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Addition of fuzzy quantities: Disjunction-conjunction approach

This paper is subjected to the problem of algebraical operations over fuzzy quantities with rational values. The concept of the fuzzy quantity was introduced in [3] and [4] and applied e.g. in [5] and [6]. It represents one of possible models of uncertainty connected with rational numerical data. The elementary properties of the addition of fuzzy quantities were shown in [3] and further developed in [8]. It is also shown there that such conception of addition leads to some unconsistency with the usual notion of fuzzy sets. Another definition of the addition of fuzzy quantities, avoiding the mentioned discrepancies, is suggested and investigated below. It is shown there that the main properties of the addition of fuzzy quantities are analogous for both concepts of the operation. Namely, the fundamental group properties can be guaranteed only up to an equivalence relation.