This paper presents an optimization method based on a particular polynomial lattice rule with interlaced factor two for estimating sensitivity indices in global sensitivity analysis, focusing on total, first-order and second-order Sobol indices.A comparison with one of the best available methods the Modified Sobol Sequence and component by component construction polynomial lattice rule have been done.Relative errors for key output quantities are analyzed and compared.Our results show that the proposed optimization method consistently outperforms other methods in accurately estimating both first-order and total-order sensitivity indices, especially for parameters with smaller effects.These findings highlight the strengths and limitations of each method, providing guidance for selecting appropriate stochastic sampling strategies in computational sensitivity analysis.

Here we propose for the first time a temporal intuitionistic fuzzy extension of the Hungarian method for solving the Travelling Salesman Problem (TIFHA-TSP) based on intuitionistic fuzzy logic and index matrices theories.The time for passing a given route between the settlements depends on different factors.The expert approach is used to determine the intuitionistic fuzzy time values for passing the routes between the settlements.The rating coefficients of the experts take the times into account.We are also developing an application for the algorithm's provision to use it on a real case of TIFHA-TSP.

The selection of the most suitable franchisee applicant in an uncertain environment in a particular moment of time is a key decision for a franchisor and the success of a franchising business.In this work, for the first time, we describe a problem for choosing the optimal candidate for the franchise chain and algorithm for a solution in terms of temporal intuitionistic fuzzy pairs and index matrices as a means for data analysis in uncertain conditions over time.We also use our software utility to demonstrate the proposed algorithm and to apply the decision support approach to a franchisee selection for the largest fast food restaurant chain in Bulgaria.

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.

In this paper, the algorithm for finding a Hamiltonian cycle in an intuitionistic fuzzy graph (IFG) is proposed, based on the theories of intuitionistic fuzzy sets (IFSs) and of index matrices (IMs).The aim of the paper is to extend the algorithm to find a fuzzy Hamiltonian cycle (FHC) in an IFG to the intuitionistic fuzzy (IFHC) using the IFSs and IMs concepts.An intuitionistic fuzzy graph example about network of Wizz air airlines is modeled by the extended IM to illustrate the proposed algorithm.In the paper also are introduced for the first time three index-type operations over IMs.

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 sup