In standard arithmetic, if we, e.g., accidentally add a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+ y. In this paper, we prove the following two results: • First, a similar possibility to invert (undo) addition holds for fuzzy numbers (although in case of fuzzy numbers, we cannot simply undo addition by subtracting y from the sum). ...

The aim of this paper is to investigate the fuzzy number intuitionistic fuzzy multiple attribute decision making problems based on the fuzzy number intuitionistic fuzzy sets and Geometric Bonferroni mean operator. Then, we have proposed two aggregation operators: fuzzy number intuitionistic fuzzy geometric Bonferroni mean (FNIFGBM) operator and fuzzy number intuitionistic fuzzy weighted geometr...

In this article, we use the fuzzy concept to consider the reliability of serial system and the reliability of parallel system. Since the population reliability Rj of the subsystem Pj (j = 1, 2, ..., n) is unknown, if we use the point estimate j R to estimate Rj from the statistical data in the past, we don’t know the probability of the error j R − Rj. Moreover, the reliability of the system may...

Here at first we are going to give a brief history of the development of fuzzy entropy. Finally, new measures for entropy of fuzzy sets in continuous cases are introduced. In this article, our main purpose is to show that the entropy of fuzzy number is very much dependent on the selection of intervals. Another important thing which can be observed from the cases discussed is that the entropy of...

The unavoidable imprecision of measurements of continuous physical quantities can be modelled by using the concept of fuzzy numbers and fuzzy vectors. Concerning a quantitative usage of such data the classical concept of relative frequencies for real data has to be extended to so-called fuzzy relative frequencies for fuzzy data, whereby the fuzzy relative frequency of a set is a fuzzy number. A...

Intuitionistic fuzzy sets can effectively deal with the support information, opposition information and abstention information of candidates in many voting. However, it may be hardly to handle some information of voting for non-candidates in some voting. In order to handle the aforementioned problem, the concept of ternary fuzzy set and ternary fuzzy number are defined, and the corresponding op...

In this paper we present a general framework to face the problem of evaluate fuzzy quantities. A fuzzy quantity is a fuzzy set that may be non normal and/or non convex. This new formulation contains as particular cases the ones proposed by Fortemps and Roubens [7], Yager and Filev [12, 13] and follows a completely different approach. It starts with idea of “interval approximation of a fuzzy num...

Jahanshahloo has suggested a method for the solving linear programming problems with zero-one variables‎. ‎In this paper we formulate fully fuzzy linear programming problems with zero-one variables and a method for solving these problems is presented using the ranking function and also the branch and bound method along with an example is presented.

The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

Fuzzy numbers, and more generally linguistic values, are approximate assessments, given by experts and accepted by decision-makers when obtaining more accurate values is impossible or unnecessary. To simplify the task of representing and handling fuzzy numbers, several authors have introduced real indices in order to capture the information contained in a fuzzy number. In this paper we propose ...