International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems

In this paper, signed distance of Symmetrical Intuitionistic Fuzzy Numbers (SIFNs) is introduced. Based on this signed distance and the crisp ranking system on real numbers, a new ranking system for SIFNs is defined, which seems to be very realistic. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. Solid Transportation Problem (STP) is formulated in intuitionistic fuzzy environment. A new method has been proposed to compute initial basic feasible solution for the same. Also the significance of the proposed approach over existing methods is illustrated. Finally numerical examples are solved to demonstrate the efficiency of the proposed methods.

Complexity of computations, particularly due to large number of focal elements (FEs), in Dempster-Shafer theory (DST) motivates the development of approximation algorithms. Existing approximation methods include efficient algorithm for special hypothesis space, Monte Carlo based techniques, and simplification procedures. In this paper, the quality of the simplification-based approximation algorithms is evaluated using a new information-based comparison methodology. To this end, three structured testbeds are introduced. Each testbed is designed with an eye on a particular form of uncertainty associated with a body of evidence (BoE) in DST, i.e., conflict and non-specificity. Three proposed testbeds along with the classic testbed are utilized to evaluate the accuracy and complexity of existing algorithms. In light of the proposed evaluation methodology, a new approximation method is presented as well. The proposed algorithm has the ability to choose the most informative FEs without being forced to select the FEs with the largest mass function. Comparison of overall qualitative performance of approximation algorithms provides accuracy versus computational time tradeoff to choose an appropriate approximation method in different applications. Moreover, experiments with testbeds indicate that our proposed algorithm enhances the accuracy and computational tractability simultaneously.

This paper studies the minimum spanning tree problem on a graph with uncertain edge weights, which are formulated as uncertain variables. The concept of ideal uncertain minimum spanning tree (ideal UMST) is initiated by extending the definition of the uncertain $\alpha$-minimum spanning tree to reect the overall properties of the α-minimum spanning tree weights at any confidence level $\alpha \in \left[\mathrm{0,1}\right]$. On the basis of this new concept, the definition of uncertain distribution-minimum spanning tree is proposed in three ways. Particularly, by considering the tail value at risk from the perspective of risk management, the notion of uncertain $\beta$-distribution-minimum spanning tree ($\beta$-distribution-UMST) is suggested. It is shown that the $\beta$-distribution-UMST is just the uncertain expected minimum spanning tree when $\beta$ = 0. For any $\beta \in \left[\mathrm{0,1}\right]$, this problem can be effectively solved via the proposed deterministic graph transformation-based approach with the aid of the $\beta$-distribution-path optimality condition. Furthermore, the proposed definitions and solutions are illustrated by some numerical examples.

In this paper, the literature associated with the covering location problems addressing uncertainty under a fuzzy approach is reviewed. Specifically, the papers related to the most commonly applied models such as set covering location problem, maximal covering location problem, and hub covering location problem are examined. An annotated bibliography is presented in which such papers have been classified according to the following criteria: the fuzzy items considered in the proposed model, the type of problem addressed, the fuzzy approach applied, the method of resolution, and field of application considered. This research provides useful information that helps to identify some opportunities for the application of fuzzy approaches to the covering location problems.

In this paper, we investigate the multiple attributes group decision making (MAGDM) problem with 2-tuple linguistic information. According to some closed operational laws of 2-tuple linguistic, some Algebra t-norm and s-norm based Heronian aggregation operators of 2-tuple linguistic information are put forward, the desired properties and the special cases where the parameters take different values are also discussed. Furthermore, a method of MAGDM under 2-tuple linguistic environment is proposed based on the Algebra t-norm and s-norm based 2-tuple linguistic Heronian mean operator or the Algebra t-norm and s-norm based 2-tuple linguistic weighted Heronian mean operator. Finally, a numerical example is presented to demonstrate the proposed method.