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 ...

Many ranking methods have been proposed so far. The fuzzy number defuzzification method with continuous weighted quasi-arithmetic means was proposed by Yoshida in the domain (−∞,+∞) . Recently in [22], the researcher used this method with the ordinary fuzzy set in a compact interval, that all the conclusions can be extended to the ordinary fuzzy set in [24] directly. This parameterized defuzzif...

Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middle-point and the spread of each $gamma$-cut of a fuzzy number, respectively. We use the value of a as the weight of the signal/noise ratio of each $gamma$-cut of a fuzzy number to calcula...

fuzzy groups and fuzzy theory have a lot of applications in several sciences such as mathematics, computer science, computer and electrical engineering. hence, counting the number of fuzzy subgroups of finite groups to classify them is an important issue in fuzzy theory. the main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of a finite cyclic group g z p1 ...

In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...