Quotients with respect to similarity relations
Fuzzy Sets and Systems - Mathematics and Fuzziness, Part 1
T -partitions of the real line generated by idempotent shapes
Fuzzy Sets and Systems - Special issue: fuzzy arithmetic
Similarity relations and BK-relational products
Information Sciences—Informatics and Computer Science: An International Journal
Fuzzy points, fuzzy relations and fuzzy functions
Discovering the world with fuzzy logic
A similarity-based generalization of fuzzy orderings preserving the classical axioms
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Fundamentals of M-vague algebra and M-vague arithmetic operations
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
The generalized associative law in smooth groups
Information Sciences—Informatics and Computer Science: An International Journal
Products of elements in vague semigroups and their implementations in vague arithmetic
Fuzzy Sets and Systems
Similarity relations and fuzzy orderings
Information Sciences: an International Journal
Vague groups and generalized vague subgroups on the basis of ([0,1],≤,Λ)
Information Sciences: an International Journal
The generalized associative law in vague groups and its applications-I
Information Sciences: an International Journal
Arithmetic of fuzzy quantities based on vague arithmetic operations
IFSA'03 Proceedings of the 10th international fuzzy systems association World Congress conference on Fuzzy sets and systems
The generalized associative law in vague groups and its applications-I
Information Sciences: an International Journal
The generalized associative law in vague groups and its applications-II
Information Sciences: an International Journal
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Products of elements and integral powers of elements in vague groups have a significant concern for the development and the applications of vague algebra. Formulation of properties of these notions basically depends on a many-valued counterpart to the generalized associative law (called the generalized vague associative law in vague groups). For this reason, the present paper and the forthcoming paper [M. Demirci, The generalized associative law in vague groups and its applications-II, Information Sciences, Submitted for publication] are devoted to the formulation of the generalized vague associative law and its applications in vague groups. The generalized vague associative law in vague semigroups, which is the main contribution of this exposition, and some elementary properties of the notion of a product of a finite number of elements in vague semigroups, which cover necessary preparatory results for Part II, are the subjects of this paper. Since the present paper forms an abstract foundation of the product and sum of a finite number of real numbers in vague arithmetic, some practical applications of the notions of product and sum of a finite number of real numbers in vague arithmetic are also given.