Uncertain set theory is a generalization of uncertainty theory that has become a new branch of mathematics for modeling human belief degrees. Uncertain set is a fundamental concept to describe unsharp concepts in uncertain set theory. The moments are important characteristics of an uncertain set. This paper studies the moments and central moments of uncertain set and gives some formulas to calc...

data envelopment analysis (dea) is a method to evaluate the relative efficiency of decision making units (dmus). in this method, the issue has always been to determine a set of weights for each dmu which often caused many problems. since the dea models also have the multi-objective linear programming (molp) problems nature, a rational relationship can be established between molp and dea problem...

Rough set approximations of Pawlak [15] are sometimes generalized by using similarities between objects rather than elementary sets. In practical applications, both knowledge about properties of objects and knowledge of similarity between objects can be incomplete and inconsistent. The aim of this paper is to define set approximations when all sets, and their approximations, as well as similari...

The fuzzy representation of the edges has been widely studied in different works. Generally, for each pixel, the authors use membership degrees linearly proportional to the magnitude of the gradient at that position of the image. This would be equivalent to using a triangular membership functions on the gradient magnitude. In this work we study the use of parametric functions in the transformat...

In many applications of fuzzy set theory, the membership of an object is not defined directly. One of its attributes (like height, age, weight, . . . ) is first mapped on a real number (often by means of a physical instrument) and a parametric function then maps this real number on a membership degree in some fuzzy set (like ‘tall’, ‘old’, ‘heavy’, . . . ). A very common parametric function is ...

In this paper we study some properties related to the distribution of membership grades for non-stationary fuzzy sets. We obtain the formulation for the distribution, where the non-stationary fuzzy sets are obtained by generating instantiations about the center values. The two cases considered are for the underlying membership functions as Triangular and Gaussian. The analytical results obtaine...

For simplicity, we follow the rules: C denotes a non empty set, c denotes an element of C, f , h, g, h1 denote membership functions of C, A denotes a FuzzySet of C, f , B denotes a FuzzySet of C, g, D denotes a FuzzySet of C, h, D1 denotes a FuzzySet of C, h1, X denotes a Universal FuzzySet of C, and E denotes an Empty FuzzySet of C. We now state four propositions: (1) For every element x of C ...

Reasoning, the most important human brain operation, is characterized by a degree of fuzziness. In the present paper we construct a fuzzy model for the reasoning process giving through the calculation of probabilities and possibilities of all possible individuals’ profiles a quantitative/qualitative view of their behaviour during the above process. In this model the main stages of human reasoni...

The article deals with mathematical and algorithmic support for sulfur prints image classification based on fuzzy sets and rules of accessories using peer inspections. In the study of the causes of unambiguous classification the authors have introduced codomains of membership function form: single classification, empty set, complete absorption and unambiguous classification. The article conceiv...