with several existing models by...

in the course of the present study, the results of parametric approach are compared with those obtained through fuzzy approach using ahp as well as multivariate regression methods for comparisons and investigating the efficiency of the fuzzy method as applied in land suitability assessments. the correlation coefficients between land index and observed yield in the study area through fuzzy appro...

In this paper, a new approach is presented to fit arobust fuzzy regression model based on some fuzzy quantities. Inthis approach, we first introduce a new distance between two fuzzynumbers using the kernel function, and then, based on the leastsquares method, the parameters of fuzzy regression model isestimated. The proposed approach has a suitable performance to<b...