Cosine and cotangent similarity measurements are critical in applications for determining degrees of difference and similarity between objects. In the literature, numerous similarity measures for various extensions of fuzzy set, soft set, Intuitionistic Fuzzy Sets (IFSs), Pythagorean Fuzzy Sets (PFSs) and HyperSoft Sets (HSSs) have been explored. Neutrosophic HyperSoft Sets (NHSSs), on the other hand, has fewer cosine and cotangent similarity measures. In this paper, we propose the trigonometric similarity measures of NHSSs. We further investigate the basic operators, theorems, and propositions for the proposed similarity measures. We know that global warming causes environmental problems. One of applications for solving global warming is the concept of renewable energy. To show the effectiveness of the proposed similarity measures, we apply them to renewable energy source selection problems. The study reveals the best geographical area to install the energy production units, under some technical attributive factors. To check the validity and superiority of the proposed work, it is compared with some existing techniques which reveal that, decision-making problems with further bifurcated attributes, have more accurate and precise results and can only be solved with this technique. In the future, the proposed techniques can be applied to case studies, in which attributes are more than one and further bifurcated along with more than one decision-maker. Also, this proposed work can be extended for several existing hybrids of hypersoft sets, intuitionistic hypersoft, neutrosophic hypersoft set, bi-polar hypersoft, m-polar hypersoft sets, and Pythagorean hypersoft set to solve Multi-Criteria Decision Making (MCDM) problems.

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Trigonometric Similarity Measures for Neutrosophic Hypersoft Sets With Application to Renewable Energy Source Selection

Abstract The task of benchmarking smart e-tourism applications based on multiple smart key concept attributes is considered a multi-attribute decision-making (MADM) problem. Although the literature review has evaluated and benchmarked these applications, data ambiguity and vagueness continue to be unresolved issues. The robustness of the fuzzy decision by opinion score method (FDOSM) and fuzzy weighted with zero inconsistency (FWZIC) is proven compared with that of other MADM methods. Thus, this study extends FDOSM and FWZIC under a new fuzzy environment to address the mentioned issues whilst benchmarking the applications. The neutrosophic fuzzy set is used for this purpose because of its high ability to handle ambiguous and vague information comprehensively. Fundamentally, the proposed methodology comprises two phases. The first phase adopts and describes the decision matrices of the smart e-tourism applications. The second phase presents the proposed framework in two sections. In the first section, the weight of each attribute of smart e-tourism applications is calculated through the neutrosophic FWZIC (NS-FWZIC) method. The second section employs the weights determined by the NS-FWZIC method to benchmark all the applications per each category (tourism marketing and smart-based tourism recommendation system categories) through the neutrosophic FDOSM (NS-FDOSM). Findings reveal that: (1) the NS-FWZIC method effectively weights the applications’ attributes. Real time receives the highest importance weight (0.402), whereas augmented reality has the lowest weight (0.005). The remaining attributes are distributed in between. (2) In the context of group decision-making, NS-FDOSM is used to uniform the variation found in the individual benchmarking results of the applications across all categories. Systematic ranking, sensitivity analysis and comparison analysis assessments are used to evaluate the robustness of the proposed work. Finally, the limitations of this study are discussed along with several future directions. 

/pdf/based-on-neutrosophic-fuzzy-environment-a-new-development-of-3saaq68a.pdf

Based on neutrosophic fuzzy environment: a new development of FWZIC and FDOSM for benchmarking smart e-tourism applications

The idea of a neutrosophic hypersoft set (NHSS) was coined by Smarandache in 2018 as a generalization of the soft set. This structure is a hybrid of a neutrosophic set with a hypersoft set. It can be a valuable structure for dealing with multi-attributes, multi-objective problems with disjoint attributive values. Similarity measures (SM) play a vital role in measuring the similarity index that how much the things are similar. Different types of similarity measures were developed in literature with different fuzzy, intuitionistic, and neutrosophic theories. It is intended to merge the neutrosophic theory with the hypersoft set theory and propose different similarity measures with the help of new proposed distances with max-min operators. Also, we proved different theorems and properties of distance and similarity measures. Then as solid waste management is a global issue, and there are some Solid Waste Management Systems (SWMS) for environment protection, so an example will be given for the site selection for SWMS to check the validity of proposed techniques. To verify the validity and superiority of the suggested work, it is contrasted to several existing methodologies, which show that decision-making issues with more bifurcation attributes provide more accurate and precise outcomes and can only be solved using this technique. In the future, the presented methodologies could be used in case studies with several qualities that are further bifurcated and multiple decision-makers. This proposed work can also be extended to many existing hypersoft set hybrids, such as Fuzzy hypersoft sets (FHSs), Intuitionistic hypersoft sets (IHSs), Bipolar hypersoft sets (Bi-HSs), m-polar HSs, and Pythagorean hypersoft sets (PHSs).

