Research article · 2023 · Full text
International Journal of Statistics and Applied MathematicsFuzzy combined effect time quantity dependent data matrix for predicting phytal fauna distribution and diversity
Volume 8(2) · Pages 09–12 · DOI: 10.22271/maths.2023.v8.i2a.939 ↗
Research areasData Mining Algorithms and ApplicationsData Management and Algorithms
Abstract
Author-writtenFuzzy logic can be used to analyse and classify flora and faunal diversity. It uses fuzzy logic to describe richness and complexity of plant and animal life. Fuzzy logic can identify patterns in data to better understand diversity of an ecosystem. This study used a fuzzy combined effect time quantity dependent data matrix to predict the distribution and diversity of phytal fauna in Erayumanthurai coast. The method involved the use of Initial Raw Data Matrix (IRDM), Average Quantity Dependent Data Matrix (AQDM), Refined Quantity Dependent Data Matrices (RQDMs) and Combined Effect Quantity Dependent Data Matrix (CEQDM). Results showed that the high number of fauna was recorded in sites at α = 0.75 level and the faunal ranges were medium at α = 0.5 level. Negative values in the sites of S2, S3, and S4 indicated that faunal composition in these sites was not preferred. This fuzzy combined effect time quantity dependent data matrix was able to predict the exact place that had more anthropogenic disturbance to disturb the diversity and distribution of phytal fauna.
Summary
Source-checkedPlain-language reading of the full paper, prepared with AI and checked against the text. Each point links to the authors' own words.
Why it matters
- Fuzzy logic is a tool used to analyze and classify the richness and complexity of flora and faunal diversity. View evidence ↗
- Understanding phytal faunal diversity is essential for the preservation of biodiversity and the promotion of sustainable development. View evidence ↗
The question
- The study aims to predict the distribution and diversity of phytal fauna on the Erayumanthurai coast using a fuzzy combined effect time quantity dependent data matrix. View evidence ↗
- The research specifically focuses on whether pollution, fishing activities, and physio-chemical parameters disturb the distribution and diversity of phytal fauna. View evidence ↗
What they did
- Phytal faunal samples were collected randomly across nine different stations (S1 through S9). View evidence ↗
- The study counted and recorded various fauna, including isopods, crustaceans, molluscs, polychaetes, and amphipods. View evidence ↗
- The methodology began by creating an Initial Raw Data Matrix (IRDM) with fauna common names as rows and point count locations as columns. View evidence ↗
- The IRDM was transformed into an Average Quantity Dependent Data (AQD) matrix. View evidence ↗
- A Combined Effect Quantity Dependent Data Matrix (CEQD Matrix) was created from the RQD matrices to show the cumulative effect of the entries. View evidence ↗
What they found
- At the α = 0.75 level, the highest number of fauna were recorded at sites S1 and S5, where bivalves and amphipods were dominant. View evidence ↗
- At the α = 0.5 level, faunal ranges were medium at sites S2, S3, and S4, consisting of polychaetes, crabs, and isopods. View evidence ↗
- Low-level fauna distribution was observed at the α = 0.25 level at sites S1, S2, S3, and S4, involving polychaetes, crabs, isopods, and amphipods. View evidence ↗
- Negative values recorded at sites S2, S3, and S4 indicate that the faunal composition in these specific locations was not preferred. View evidence ↗
What it means
- The authors conclude that the fuzzy combined effect time quantity dependent data matrix can accurately predict locations with higher anthropogenic disturbance affecting phytal fauna. View evidence ↗
Visual summary
2 visualsIllustrations explain the paper; charts are replotted from the paper's own table values.
Fuzzy Matrix Transformation Workflow
AI-generated conceptual illustration (various forest insects and arthropods). It explains the idea and does not show study data.
View source evidence ↗
S1 and S4: Amphipods vs Bivalves
Replotted from Table 1 (page 2) of the original paper. Every bar is the paper's own table value.
View source evidence ↗Figures & tables
From the original paper
Table 1
Table 2
Table 3
Figure 1
Figure 2Introduction
Fuzzy logic can be used to analyse and classify different types of flora and faunal diversity. Phytal faunal diversity is a concept that uses fuzzy logic to describe the richness and complexity of plant and animal life. Fuzzy logic can be used to identify patterns in the data, which can be used to better understand the diversity of a particular ecosystem De Cáceres, et al. [1] . Fuzzy logic allows us to think about things in terms of degrees of membership and gradations of similarity Fiorentino Dario et al. [2] ; Bagnaro et al. [3] . In the case of phytal faunal diversity, this means that species are grouped together based on their shared characteristics and the degree of similarity between them. This concept is important to understand in order to preserve biodiversity and promote sustainable development De Cáceres, et al. [1] ; Bandelj et al. [4] . Fuzzy matrices and fuzzy cognitive maps were used by Bart Kosko [5]; Vasantha Kandasamy [6] . They studied on socioeconomic and psychological problems using theory of fuzzy matrices and fuzzy based models. They assumed four categories of matrices such as, initial raw data matrix (IRDM), average time dependent data matrix (ATDM), refined time dependent data matrix (RTDM), and combined effect time dependent data matrix (CETDM), respectively. Afterward these concepts were successively applied in medical sciences, engineering sciences, Industry and biological diversity studies. Raw Data Matrix (IRDM) is essential for biodiversity research because it provides a complete picture of the structure of a particular ecosystem. It includes the abundance, species composition, and distribution of organismal, functional, and taxonomic groups. This information can be used to assess the current state of an ecosystem and make predictions about how it may respond to future changes. Average Quantity Dependent Data Matrix (AQDM) is provides an average value for the abundance of certain species or groups over a period of time. This provides an indication of the relative abundance of different species in a given ecosystem.
