in this paper, we use the parametric form of fuzzy numbers, and aniterative approach for obtaining approximate solution for a classof fuzzy nonlinear fredholm integral equations of the second kindis proposed. this paper presents a method based on newton-cotesmethods with positive coefficient. then we obtain approximatesolution of the fuzzy nonlinear integral equations by an iterativeapproach.

in this paper we classify fuzzy subgroups of the dihedral group $d_{pqrs}$  for distinct primes  $p$, $q$, $r$ and $s$. this follows similar work we have done on distinct fuzzy subgroups of some dihedral groups.we present formulae for the number of (i) distinct maximal chains of subgroups, (ii) distinct fuzzy subgroups and (iii) non-isomorphic classes of fuzzy subgroups under our chosen equival...

In this paper we discuss on some different representations of the cardinality of a fuzzy set and their use in fuzzy quantification. We have considered the widely employed sigma-count, fuzzy numbers, and gradual numbers. Gradual numbers assign numbers to values of a relevance scale, typically [0,1]. Contrary to sigma-count and fuzzy numbers, they provide a precise representation of the cardinali...

This paper aims at applying a fuzzy arithmetic of intervals calculus and fuzzy quantities to automatic control. This one called φ–calculus fuzzy arithmetic is more practical than the extension principle one and -cut based methods. It comes from a different representation of fuzzy numbers. The present paper follows up work in introducing. The present paper is interested in its use for a fuzzy in...

This paper proposes two mixed models to study a consumer’s optimal saving in the presence of two types of risk: income risk and background risk. In the first model, income risk is represented by a fuzzy number and background risk by a random variable. In the second model, income risk is represented by a random variable and background risk by a fuzzy number. For each model, three notions of prec...

In this paper, we discuss the analysis of students’ evaluation, especially in the case of the students’ answerscripts under the evaluation grade of linguistic data. We transfer mostly linguistic data, subjective message into triangular fuzzy numbers, and use the function principle instead of the extension principle to calculate the students’ score. In addition to, we use the degree of similarit...

We give some sufficient conditions such that a crisp, interval, triangular, trapezoidal, parametric approximation of a fuzzy number, with or without additional requirements, to have the properties of invariance to translations or scale invariance.

Many training algorithms use mean square error (MSE) for training when we have numeric data, with MSE also used to indicate the quality of the results. In many real world applications we are also interested in the number of samples which are “close enough” to the correct value and would also use the number of samples which could be mapped to correct classifications in reporting our results. We ...