Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part III: constructions of vague algebraic notions and vague arithmetic operations

As a continuation of Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic notions", Int. J. Gen. Syst. 32, 157-175], starting from the algebraic concepts in the classical sense, this paper deals with the con...

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Published in:International journal of general systems Vol. 32; no. 2; pp. 177 - 201
Main Author: Demirci, Mustafa
Format: Journal Article
Language:English
Published: Taylor & Francis Group 01.04.2003
Subjects:
Fuzzy algebra, fuzzy group, vague group, vague arithmetic, fuzzy arithmetic, fuzzy function
ISSN:0308-1079, 1563-5104
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Abstract As a continuation of Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic notions", Int. J. Gen. Syst. 32, 157-175], starting from the algebraic concepts in the classical sense, this paper deals with the constructions of vague semigroups, vague monoids, vague groups, vague rings and vague fields on the basis of many-valued equivalence relations. Vague addition operations and vague multiplication operations on the basis of many-valued equivalence relations, which are naturally derived from vague algebraic notions in Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic notions", Int. J. Gen. Syst. 32, 157-175], and their constructions from the arithmetic operations in the classical sense are also subjects of this paper.
AbstractList As a continuation of Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic notions", Int. J. Gen. Syst. 32, 157-175], starting from the algebraic concepts in the classical sense, this paper deals with the constructions of vague semigroups, vague monoids, vague groups, vague rings and vague fields on the basis of many-valued equivalence relations. Vague addition operations and vague multiplication operations on the basis of many-valued equivalence relations, which are naturally derived from vague algebraic notions in Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic notions", Int. J. Gen. Syst. 32, 157-175], and their constructions from the arithmetic operations in the classical sense are also subjects of this paper.
As a continuation of Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part 11: vague algebraic notions", Int. J. Gen. Syst. 32, 157-175], starting from the algebraic concepts in the classical sense, this paper deals with the constructions of vague semigroups, vague monoids, vague groups, vague rings and vague fields on the basis of many-valued equivalence relations. Vague addition operations and vague multiplication operations on the basis of many-valued equivalence relations, which are naturally derived from vague algebraic notions in Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part 11: vague algebraic notions", Int. J Gen. Syst. 32, 157-175], and their constructions from the arithmetic operations in the classical sense are also subjects of this paper.
Author Demirci, Mustafa
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Cites_doi 10.1142/S0218488502001326
10.1080/0308107031000090765
10.1016/0165-0114(94)90311-5
10.1080/0308107031000090774
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Snippet As a continuation of Demirci [(2003b) "Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part II: vague algebraic...
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SubjectTerms Fuzzy algebra, fuzzy group, vague group, vague arithmetic, fuzzy arithmetic, fuzzy function
Title Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part III: constructions of vague algebraic notions and vague arithmetic operations
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