Refined Quantity Dependent Data Matrices (RQDMs) is provide more detailed information about the abundance of particular species or groups within a given ecosystem. This data can be used to identify areas of high diversity and to assess the impact of human activities on species distributions. Combined Effect Quantity Dependent Data Matrix (CEQDM) is combines the information from the IRDM, AQDM, and RQDMs to provide a more comprehensive view of the abundance of different species in a given ecosystem Vasantha Kandasamy [6] . Victor Devadoss et al., [7] worked on dimensions of women personality in Chennai using combined effect time dependent data matrix. Narayanamoorthy [8] estimated the maximum age group of silk weaver as bounded labours using fuzzy combined effect time dependent data matrix. Narayanamoorthy et al., [9] obtained maximum age group of endosulfan pesticide victims in Kerela using fuzzy combined effect time dependent-data-matrix. Kokila [10] worked on student's information gathering attitude by applying fuzzy matrix combined effect time dependent data matrix. Jon Arockiaraj and Murali [11] reported that the using fuzzy matrix analysis of seasonal fishing in Cuddalore. Iftikhar et al., [12] estimated the maximum age group of stressed students studying in Higher Education using combined effect time dependent data matrix. Radhika. et al., [13,14] studied that the risk factor of breast cancer and uses in aquaculture by using CETD data matrix analysis. In this study, we used the combined effect time quantity dependent data matrix for the prediction of distribution and diversity of phytal fauna in Erayumanthurai coast. The present study focus on whether the physio-chemical parameters, fishing activities and pollution disturb the diversity and distribution of phytal fauna by using fuzzy combined effect time quantity dependent data matrix.
Preliminaries
This section includes some basic definitions and notations on different types of fuzzy matrices. Definition 2.1: An initial raw data matrix (IRDM) is the collection of initial data into matrix form by taking birds common name as rows and point count sites as the columns. Definition 2.2: An average quantity dependent data matrix (AQDM) is derived by transforming initial raw-data matrix by dividing each row with the percentage difference in given point count sites.
Definition 2.3:
A number of refined quantity dependent data matrices (RQDMs) are derived by varying a parameter 𝛼𝛼∈ [0, 1] and using mean and standard deviation methods. The only entries of refined quantity dependent data matrices are -1, 0 or 1.
Definition 2.4:
A transformation of average quantity dependent data matrix into a number of refined quantity dependent data matrices by varying a parameter𝛼𝛼∈ [0, 1] and using mean and standard deviation is obtained using the following mathematical formulae:
Else if 𝑎𝑎 𝑖𝑖𝑖𝑖 ∈ (𝜇𝜇 𝑖𝑖 -𝛼𝛼𝜎𝜎 𝑖𝑖 , 𝜇𝜇 𝑖𝑖 + 𝛼𝛼𝜎𝜎 𝑖𝑖 ) then 𝑏𝑏 𝑖𝑖𝑖𝑖 = 0
Where 𝜇𝜇 𝑖𝑖 simple mean and𝜎𝜎 𝑖𝑖 is standard deviation of corresponding to each column of the average quantity dependent data matrix, respectively. Definition 2.5: A combination of different refined quantity dependent data matrices by varying 𝛼𝛼∈ [0, 1] gives cumulative effect of all the entries, and known as combined effect quantity dependent data matrix (CETDM).
Observed Attributes with Short Descriptions
The collection of phytal fauna associated with the seaweeds was carried out following the procedure advocated by Azhaguraj et al. [15] . Phytal faunal samples were collected by randomly at each stations (S1, S2, S3, S4 S5, S6, S7, S8, and S9). The faunas of amphipods, polychaetes, molluscs, amphipods, crustaceans and isopods were counted and recorded. The examination of phytal fauna on the Erayumanthurai, revealed the presence of a rich variety of crabs, isopods and amphipods. In addition, a number of polychaetes, gastropods and bivalvia were also present.
Methodology
Step 1: Using entries of phytal faun as common name as rows and point count locations as columns, we provide the raw data as a matrix.
Step 2: The initial matrix is transformed into an average quantity dependent data (AQD) matrix in the second stage.
