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...

Most fuzzy controllers and fuzzy expert systems must predefine membership functions and fuzzy inference rules to map numeric data into linguistic variable terms and to make fuzzy reasoning work. In this paper, we propose a general learning method as a framework for automatically deriving membership functions and fuzzy if-then rules from a set of given training examples to rapidly build a protot...

The contact behaviour between the grinding wheel and workpiece in abrasive machining processes has been investigated. This has revealed the ambiguity in deciding the size of the contact region from a measured contact signal. For improved representation of the contact conditions, fuzzy set theory was used. A membership function for the fuzzy representation of the extent of wheelworkpiece contact...

Fuzzy AHP is a hybrid method that combines Fuzzy Set Theory and AHP. It has been developed to take into account uncertainty and imprecision in the evaluations. Fuzzy Set Theory requires the definition of a membership function. At present, there are no indications of how these membership functions can be constructed. In this paper, a way to calibrate the membership functions with comparisons giv...

In this work we study the asymptotic behavior of fuzzy solutions obtained by using Zadeh’s extension at the deterministic solutions of initial value problems. We obtain some result regarding the existence of fuzzy equilibrium points that generalize the already known results. As show earlier, the membership function of the fuzzy equilibrium points may be obtained in a relatively simple way. Also...

Fuzzy numbers with a unimodal membership function are presented, which have found application in the fuzzy analysis of such subject fields as ecology, chemical technology. In this article, set an special type is considered. Two binary operations (addition and multiplication) given over set, formulas for calculation obtained some properties algebra investigated. It proved that addition multiplic...

A fuzzy based method has been proposed for identification of probable capacitor nodes of radial distribution system. Simulated annealing technique has been used for final selection of the capacitor sizes. New fuzzy membership functions have been formulated where the active power membership is an exponential function of the nodal per unit active power and branch active power loss, the reactive m...