On some difficulties in the addition of trapezoidal ordered fuzzy numbers

TL;DR

This paper examines the challenges in adding trapezoidal ordered fuzzy numbers, revising the Kosinski definition, analyzing associativity, and showing the sum's dependence on summand order.

Contribution

It introduces a revised sum definition for ordered fuzzy numbers and investigates its properties, highlighting issues with associativity and order dependence.

Findings

Revised sum definition differs from Kosinski's original.

Associativity of the revised sum is not guaranteed.

The sum depends on the order of summands.

Abstract

At the first, we revise the Kosinski definition of the sum of ordered fuzzy numbers. The associativity of revised sum is investigated here. In addition, we show that the multiple revised sum of finite sequence of trapezoidal ordered fuzzy numbers depends on its summands ordering.