*Correspondence: [email protected] 1Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, 31261, Saudi Arabia 2Permanent address: Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India Full list of author information is available at the end of the article Abstract This paper is devoted to study interval-valued optimization p...

We sought to investigate (1) the characteristics of epileptiform discharge (ED) duration and interdischarge interval (IDI) and (2) the influence of vigilance state on the ED duration and IDI in genetic generalized epilepsy (GGE). In a cohort of patients diagnosed with GGE, 24-h ambulatory EEG recordings were performed prospectively. We then tabulated durations, IDI, and vigilance state in relat...

Di erent representations of imprecise probabilities have been proposed, where interval-valued probabilities are used such that uncertainty is distinguished from variability. In this paper, we present a new form of imprecise probabilities for reliability assessment based on generalized intervals. Generalized intervals have group properties under the Kaucher arithmetic, which provides a concise r...

Many practical optimization problems are nonsmooth, and derivative-type methods cannot be applied. To overcome this difficulty, there are different approaches to replace the derivative of a function f : Rn → R: interval slopes, semigradients, generalized gradients, and slant derivatives are some examples. In this paper we study the relationships among these approaches for nonsmooth Lipschitz op...

Let an (r, s)-formation be a concatenation of s permutations of r distinct letters, and let a block of a sequence be a subsequence of consecutive distinct letters. A k-chain on [1,m] is a sequence of k consecutive, disjoint, nonempty intervals of the form [a0, a1][a1 + 1, a2] . . . [ak−1 + 1, ak] for integers 1 6 a0 6 a1 < . . . < ak 6 m, and an s-tuple is a set of s distinct integers. An s-tup...

A generalized decision logic in interval-set-valued information tables is introduced, which is an extension of decision logic studied by Pawlak. Each object in an interval-set-valued information table takes an interval set of values. Consequently, two types of satisfiabilities of a formula are introduced. Truth values of formulas are defined to be interval-valued, instead of single-valued. A se...

In the present paper, the notions of interval valued (∈,∈ ∨(k̃∗, qk̃))-fuzzy bi-ideals and interval valued (∈,∈ ∨(k̃∗, qk̃))-fuzzy quasiideals of ordered semigroups are introduced, and their related properties are investigated. Furthermore, we characterize different classes of ordered semigroups by using the properties of these interval valued generalized fuzzy ideals. 2010 AMS Classification: 06F0...

The work presents a necessary and sufficient condition for the generalized AE-solution sets to interval linear systems of equations to be unbounded. The criterion requires solvability of one of the totality of 2 linear inequalities constructed from the initial interval system. It is shown that the problem of recognizing the boundedness of AE-solution sets is NP-complete in general.

Optimization methods have been widely applied in statistics. Among them, capability measuring techniques are widely applied in industries. Process Capability Indices (PCIs) have been proposed for measuring process production capability. This paper concentrates, the lower and upper confidence limits for the PCIs are obtained from generalized pivotal quantity of random model and also, use this co...