Scaled aggregation operations over two- and three-dimensional index matrices

Traneva, Velichka; Tranev, Stoyan; Stoenchev, Miroslav; Atanassov, Krassimir

doi:10.1007/s00500-018-3315-6

Cited by 35 publications

(19 citation statements)

References 6 publications

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“…Over every two 3-D IVIFIMs A and B we can apply the operations addition, transposition, multiplication, projection and substitution, as defined in [4], [8], [21]. [22] defines the operation "aggregation by one dimension".…”

Section: B Interval-valued Intuitionistic Fuzzy Index Matricesmentioning

confidence: 99%

Interval-Valued Intuitionistic Fuzzy Decision-Making Method using Index Matrices and Application in Outsourcing

Traneva¹,

Tranev²,

Mavrov³

2021

Annals of Computer Science and Information Systems

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Selecting a suitable outsourcing service provider is a challenging problem that requires discussion among a group of experts. The problems of this type belongs to the area of multicriteria decision-making. Interval-valued intuitionistic fuzzy sets, which are an extension of intuitionistic fuzzy sets, are a capable tool in modeling uncertain problems. In this paper we will formulate an optimal interval-valued intuitionistic fuzzy multicriteria decision-making problem in outsourcing and propose a new approach for the selection of the most appropriate candidates; as well as a software program for its automated solution, based on our previous libraries. As an example of a case study, an application of the algorithm on real data from a refinery is demonstrated.

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Section: B Interval-valued Intuitionistic Fuzzy Index Matricesmentioning

confidence: 99%

Interval-Valued Intuitionistic Fuzzy Decision-Making Method using Index Matrices and Application in Outsourcing

Traneva¹,

Tranev²,

Mavrov³

2021

Annals of Computer Science and Information Systems

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“…Let us use the operations # q , (q ≤ i ≤ 3) from [50] for scaling aggregation operations over two IFPs x = ⟨a, b⟩ and y = ⟨c, d⟩:…”

Section: Aggregation Operationsmentioning

confidence: 99%

“…Let k 0 / ∈ K be a fixed index. The definition of the aggregation operation by the dimension K is [21], [50]: is:…”

Section: Aggregation Operationsmentioning

confidence: 99%

Two-Stage Intuitionistic Fuzzy Transportation Problem through the Prism of Index Matrices

Traneva¹,

Tranev²

2021

Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems

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ÐIn today's market environment not all the parameters of the transportation problems may not be known precisely. Uncertain data can be represented by fuzzy sets (FSs). Intuitionistic FSs (IFSs) are an extension of FSs with a degree of hesitancy. The paper presents a new approach for solution of a two-stage intuitionistic fuzzy transportation problem (2-S IFTP) through the prism of index matrices (IMs). Its main objective is to find the quantities of delivery from manufacturers and resselers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The solution procedure is demonstrated by a numerical example.

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“…Let us use the operations # q , (q ≤ i ≤ 3) from [47] for scaling aggregation operations over two IFPs x = a, b and y = c, d :…”

Section: Aggregation Operationsmentioning

confidence: 99%

“…Let k 0 / ∈ K be a fixed index. The definition of the aggregation operation by the dimension K is [20], [47]: is:…”

Section: Aggregation Operationsmentioning

confidence: 99%

Intuitionistic Fuzzy Transportation Problem by Zero Point Method

Traneva¹,

Tranev²

2020

Proceedings of the 2020 Federated Conference on Computer Science and Information Systems

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The transportation problems (TPs) support the optimal management of the transport deliveries. In classical TPs the decision maker has information about the crisp values of the transportation costs, availability and demand of the products. Sometimes in the parameters of TPs in real life there is ambiguity and vagueness caused by uncontrollable market factors.Uncertain values can be represented by fuzzy sets (FSs) of Zadeh. The FSs have the degrees of membership and nonmembership. The concept of intuitionistic fuzzy sets (IFSs) originated in 1983 as an extension of FSs. Atanasov's IFSs also have a degree of hesitansy to representing the obscure environment.In this paper we formulate the TP, in which the transportation costs, supply and demand values are intuitionistic fuzzy pairs (IFPs), depending on the diesel prices, road condition, weather and other factors. Additional constraints are included in the problem: limits for the transportation costs. Its main objective is to determine the quantities of delivery from producers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The aim of the paper is to extend the fuzzy zero point method (FZPM [35]) to the intuitionistic FZPM (IFZPM) to find an optimal solution of the intuitionistic fuzzy TP (IFTP) using the IFSs and index matrix (IM) concepts, proposed by Atanassov. The solution algorithm is demonstrated by a numerical example. Its optimal solution is compared with that obtained by the intuitionistic fuzzy zero suffix method (IFZSM). This work on Sect. I and Sect. II is supported by the project of Asen Zlatarov University under Ref. No. NIX-423/2019 "Innovative methods for extracting knowledge management" The work on Sect. III and Sect. IV is supported by the Ministry of Education and Science under the Programme "Young scientists and postdoctoral students", approved by DCM # 577/17.08.2018.

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Scaled aggregation operations over two- and three-dimensional index matrices

Cited by 35 publications

References 6 publications

Interval-Valued Intuitionistic Fuzzy Decision-Making Method using Index Matrices and Application in Outsourcing

Interval-Valued Intuitionistic Fuzzy Decision-Making Method using Index Matrices and Application in Outsourcing

Two-Stage Intuitionistic Fuzzy Transportation Problem through the Prism of Index Matrices

Intuitionistic Fuzzy Transportation Problem by Zero Point Method

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