Since almost all objects of mathematics can be described by sets (e.g., a function as a set of ordered pairs), one can establish fuzzy generalizations for nearly all of those. In the previous sections, we have seen that fuzzy mathematical concepts occur ‘naturally’, that is, considering the uncertainty involved in the application, the need to generalize creates fuzzy mathematical objects. We co...

generalization of Rosenfeld's fuzzy subgroup, and Bhakat and Das's fuzzy subgroup is given in [20]. Lie algebras are so-named in honor of Sophus Lie, a Norwegian mathematician who pioneered the study of these mathematical objects. Lie's discovery was tied to his investigation of continuous transformation groups and symmetries. The structure of the laws in physics is largely based on symmetries....

Fuzzy economic models to evaluate the economic feasibility of information security investment for decision-makers is derived in this study. The Net Present Value and discounted Return on Investment models are proposed for the execution of cost-benefit analysis. Fuzzy mathematics is based on the extended principles which ensured that the resultant fuzzy number continuously maintained its fuzzy p...

We consider cyclic non homogeneous fuzzy Markov chains where there are uncertainties in the transition possibilities. These uncertainties are modeled by triangular fuzzy number. Using the algorithm for finding the greatest eigen fuzzy sets we have analyzed the long term behavior of the system and this is illustrated with the numerical example. Mathematics Subject Classification: 03E72, 60J10

In this paper, Multi objective two stage Fuzzy transportation problem is solved in a feasible method. For this solution zero suffix method is used in which the supplies and demands are trapezoidal fuzzy numbers and fuzzy membership of the objective function is defined. Here a numerical example is solved to check the validity of the proposed method. Mathematics Subject Classifications: 90C08, 90C90

The notion of intuitionistic fuzzy ideals with thresholds of an ordered semigroup is considered and some of its properties are given. An embedding theorem of the set of all intuitionistic fuzzy ideals with thresholds is presented and the homomorphic images and inverse images of intuitionistic fuzzy ideals with thresholds are studied too. 2010 Mathematics Subject Classification: 06F05

In this paper we introduce the concept of fuzzy generalized bi-ideal of a Γsemigroup, which is an extension of the concept of a fuzzy bi-ideal of a Γsemigroup and characterize regular Γ-semigroups in terms of fuzzy generalized bi-ideals. AMS Mathematics Subject Classification(2000): 08A72, 20M12, 3F55

In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which both hypotheses and observations are imprecise. In this paper, we redefine some concepts about fuzzy hypotheses testing, and then we give the Neyman-Pearson lemma for fuzzy hypotheses testing with fuzzy observations. Finally, we give some applied examples. Mathematics ...

In this paper some algebraic structures for linguistic fuzzy models are defined for the first time. By definition linguistic fuzzy norm, stability of these systems can be considered. Two methods (normed-based & graphical-based) for stability analysis of linguist fuzzy systems will be presented. At the follow a new simple method for linguistic fuzzy numbers calculations is defined. At the end tw...

In this paper, we apply the concept of interval valued fuzzy sets to hemirings. The concept of interval valued fuzzy left (right) h-ideals of hemirings is introduced, and some related properties are investigated. Also, the characterization of h-hemiregular and h-intra-hemiregular hemirings in terms of interval valued fuzzy left (right) h-ideals is studied. Mathematics Subject Classification: 03E72