Two different but related measurement problems are considered within the fuzzy set theory. The first problem is the membership measurement and the second is property ranking. These two measurement problems are combined and two axiomatizations of fuzzy set theory are obtained. In the first one, the indifference is transitive but in the second one this drawback is removed by utilizing interval or...

This paper examines type-2 fuzzy arithmetic using interval analysis. It relies heavily on alpha-cuts and alpha-planes. Furthermore, we discuss the use of quasi type-2 fuzzy sets proposed by Mendel and Liu and define quasi type-2 fuzzy numbers. Arithmetic operations of such numbers are defined and a worked example is presented. Keywords— Fuzzy Arithmetic, Type-2 Fuzzy Arithmetic, Type-2 Fuzzy Nu...

Abstract Some industrial data often come with uncertainty, which in some cases depends on the decision of those responsible for taking measurement production process. While fuzzy approach helps to tackle ambiguity that arises measurement, an interval type-2 set deals such uncertainty better due its flexibility over control limits chart. This paper aims develop Interval Type-2 Exponentially Weig...