Extended Fuzzy Sets and Their Applications

This contribution deals with introducing the innovative concept of extended fuzzy set (E-FS), in which the S-norm function of membership and non-membership grades is less than or equal to one. The proposed concept not only encompasses the concept of the fuzzy set (FS), but it also includes the concepts of the intuitionistic fuzzy set (IFS), the Pythagorean fuzzy set (PFS) and the p-rung orthopair fuzzy set (p-ROFS). In order to explore the features of the E-FS concept, set and algebraic operations on E-FSs, average and geometric operations of E-FSs are studied and an E-FS score function is defined. The superiority of the E-FS concept is further confirmed with a score-based decision making technique in which the concepts of FS, IFS, PFS and p-ROFS do not make sense

Mineral lick use by a community of large herbivores in northern Iran

Natural mineral licks are ecologically valuable resources to meet the physiological needs of herbivores, particularly in temperate forests. Importantly, licking sites can harbor high anthropogenic risk for conservation‐dependent herbivores through higher chance of pathogen spillover from livestock and increased levels of poaching risks. However, to the best of our knowledge, there is no information on the mineral lick use in temperate forests of west Asia and the Caucasus where a few threatened deer species exist. We monitored four naturally occurring mineral licks in Central Alborz Protected Area, northern Iran during May–July 2019 using camera traps and analyzed the mineral content of the licking sites. A total of 53 independent mineral lick visits were obtained from only three species of herbivores, i.e., Caspian red deer (Cervus elaphus maral; n = 21), roe deer (Capreolus capreolus; n = 26), and wild pig (Sus scrofa; n = 6). The sex ratio of visiting Caspian red deer was highly skewed toward females (3M:18F), whereas it was more balanced in visiting roe deer (11M:15F). The species‐level distribution of visits corresponded to diurnal and cathemeral for Caspian red deer and for roe deer, respectively, without any evidence of different activity curves. There was a negative nonlinear relationship between the ambient temperature and the visitation rate. Our findings showed that mineral licks are important habitat features for these large herbivores and need to be included in spatial mapping and habitat protection measures

A decision making methodology based on the weighted correlation coefficient in weighted extended hesitant fuzzy environments

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Correlation is an important index in decision-making. In weighted extended hesitant fuzzy sets (WEHFSs) environment, researchers have only defined a class of correlation coefficients between WEHFSs with values in the unit interval [0, 1]. This is not ideal because it does not extend the classical correlation coefficient in the case of classical sets. In fact, the negative values of the interval [−1, 1] are ignored, and such a neglectfulness leads to unreasonable results in decision making. In other words, the existing definitions are unconvincing and lack consistency, which hinder their application potentials. This article addresses this issue by introducing a new class of weighted correlation coefficients of WEHFSs with values in the interval [−1, 1]. Three decision making methodologies based on the weighted correlation coefficients of WEHFSs are compared with the existing methodologies based on their respective correlation coefficients in the unit interval [0, 1]. The comparative analysis shows both the efficiency and effectiveness of the new correlation index

A family of similarity measures for q‐rung orthopair fuzzy sets and their applications to multiple criteria decision making

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.One worthwhile way of expressing imprecise information is the q‐rung orthopair fuzzy sets (q‐ROFSs), which extend intuitionistic fuzzy sets and Pythagorean fuzzy sets. The main goal of this contribution is to further extend the concept of similarity measure for q‐ROFSs, which not only endows the similarity framework with more ability to create new ones but also inherits all essential properties of a logical similarity measure. This contribution proposes a class of novel similarity measures for q‐ROFSs by drawing a general framework of existing q‐ROFS similarity and q‐ROFS distance measures. These q‐ROFS similarity measures enable us to overcome the theoretical drawbacks of the existing measures in the case where they are used individually. In the application part of the contribution, a pattern recognition problem on classification of building materials with a number of known building materials is reconsidered. The study of this particular case shows that the proposed family of similarity measures consistently classify the unknown building material pattern with the same known building material pattern. Then, an experimental case study regarding a problem of classroom teaching quality is re‐examined for the comparison of the performance of proposed similarity measures against the existing ones. The salient features of the proposed similarity measures in comparison to the existing qROFS similarity measures, are as follows: (i) a number of existing q‐ROFS similarity measures are inherently correlation coefficients, and they satisfy only a limited number of essential properties of a comprehensive similarity measure; (ii) several existing q‐ROFS similarity measures lead sometimes to nonlogical results, more specifically, to the same maximum similarity value for different q‐ROFSs; (iii) a variety of existing q‐ROFS similarity measures depend on subjective parameters, which either hinder their application in practice or increase their computational cost. In brief, following this direction of research, we will prove the superiority of the developed similarity measures over the existing ones from both theoretical and experimental viewpoints

Utilizing Generative Adversarial Networks Using a Category of Fuzzy-Based Structural Similarity Indices for Constructing Datasets in Meteorology

Machine learning and image processing are closely related fields that have undergone major development and application in recent years. Machine learning algorithms are being used to develop sophisticated techniques for analyzing and interpreting images, such as object detection, image classification, and image segmentation. One important aspect of image processing is the ability to compare and measure the similarity between different images by providing a way to quantify the similarity between images using various features such as contrast, luminance, and structure. Generally, the flexibility of similarity measures enables fine-tuning the comparison process to achieve the desired outcomes. This is while the existing similarity measures are not flexible enough to address diverse and comprehensive practical aspects. To this end, we utilize triangular norms (t-norms) to construct an inclusive class of similarity measures in this article. As is well-known, each t-norm possesses distinctive attributes that allow for novel interpretations of image similarities. The proposed class of t-norm-based structural similarity measures offers numerous options for decisionmakers to consider various issues and interpret results more broadly in line with their objectives. For more details, in the Experiments section, the proposed method is applied to grayscale and binarized images and a specific experiment related to meteorology. Eventually, the presented diverse case studies confirm the efficiency and key features of the t-norm-based structural similarity

Mineral lick use by a community of large herbivores in northern Iran

Natural mineral licks are ecologically valuable resources to meet the physiological needs of herbivores, particularly in temperate forests. Importantly, licking sites can harbour high anthropogenic risk for conservation-dependent herbivores through higher chance of pathogen spillover from livestock and increased levels of poaching risks. However, to the best of our knowledge, there is no information on the mineral lick use in temperate forests of west Asia and the Caucasus where a few threatened deer species exist. We monitored four naturally occurring mineral licks in Central Alborz Protected Area, northern Iran during May-July 2019 using camera traps and analysed the mineral content of the licking sites. A total of 53 independent mineral lick visits were obtained from only three species of herbivores, i.e., Caspian red deer (Cervus elaphus maral; n=21), roe deer (Capreolus capreolus; n=26) and wild pig (Sus scrofa; n=6). The sex ratio of visiting Caspian red deer was highly skewed towards females (3 M: 18 F) whereas it was more balanced in visiting roe deer (11 M: 15 F). The species-level distribution of visits corresponded to diurnal and cathemeral for Caspian red deer and for roe deer, respectively, without any evidence of different activity curves. There was a negative non-linear relationship between the ambient temperature and the visitation rate. Our findings showed that mineral licks are important habitat features for these large herbivores and need to be included in spatial mapping and habitat protection measures