in this paper, we introduce  the notions of   interval-valued and $(in,ivq)$-interval-valued fuzzy ($p$-,$q$- and $a$-) ideals    of   bci algebras   and investigate some of their properties.   we then derive characterization theorems for these generalized interval-valued fuzzy ideals  and discuss their relationship.

The Weibull distribution is a very applicable model for the lifetime data. For inference about two Weibull distributions using records, the shape parameters of the distributions are usually considered equal. However, there is not an appropriate method for comparing the shape parameters in the literature. Therefore, comparing the shape parameters of two Weibull distributions is very important. I...

Recently we proposed a new form of imprecise probability based on the generalized interval, where the probabilistic calculus structure resembles the traditional one in the precise probability because of the Kaucher arithmetic. In this paper, we study the independence properties of the generalized interval probability. It resembles the stochastic independence with proper and improper intervals a...

We survey the all-interval chords of small order and the interval systems in which they are situated. We begin with an examination of traditional all-interval chords in chromatic pitch-class spaces, and extend the notion of their structure to their counterparts in David Lewin’s Generalized Interval Systems. Mathematically, we observe that these chords belong to three categories of difference se...

This paper presents a method for pattern discovery based on viewpoints and feature set patterns. The representation for pattern components accommodates in a fully general way the taxonomic relationships that may exist between interval classes. A heuristic probabilistic hill climbing algorithm is developed to rapidly direct the search towards interesting patterns. The method can be used for sing...