In this paper we introduce Euler method for solving one dimensional FUZZY differential inclusion. FUZZY REACHABLE SET can be approximated by Euler method with complete analysis. The method is illustrated by numerical example.

The prime goal of this article is to initiate the notion of FUZZY    $\mu^*$-open(closed) SETs and FUZZY $\mu^*$-continuous functions and characterize  them. These concepts are defined in a FUZZY topological space in presence of a  generalized FUZZY topology, which becomes a new tool to study FUZZY topological spaces. It is observed that this class of FUZZY SETs fail to form a FUZZY topology but it form a generalized FUZZY topology. Furthermore, the relationship of these FUZZY SETs and FUZZY continuity with some existing FUZZY notions are established. Also the notion of FUZZY $(\tau, \mu^*)$-open(closed) functions is introduced and their equivalent conditions with  FUZZY $\mu^*$-continuous functions are established.

The existing Data Envelopment Analysis models for evaluating the relative eficiency of a SET of decision making units by using various inputs to produce various outputs are limited to crisp data in crisp production possibility SET. In this paper, first of all the production possibility SET is extended to the FUZZY production possibility SET by extension principle in constant return to scale, and then the FUZZY model of Charnes, Cooper and Rhodes in input oriented is proposed so that it satisfies the initial concepts with crisp data. Finally, the FUZZY model of Charnes, Cooper and Rhodes for evaluating decision making units is illustrated by solving two numerical examples.

In this work, we develop a reasoning mechanism under uncertainty for a typical class of decision making problems based on the theory of FUZZY soft SET. Accordingly, we consider a logic of FUZZY soft SETs. In the sequel, implication operations dealing with FUZZY soft SETs over different universal SETs and different SETs of parameters have been studied extensively. An algorithm for rule based reasoning has been developed for a modus ponens type rule of inference using the proposed logical structure. The entire proposal is illustrated with an example. Results of application of our proposed inference are compared with those obtained by Mondal and Raha on the problem of management of hypertension using a medical diagnostic support system.

Since the problems of everyday life are relative, so far various tools such as FUZZY SETs, intuitive FUZZY SETs, etc. have been expressed to express these ambiguities in mathematical modeling. In 2009, Torra introduced a new horizon for the discussion of hesitant FUZZY SETs to discuss issues that are uncertain about decision making. In the course of his work, the quantitative and qualitative expansion of uncertain FUZZY SETs is discussed. In this article, for the purpose of introducing more researchers to hesitant FUZZY SETs, we review the types of hesitant FUZZY SETs such as dual uncertain FUZZY SETs, generalized hesitant FUZZY SETs, and so on.

This work is towards the study of the relationship between FUZZY preordered SETs and Alexandrov (left/right) FUZZY topologies based on generalized residuated lattices here the FUZZY SETs are equipped with generalized residuated lattice in which the commutative property doesn’t' t hold. Further, the obtained results are used in the study of FUZZY automata theory.

Abstract. In this work, we de ne a FUZZY soft SET theory and its related properties. We then de ne FUZZY soft aggregation operator that allows constructing more efficient decision making method. Finally, we give an example which shows that the method can be successfully applied to many problems that contain uncertainties.