We show that analogously to classical probability theory the conditional expectation E ( ? ~ X ) of a fuzzy random variable Y w.r.t. a fuzzy random variable X is w.r.t. a suitable metric the best approximation o f ? by measurable functions ofX. Furthermore, several linear regression functions, i.e. best approximation of ? by linear functions o f z and examples for random LR-fuzzy numbers and Ga...

The aim of this paper is to provide new results regarding the effective practical computation of t-norm-based additions of LR-fuzzy intervals.

It is significant to discover a global optimization in the problems dealing with large dimensional scales to increase the quality of decision-making in the mining operation. It has been broadly confirmed that the long-term production scheduling (LTPS) problem performs a main role in mining projects to develop the performance regarding the obtainability of constraints, while maximizing the whole...

This paper suggests  a novel approach for ranking the most applicable fuzzy numbers, i.e.  $LR$-fuzzy numbers. Applying the  $alpha$-optimistic values of a fuzzy number, a preference criterion is proposed for ranking fuzzy numbers using the Credibility index. The main properties of the proposed  preference criterion  are also studied.  Moreover, the proposed method is   applied for ranking fuzz...

This article presents a new similarity measure for LR-type fuzzy numbers. The proposed similarity measure is based on a defined metric between LR-type fuzzy numbers. It is known that an exponential operation is highly useful in dealing with the classical Shannon entropy and cluster analysis. We adopted, therefore, the exponential operation on this metric. Furthermore, we analyze its properties ...

Introduction: Microcystin-leucine arginine (MC-LR) is a toxin with harmful effects on the liver, kidney, heart, and gastrointestinal tract. So, effective removal of MC-LR from water resources is of great importance. The aim of this study was to remove microcystin-LR (MC-LR) from aqueous solution by Titanium Dioxide (TiO2). Materials and Methods: In the present study, TiO2, as a semiconductor, ...