How to Make Sure that "~100" + 1 is ~100 in Fuzzy Arithmetic: Solution and its (Inevitable) Drawbacks
نویسندگان
چکیده
From the commonsense viewpoint, if a person who weighs around 100 kilograms gains one more kilogram, his weight is still around 100 kilograms. Alas, not so in traditional fuzzy arithmetic. In this paper, we propose a modification of fuzzy arithmetic which does have this property. We gain the desired property, but there is no free lunch, we have to lose two important properties of the traditional fuzzy arithmetic: first, addition is no longer always associative; second, addition is no longer always easily computable.
منابع مشابه
Several new results based on the study of distance measures of intuitionistic fuzzy sets
It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their...
متن کاملA note on "An interval type-2 fuzzy extension of the TOPSIS method using alpha cuts"
The technique for order of preference by similarity to ideal solution (TOPSIS) is a method based on the ideal solutions in which the most desirable alternative should have the shortest distance from positive ideal solution and the longest distance from negative ideal solution. Depending on type of evaluations or method of ranking, different approaches have been proposing to calculate distances ...
متن کاملARITHMETIC-BASED FUZZY CONTROL
Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence funct...
متن کاملA New Definition of the Fuzzy Set
The present fuzzy arithmetic based on Zadeh’s possibilistic extension principle and on the classic definition of a fuzzy set has many essential drawbacks. Therefore its application to the solution of practical tasks is limited. In the paper a new definition of the fuzzy set is presented. The definition allows for a considerable fuzziness decrease in the number of arithmetic operations in compar...
متن کاملCrisis in Venezuela: A Politico Economic Understanding
More than five years down the line Venezuela had been slipping into an economic cri-sis. An economy wholly dependent on the sale of oil and no diversification of economic production is sure to face such a crisis. The fluctuation in oil prices is sure to hurt the market and the economy. To make matters worse, Venezuela now faces a political crisis with two individuals claiming themselves to be P...
متن کامل