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n-Dimensional Extended Index Matrices Part 1
Krassimir T. Atanassov 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.2
Index Matrices (IMs) are extensions of the ordinary matrices. They are also object of extensions and modifications, e.g., extended index matrices. In the present research, we describe extended index matrices, havingd as elements whole index matrices.
Index matrices with elements index matrices
Krassimir T. Atanassov 장전수학회 2018 Proceedings of the Jangjeon mathematical society Vol.21 No.2
Index Matrices (IMs) are extensions of the ordinary matrices. They are also object of extensions and modications, e.g., extended index matrices. In the present research, we describe extended index matrices, havind as elements whole index matrices.
An extension of one of Klamkin's inequalities
Krassimir T. Atanassov 장전수학회 2011 Advanced Studies in Contemporary Mathematics Vol.21 No.4
An extension of the standard Klamkin's inequality and of two of its modifications are formulated and proved.
ON INDEX MATRICES Part 3: On the hierarchical operation over index matrix
Krassimir T. Atanassov 장전수학회 2013 Advanced Studies in Contemporary Mathematics Vol.23 No.2
In this paper the definition of a new operation is introduced. It extends the hierarchical operation over index matrix, defined in [3]. Theorems for its representation are given.
n-Dimensional Extended Index Matrices Part 2
Krassimir T. Atanassov 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.1
Index Matrices (IMs) are extensions of the ordinary matrices. They are also object of extensions and modifications, e.g., extended index matrices. The present paper is the second part of our research over n-dimensional extended IMs. Here, we introduce new operations and relations over these matrices.
A GENERALIZED NET MODEL OF DECISION MAKING PROCESS
Krassimir Atanassov 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.2
In this paper, a generalized net model of a decision making process is described. It is an extension of the existing generalized net models of such systems.
Cartesian products over extended index matrices
Krassimir Atanassov 장전수학회 2022 Advanced Studies in Contemporary Mathematics Vol.32 No.1
By the moment, two different Cartesian products and defined over intu- itionistic fuzzy index matrices. In the preset paper, seven new definitions of oper- ation Cartesian product are introduced in the more general case of extended index matrices and some of their properties are studied. In a particular case, it is shown how these definitions can be modified for the intuitionistic fuzzy index matrices.
ON INDEX MATRICES Part 2: Intuitionistic fuzzy case
Krassimir T. Atanassov 장전수학회 2010 Proceedings of the Jangjeon mathematical society Vol.13 No.2
In this paper the concept of intuitionistic fuzzy index matrix is introduced and its basic properties are discussed. statements are formulated.
Ordered sets and operations “negation” over their elements
Krassimir Atanassov 장전수학회 2020 Advanced Studies in Contemporary Mathematics Vol.30 No.1
The idea for dening of operations "negation" over ordered sets is discussed. Five types of negations are introduced and their basic properties are studied.
Two new intuitionistic fuzzy implications
Krassimir T. Atanassov,Trifon A. Trifonov 장전수학회 2006 Advanced Studies in Contemporary Mathematics Vol.13 No.1
Two new intutionistic fuzzy implications are constructed. Their relations with some forms of Modus Ponens, Klir and Yuan's axioms and intuitionistic logic axioms are studied. The intuitionistic fuzzy negations generated by the two implications are constructed and some of their properties are discussed.