https://ieeexplore.ieee.org/ielx7/6287639/9668973/09684360.pdf

Distance and Similarity Measures using Max-Min Operators of Neutrosophic Hypersoft Sets with Application in Site Selection for Solid Waste Management Systems

The idea of a neutrosophic hypersoft set (NHSS) was coined by Smarandache in 2018 as a generalization of the soft set. This structure is a hybrid of a neutrosophic set with a hypersoft set. It can be a valuable structure for dealing with multi-attributes, multi-objective problems with disjoint attributive values. Similarity measures (SM) play a vital role in measuring the similarity index that how much the things are similar. Different types of similarity measures were developed in literature with different fuzzy, intuitionistic, and neutrosophic theories. It is intended to merge the neutrosophic theory with the hypersoft set theory and propose different similarity measures with the help of new proposed distances with max-min operators. Also, we proved different theorems and properties of distance and similarity measures. Then as solid waste management is a global issue, and there are some Solid Waste Management Systems (SWMS) for environment protection, so an example will be given for the site selection for SWMS to check the validity of proposed techniques. To verify the validity and superiority of the suggested work, it is contrasted to several existing methodologies, which show that decision-making issues with more bifurcation attributes provide more accurate and precise outcomes and can only be solved using this technique. In the future, the presented methodologies could be used in case studies with several qualities that are further bifurcated and multiple decision-makers. This proposed work can also be extended to many existing hypersoft set hybrids, such as Fuzzy hypersoft sets (FHSs), Intuitionistic hypersoft sets (IHSs), bipolar hypersoft sets (Bi-HSs), m-polar HSs, and Pythagorean hypersoft sets (PHSs). 

/pdf/distance-and-similarity-measures-using-max-min-operators-of-27gu5vhb.pdf

Distance and Similarity Measures Using Max-Min Operators of Neutrosophic Hypersoft Sets With Application in Site Selection for Solid Waste Management Systems

These days, Google Map is used to find any location and/or to define the route to any given place. Its accuracy is up to 30 meters but if neutrosophic numbers are used, it gives more accuracy. To check the implementation of neutrosophic numbers in Google Map, a system is developed based on Fuzzy Logic Controller (FLC) using neutrosophic numbers to find the gas station which is nearest, less parking car units and with few traffic signals on the way. In this way, it takes less time to reach the available gas station. This system enables the driver to find a fuel station with more accuracy. We took five linguistic inputs including distance, gas availability, parking car unit, amount of gas, and the number of traffic signals to get one output, that is, time. We assigned different neutrosophic soft sets to each linguistic input. FLC inference was designed using 108 rules based on if-then statements to select time to reach the gas station. The results were veriﬁed by MATLAB’s Fuzzy Logic Toolbox.

https://journals.umt.edu.pk/index.php/SIR/article/download/868/454

The Best Way to Access Gas Stations using Fuzzy Logic Controller in a Neutrosophic Environment

Similarity measures have wide range of applications in realworld such as patterns, face recognitions, codding etc. In this paper it is intended to determine the tangent, cosine and cotangent similarity measure for single valued Neutrosophic sets and will compare the accuracy of all above similarity measures and applied it in decision making problems such as selection of an academic programs.

/pdf/similarity-measures-of-tangent-cotangent-and-cosines-in-4yqznv4gpt.pdf

Nazia Nawaz

Papers

Similarity Measures of Tangent, Cotangent and Cosines in Neutrosophic Environment and their Application in Selection of Academic Programs