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...

This paper presents a fuzzy goal programming (FGP) methodology for solving bi-level quadratic programming (BLQP) problems. In the FGP model formulation, firstly the objectives are transformed into fuzzy goals (membership functions) by means of assigning an aspiration level to each of them, and suitable membership function is defined for each objectives, and also the membership functions for vec...

This paper introduces a B ezier curve-based mechanism for constructing membership functions of convex normal fuzzy sets. The mechanism can fit any given data set with a minimum level of discrepancy. In the absence of data, the mechanism can be intuitively manipulated by the user to construct membership functions with the desired shape. Some numerical experiments are included to compare the perf...

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...

An interactive multiobjective fuzzy inventory problem with two resource constraints is presented in this paper. The cost parameters and index parameters, the storage space, the budgetary cost, and the objective and constraint goals are imprecise in nature. These parameters and objective goals are quantified by linear/nonlinear membership functions. A compromise solution is obtained by geometric...