This paper, deals with some equivalence relations in fuzzy subgroups. Further the probability of commuting two fuzzy subgroups of some finite abelian groups is defined.

Fuzzy modeling has many advantages over the non-fuzzy methods, such as robustness against uncertainties and less sensitivity to the varying dynamics of nonlinear systems. Data-driven fuzzy modeling needs to extract fuzzy rules from the input/output data, and train the fuzzy parameters. This paper takes advantages from deep learning, probability theory, fuzzy modeling, and extreme learning machi...

this paper presents a mathematical model for a flow shop scheduling problem consisting of m machine and n jobs with fuzzy processing times that can be estimated as independent stochastic or fuzzy numbers. in the traditional flow shop scheduling problem, the typical objective is to minimize the makespan). however,, two significant criteria for each schedule in stochastic models are: expectable m...

In a 1968 article, ‘Probability Measures of Fuzzy Events’, Lotfi Zadeh proposed accounts of absolute and conditional probability for fuzzy sets (Zadeh, 1968). Where P is an ordinary (“classical”) probability measure defined on a σ-field of Borel subsets of a space X, and μA is a fuzzy membership function defined on X, i.e. a function taking values in the interval [0, 1], the probability of the ...

This paper surveys some of the recent results that have been obtained in fuzzy quantum probability theory. In this theory fuzzy events are represented by quantum effects and fuzzy random variables are represented by quantum measurements. Probabilities, conditional probabilities and sequential products of effects are discussed. The relationship between the law of total probability and compatibil...

In this paper we deal with a new approach to probabilistic reasoning in a logical frame­ work. Nearly almost all logics of probabil­ ity that have been proposed in the litera­ ture are based on classical two-valued logic. After making clear the differences between fuzzy logic and probability theory, here we propose a fuzzy logic of probability for which completeness results (in a probabilistic ...

In economic practice, we often deal with events that are defined only vaguely. Such indeterminate events can be modelled by fuzzy sets. In the paper, we examine two main ways of expressing a probability of fuzzy events that are proposed in the literature. We study their mathematical properties and discuss their interpretation. We conclude that none of the approaches gives an appropriate probabi...

The concept of (fuzzy) probability density function of fuzzy random variable is proposed in this paper. Due to the "resolution identity", we can construct a closed fuzzy number from a family of closed intervals. Using the same technique, we can construct the (fuzzy) probability density function of fuzzy random variable from the known probability density function. The basic idea of the new metho...

Many applications of probability theory are based on the assumption that, as the number of cases increase, the relative frequency of cases with a certain property tends to a number { probability that this property is true. L. Zadeh has shown that in many reallife situations, the frequency oscillates and does not converge at all. It is very di cult to describe such situations by using methods fr...