<p>This study addresses a major challenge faced by farmers in recent years namely selecting the best seeds for irrigation under unpredictable seasonal changes caused by climate change. To address this issue, a new mathematical model called the Bipolar Complex Neutrosophic Fuzzy Set (BCNFS) is introduced. This advancement enables the model to capture both bipolarity (positive and negative effects) and periodicity (seasonal patterns) in agricultural data. As a result, it converts detailed human expertise into accurate mathematical form without losing important information. In BCNFS, membership values are written as complex numbers. Positive values range from 0 to 1 with phase angles between 0 and <InlineEquation ID="IEq1"><EquationSource Format="TEX">$2\pi $</EquationSource><EquationSource Format="MATHML"><math><mrow><mn>2</mn><mi>π</mi></mrow></math></EquationSource></InlineEquation>, expressed as <InlineEquation ID="IEq2"><EquationSource Format="TEX">$[0,1]e^{i\omega [0,2\pi ]}$</EquationSource><EquationSource Format="MATHML"><math><mrow><mrow><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo stretchy="false">]</mo></mrow><msup><mi>e</mi><mrow><mi>i</mi><mi>ω</mi><mo stretchy="false">[</mo><mn>0</mn><mo>,</mo><mn>2</mn><mi>π</mi><mo stretchy="false">]</mo></mrow></msup></mrow></math></EquationSource></InlineEquation>. Negative values range from <InlineEquation ID="IEq3"><EquationSource Format="TEX">$-1$</EquationSource><EquationSource Format="MATHML"><math><mrow><mo>-</mo><mn>1</mn></mrow></math></EquationSource></InlineEquation> to 0 with phase angles between <InlineEquation ID="IEq4"><EquationSource Format="TEX">$-2\pi $</EquationSource><EquationSource Format="MATHML"><math><mrow><mo>-</mo><mn>2</mn><mi>π</mi></mrow></math></EquationSource></InlineEquation> and 0, expressed as <InlineEquation ID="IEq5"><EquationSource Format="TEX">$[-1,0]e^{i\omega [-2\pi ,0]}$</EquationSource><EquationSource Format="MATHML"><math><mrow><mrow><mo stretchy="false">[</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo stretchy="false">]</mo></mrow><msup><mi>e</mi><mrow><mi>i</mi><mi>ω</mi><mo stretchy="false">[</mo><mo>-</mo><mn>2</mn><mi>π</mi><mo>,</mo><mn>0</mn><mo stretchy="false">]</mo></mrow></msup></mrow></math></EquationSource></InlineEquation>. The main contribution of this research is a strong Multi-Criteria Decision Making (MCDM) method based on BCNFS. Several mathematical, geometric, theoretical, and matching distance and similarity measures are developed to evaluate, rank and identify the most suitable seeds under changing seasonal conditions. The proposed model is validated with a practical example and can also be applied to other decision-making problems.</p>

A bipolar complex neutrosophic fuzzy approach using multiple similarity measures for optimal seed selection suitable for all seasons

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2026年8月1日

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Velan Kalaiyarasan,
Krishnan Muthunagai

摘要

This study addresses a major challenge faced by farmers in recent years namely selecting the best seeds for irrigation under unpredictable seasonal changes caused by climate change. To address this issue, a new mathematical model called the Bipolar Complex Neutrosophic Fuzzy Set (BCNFS) is introduced. This advancement enables the model to capture both bipolarity (positive and negative effects) and periodicity (seasonal patterns) in agricultural data. As a result, it converts detailed human expertise into accurate mathematical form without losing important information. In BCNFS, membership values are written as complex numbers. Positive values range from 0 to 1 with phase angles between 0 and $2\pi $ $2 π$ , expressed as $[0,1]e^{i\omega [0,2\pi ]}$ $[0, 1] e^{i ω [0, 2 π]}$ . Negative values range from $-1$ $- 1$ to 0 with phase angles between $-2\pi $ $- 2 π$ and 0, expressed as $[-1,0]e^{i\omega [-2\pi ,0]}$ $[- 1, 0] e^{i ω [- 2 π, 0]}$ . The main contribution of this research is a strong Multi-Criteria Decision Making (MCDM) method based on BCNFS. Several mathematical, geometric, theoretical, and matching distance and similarity measures are developed to evaluate, rank and identify the most suitable seeds under changing seasonal conditions. The proposed model is validated with a practical example and can also be applied to other decision-making problems.