Choices in business processes are often based on the process history saved as a log-file listing events and their time stamps. In this paper we introduce a finite-path variant of the timed propositional logics with past for specifying guards in business process models. The novelty is due to the introduction of boundary points start and now corresponding to the starting and current observation p...

This paper shows the best operators for sumof-products expressions. We first describe conditions of functions for product and sum operations. We examine all two-variable functions and select those that meet the conditions and then evaluate the number of product terms needed in the minimum sum-of-products expressions when each combination of selected product and sum functions is used. As a resul...

it is firstly proved that the multi-input-single-output (miso) fuzzy systems based on interval-valued $r$- and $s$-implications can approximate any continuous function defined on a compact set to arbitrary accuracy.  a formula to compute the lower upper bounds on the number  of interval-valued fuzzy sets needed to achieve a pre-specified approximation  accuracy for an arbitrary multivariate con...

In this paper, we shall firstly illustrate why we should discuss the Aumann type set-valued Lebesgue integral of a set-valued stochastic process with respect to time t under the condition that the set-valued stochastic process takes nonempty compact subset of d-dimensional Euclidean space. After recalling some basic results about set-valued stochastic processes, we shall secondly prove that the...

‎In this paper‎, ‎we propose a new one-step iterative process for a‎ ‎countable family of quasi-nonexpansive multi-valued mappings in a‎ ‎CAT(0) space‎. ‎We also prove strong and $Delta$-convergence theorems‎ ‎of the proposed iterative process under some control conditions‎. ‎Our‎ ‎main results extend and generalize many results in the literature.

Some phenomena develop over time, while they are uncertain sets at each moment. From an set, we mean unsharp concept that is not clearly defined, even for expert. The potential values of parameters describing this guide one to explain it quantitatively. For instance, in “recovering” from some disease, different levels health might be meaning specific being healthy measured by belonging paramete...