In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval 0; 1]. There are only denu-merable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathemat...

the purpose of the present work is to establish a one-to-one correspondence between the family of interval type-2 fuzzy reflexive/tolerance approximation spaces and the family of interval type-2 fuzzy closure spaces.

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and Applied Analysis 3 2.1. Fuzzy Numbers In this section, we give certain essential concepts of fuzzy numbers and their basic properties. For further information see 2, 3 . A fuzzy set à on a set X is a function à : X → 0, 1 . Generally, the symbol μà is used for the function à and it is said that the fuzzy set à is characterized by itsmembership function μà : X → 0, 1 which associates with ea...

the sst decomposition method for solving system of linear equations make it possible to obtain the values of roots of the system with the specified accuracy as the limit of the sequence of some vectors. in this topic we are going to consider vectors as fuzzy vectors. we have considered a numerical example and tried to find out solution vector x in fuzzified form using method of sst decomposition.

In this work, a new concept of upper dense sequence in interval (0,1] is introduced. There are infinitely many upper dense sequences in interval (0,1]. Using any upper dense sequence, a new decomposition theorem for fuzzy sets is established and proved. Then, using a chosen upper dense sequence as one of the necessary reference systems, infinitely many total orderings on the set of all fuzzy nu...