t is the purpose of this paper to contribute to the discussion initiated byWachter about the parallelism between principal component (PC) and atypological grade of membership (GoM) analysis. The author testedempirically the close relationship between both analysis in a lowdimensional framework comprising up to nine dichotomous variables and twotypologies. Our contribution to the subject is also...

A real world fuzzy set should be able to tolerate ”small amounts” of perturbations. In type II fuzzy set represents each grade is represented by a fuzzy number. In other words, each grade may be perturbed independently. Such an ”independent perturbation” is inadequate, when a membership function is required to be continuous, differentiable, and etc. Pointwise perturbation cannot guarantee the c...

Soft set theory, proposed by Molodtsov has been regarded as an effective mathematical tool to deal with uncertainties. Vague set is a set of objects, each of which has a grade of membership whose value is a continuous subinterval of [0, 1]. Such a set is characterized by a truth-membership function and a falsemembership function. Thus, a vague set is actually a form of fuzzy set, albeit a more ...

the aim of this paper is the study of the sequence of join spacesand fuzzy subsets associated with a hypergroupoid. in thispaper we give some properties of the membership function$widetildemu_{otimes}$ corresponding to the direct pro-duct oftwo hypergroupoids and we determine the fuzzy grade of thehypergroupoid $langle htimes h, otimesrangle$ in a particularcase.

Latent class and the Grade of Membership (GoM) models are two examples of latent structure models. Latent class models are discrete mixture models. The GoM model has been originally developed as an extension of latent class models to a continuous mixture. This note describes a constrained latent class model which is equivalent to the GoM model, and provides a detailed proof of this equivalence....

The Grade of Membership (GoM) model is a hierarchical mixed-membership model used to characterize underlying latent classes based on categorical data. When using GoM models to analyze survey data, the sampling design needs to be appropriately modeled. Linear mixed-effect models (LME’s) easily model the stratification and clustering in sampling designs. This paper introduces a modification of th...

In recent years, the use of Fuzzy set theory has been popularised for handling overlap domains in control engineering but this has mostly been within the context of triangular membership functions. In actual practice however, such domains are hardly triangular and in fact for most engineering applications the membership functions are usually Gaussian and sometimes cosine. In an earlier paper, w...