Step 3: To make the computations simpler and easier, we apply basic average techniques in the third step to transform the above-average quantity-dependent data matrix into a matrix with entries𝑏𝑏 𝑖𝑖𝑖𝑖 ∈ {-1,0,1}.This matrix has the term Refined Quantity Dependent Data Matrix (RQD Matrix).
Step 4: Using the RQD matrices, we create the Combined Effect Quantity Dependent Data Matrix (CEQD Matrix), which shows the cumulative effect of all these entries.
Step 5: Finally, we derive the CEQD matrix's row sums. Each stage's tables are self-explanatory. Using Python, the graphs of the RQD matrix and CEQD matrix are shown. Obtaining various refined quantity dependent data matrices by taking 𝛼𝛼 = 0.25, 0.5, 0.75 and computing their related row sums as column matrices Obtained RQD matrix for 𝛼𝛼 = 0.25 Obtained Row Sum Matrix
Obtained RQD matrix for 𝛼𝛼 = 0.5 Obtained Row Sum Matrix 1 1 1 0 0 0 1 0 1 3 0 1 0 0 1 0 0 0 0 1
Obtained RQD matrix for 𝛼𝛼 = 0.75 Obtained Row Sum Matrix 1 1 1 0 0 0 1 0 1 3 0 1 0 0 0 0 0 0 0 1 0 0 1 1 0 1 1 0 1 2 0 0 0 1 0 1 1 0 0 1 0 1 0 1 1 1 1 1 1 2 0 0 0 0 0 1 0 0 0 0
Finally, by combining all three matrices, the Combined Effect Quantity Dependent Data Matrix (CEQD -Matrix) is generated, which provides the Cumulative effect of all these entries. This yields the CEQD-Matrix as well as the CEQD Row matrix:
Obtained CEQD matrix Obtained Row Sum Matrix
Fig 1:
The maximum phytal fauna is depicted graphically for 𝛼𝛼 = 0.25, 0.5, and 0.75.
Plotting Graph for the CEQD to Depicting phytal fauna
Combining distinct refined quantity dependent data matrices by altering 𝛼𝛼∈ [0, 1] yields a combined effect quantity dependent data matrix, which represents the cumulative impact of all the entries. The combined effect quantity dependent data matrix is essential in showing the combine effect of all produced RQD matrices for various values of 𝛼𝛼 = 0.25, 0.5 and 0.75.
Fig 2:
The combined effect quantity dependent data matrix of. 𝛼𝛼 = 0.25, 0.5 and 0.75.
Conclusion
From the above studies and depicted fuzzy graphs for different values of α = 0.25, 0.
Acknowledgement
The authors acknowledge the support given by the Management, St. Xavier's College (Autonomous), Palayamkottai, India.
Figures and tables from the paper
| Common Name | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 |
|---|---|---|---|---|---|---|---|---|---|
| Amphipods | 205 | 183 | 142 | 76 | 62 | 49 | 162 | 147 | 198 |
| Isopods | 34 | 36 | 22 | 43 | 29 | 45 | 65 | 69 | 42 |
| Crab | 28 | 65 | 1 | 12 | 18 | 14 | 17 | 15 | 10 |
| Polychaetes | 19 | 46 | 15 | 21 | 17 | 19 | 19 | 27 | 21 |
| Bivalves | 32 | 140 | 35 | 132 | 181 | 123 | 125 | 302 | 203 |
| Gastropods | 35 | 63 | 28 | 82 | 71 | 89 | 46 | 24 | 17 |
Table text extracted from the original PDF; superscript letters are shown inline. The original table image is below.
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| Common Name | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 |
|---|---|---|---|---|---|---|---|---|---|
| Amphipods | 2.05 | 1.83 | 1.42 | 0.76 | 0.62 | 0.49 | 1.62 | 1.47 | 1.98 |
| Isopods | 0.34 | 0.36 | 0.22 | 0.43 | 0.29 | 0.45 | 0.65 | 0.69 | 0.42 |
| Crab | 0.28 | 0.65 | 0.01 | 0.12 | 0.18 | 0.14 | 0.17 | 0.15 | 0.1 |
| Polychaetes | 0.19 | 0.46 | 0.15 | 0.21 | 0.17 | 0.19 | 0.19 | 0.27 | 0.21 |
| Bivalves | 0.32 | 1.4 | 0.35 | 1.32 | 1.81 | 1.23 | 1.25 | 3.02 | 2.03 |
| Gastropods | 0.35 | 0.63 | 0.28 | 0.82 | 0.71 | 0.89 | 0.46 | 0.24 | 0.17 |
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| — | S1 | S2 | S3 | S4 | S5 | S6 | S7 | S8 | S9 |
|---|---|---|---|---|---|---|---|---|---|
| Mean | 0.58833 | 0.88833 | 0.405 | 0.61 | 0.63 | 0.565 | 0.72333 | 0.97333 | 0.81833 |
| Standard Deviation | 0.71843 | 0.58901 | 0.51072 | 0.44793 | 0.62106 | 0.42141 | 0.59106 | 1.1159 | 0.92549 |
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