A hesitant fuzzy SMART method based on a new score function for information literacy assessment of teachers

As two powerful and flexible tools for decision-makers (DMs) to model the complex cognition, the hesitant fuzzy set (HFS) and hesitant fuzzy linguistic term set (HFLTS) allow DMs to express their opinions with several possible membership values or linguistic terms on the objects over each criterion. The aim of this article is to develop a novel score function of the HFS and HFLTS including hesitant degree and fuzzy degree information. For this purpose, the notion of fuzzy degree of the hesitant fuzzy element (HFE) and hesitant fuzzy linguistic element (HFLE) is introduced first. Then, considering both the hesitant degree and fuzzy degree information in expressions, the new score function, namely the Score-H&FD, is designed. Based on which, we extend the classical SMART (simple multi-attribute rating technique) method to the hesitant fuzzy environment. As a result, the hesitant fuzzy SMART (HF-SMART) method is developed in this article. Afterwards, we apply our proposed approach to assess and rank several teachers concerning information literacy. Finally, sensitive analysis and comparative analysis are carried out. The results show that the proposed method in this article has substantial advantages and applicability

Notes on Interval-Valued Hesitant Fuzzy Soft Topological Space

In this paper we introduce the notion of interval valued hesitant fuzzy soft topological space. Also the concepts of interval valued hesitant fuzzy soft closure; interior and neighbourhood are introduced here and established some important results

Extended Nonstandard Neutrosophic Logic, Set, and Probability Based on Extended Nonstandard Analysis

We extend for the second time the nonstandard analysis by adding the left monad closed to the right, and right monad closed to the left, while besides the pierced binad (we introduced in 1998) we add now the unpierced binad—all these in order to close the newly extended nonstandard space under nonstandard addition, nonstandard subtraction, nonstandard multiplication, nonstandard division, and nonstandard power operations

Some New Operations of ( alpha, , ) Interval Cut Set of Interval Valued Neutrosophic Sets

In this paper, we define the disjunctive sum, difference and Cartesian product of two interval valued neutrosophic sets and study their basic properties

An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions

International audienceThis paper proposes a novel implementation of fuzzy arithmetics that exploits both fuzzy intervals and hardware specificities. First, we propose and evaluate the benefit of an alternative representation format to the traditional lower-upper and midpoint-radius representation formats for intervals. Thanks to the proposed formats, we show that it is possible to halve the number of operations and memory requirements compared to conventional methods. Then, we show that operations on fuzzy intervals are sensitive to hardware specificities of accelerators such as GPU. These include static rounding, memory usage, instruction level parallelism (ILP) and thread-level parallelism (TLP). We develop a library of fuzzy arithmetic operations in CUDA and C++ over several formats. The proposed library is evaluated using compute-bound and memory-bound benchmarks on Nvidia GPUs, and shows a performance gain of 2 to 20 over traditional approaches

AN EXTENDED SINGLE-VALUED NEUTROSOPHIC AHP AND MULTIMOORA METHOD TO EVALUATE THE OPTIMAL TRAINING AIRCRAFT FOR FLIGHT TRAINING ORGANIZATIONS

Aircraft’s training is crucial for a flight training organization (FTO). Therefore, an important decision that these organizations should wisely consider the choice of aircraft to be bought among many alternatives. The criteria for evaluating the optimal training aircraft for FTOs are collected based on the survey approach. Single valued neutrosophic sets (SVNS) have the degree of truth, indeterminacy, and falsity membership functions and, as a special case, neutrosophic sets (NS) deal with inconsistent environments. In this regard, this study has extended a single-valued neutrosophic analytic hierarchy process (AHP) based on multi-objective optimization on the basis of ratio analysis plus a full multiplicative form (MULTIMOORA) to rank the training aircraft as the alternatives. Moreover, a sensitivity analysis is performed to demonstrate the stability of the developed method. Finally, a comparison between the results of the developed approach and the existing approaches for validating the developed approach is discussed. This analysis shows that the proposed approach is efficient and with the other methods

A distance-based decision model in interval-valued hesitant fuzzy setting for industrial selection problems

In a classical Group Decision-Making (GDM) analysis, the ratings of potential alternatives and the weights of criteria or Decision Makers (DMs) are known precisely. However, for dealing with uncertain situations, the DMs can de ne their opinions in linguistic variables based on fuzzy sets in industrial selection problems. In this respect, an Interval-Valued Hesitant Fuzzy Set (IVHFS) is the suitable and capable theory that could help the DMs with assigning some interval-valued membership degrees to a candidate or option under a set. This paper introduces a novel Interval-Valued Hesitant Fuzzy Distance-Based Group Decision (IVHF-DBGD) model by a group of DMs, in which the best potential alternative can be appraised and selected among the con icting criteria. In the proposed IVHF-DBGD model, the weight of each criterion is determined by extended IVHF-entropy method along with the DMs' opinions about the criteria's weights. Also, the weight of each DM is computed by a new IVHF-order preference method with the relative closeness. Moreover, this paper introduces a new IVHF-collective index to discriminate among potential alternatives in the selection process. Finally, the computational results with a robot selection from the literature indicate that the proposed IVHF-DBGD model is the suitable group decision-making tool for the industrial selection problems