In this article, we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent, which indicates that they have the same number of elements. The concepts of fuzzy sets and fuzzy classes in the class of all countable sets are introduced, and several standard relations and constructions, such as the fuzzy power set and exponentiation, are defi...

quality control plays an important role in increasing the product quality. fuzzy control charts are more sensitive than shewhart control chart. hence, the correct use of fuzzy control chart leads to producing better-quality products. this area is complex because it involves a large scope of industries, and information is not well organized. in this research, we provide a literature review of th...

in this paper, we consider portfolio selection problem in which security returns are regarded as fuzzy variables rather than random variables. we first introduce a concept of absolute deviation for fuzzy variables and prove some useful properties, which imply that absolute deviation may be used to measure risk well. then we propose two mean-absolute deviation models by defining risk as abs...

The fuzzy logic concept provides a natural way of dealing with problems in which the source of imprecision is an absence of sharply defined criteria rather than the presence of random variables. The fuzzy approach considers cases where uncertainties play a role in the control mechanism of the concerned phenomena. Fuzzy modeling includes fuzzification, fuzzy analysis and defuzzification. In this...

In many scientific and engineering applications, the fuzzy set concept plays an important role. The fuzziness appears when we need to perform, on manifold, calculations with imprecision variables. The fuzzy set theory was introduced initially by Zadeh [1] in 1965. In the theory and applications of fuzzy sets, convexity is a most useful concept. In fact, in the basic and classical paper [1], Zad...

Popper’s Logic of Scientific Discovery and Kuhn’s Structures of Scientific Revolutions are enormous important concepts on theories and their dynamic in 20 th century history and philosophy of science. How-ever, the works of the two have been criticized in the last half century and new views on theory nets and theory evolution appeared. In the last decades also new scientific methods and tools s...

Fuzzy Set Theory has been applied in many fields such as Operations Research, Control Theory, and Management Sciences etc. In particular, an application of this theory in Managerial Decision Making Problems has a remarkable significance. In this Paper, we consider a solution of Rectangular Fuzzy game with pay-off as imprecise numbers instead of crisp numbers viz., interval and LR-type Trapezoid...

After the definition of the concept of fuzzy metric space by some authors 1–3 , the fixed point theory on these spaces has been developing see, e.g., 4–9 . Generally, this theory on fuzzy metric space is done for contractive or contractive-type mappings see 2, 10–13 and references therein . In this paper we introduce the concept of fuzzy order ψ-contractive mappings and give two fixed point the...

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openn...