[Paper Review] Interval Valued Bipolar Neutrosophic Sets and Their Application in Pattern Recognition

İrfan Deli̇, Yusuf Şubaş+2 more|arXiv (Cornell University)|Jan 4, 2016

Multi-Criteria Decision Making9 citations

TL;DR

This paper introduces Interval Valued Bipolar Neutrosophic Sets (IVBN-sets), a novel extension of fuzzy, bipolar fuzzy, neutrosophic, and bipolar neutrosophic sets that enhances flexibility in handling uncertain information during decision-making. By incorporating interval-valued truth, indeterminacy, and falsity degrees for both positive and negative preferences, IVBN-sets enable more precise modeling of complex uncertainty, particularly in pattern recognition tasks.

ABSTRACT

Interval valued bipolar neutrosophic set(IVBN-set) is a new generalization of fuzzy set, bipolar fuzzy set, neutrosophic set and bipolar neutrosophic set so that it can handle uncertain information more flexibly in the process of decision making.

Motivation & Objective

• To address the limitations of existing fuzzy and neutrosophic sets in representing complex, uncertain, and bipolar (positive/negative) information.
• To develop a new mathematical framework that integrates interval-valued membership degrees with bipolarity for improved decision-making under uncertainty.
• To extend the capabilities of neutrosophic sets by incorporating both positive and negative assessments using intervals for greater flexibility.
• To apply the proposed IVBN-set model to pattern recognition, demonstrating its effectiveness in handling real-world uncertainty.

Proposed method

• Proposes a new set-theoretic model, the Interval Valued Bipolar Neutrosophic Set (IVBN-set), defined by interval-valued truth, indeterminacy, and falsity membership functions for both positive and negative domains.
• Defines operations such as union, intersection, complement, and score function for IVBN-sets to support computational processing.
• Introduces a score function to rank IVBN-subssets, enabling comparison and selection in decision-making processes.
• Applies the IVBN-set model to a pattern recognition problem by computing similarity measures between IVBN-subssets and reference patterns.
• Uses interval-valued parameters to represent uncertainty in both positive and negative evaluations, allowing for more nuanced representation than point-valued models.
• Employs a similarity measure based on the distance between IVBN-subssets to classify patterns in uncertain environments.

Experimental results

Research questions

• RQ1 How can interval-valued membership degrees improve the representation of uncertainty in bipolar neutrosophic sets?
• RQ2 What mathematical operations are necessary to support decision-making with IVBN-sets?
• RQ3 How does the IVBN-set model enhance pattern recognition performance compared to existing fuzzy and neutrosophic models?
• RQ4 What is an effective similarity measure for IVBN-sets in classification tasks?
• RQ5 Can IVBN-sets effectively model both positive and negative assessments with interval-valued uncertainty?

Key findings

• The IVBN-set model provides a more flexible framework for representing uncertain information by incorporating interval-valued truth, indeterminacy, and falsity degrees.
• The proposed operations on IVBN-sets, including score functions and similarity measures, enable systematic comparison and decision-making.
• The model effectively captures both positive and negative evaluations of elements, enhancing its applicability in real-world decision scenarios.
• The application to pattern recognition demonstrates that IVBN-sets can handle complex uncertainty more effectively than traditional fuzzy or neutrosophic models.
• The use of interval-valued parameters allows for a more accurate reflection of imprecise human judgments in decision-making processes.
• The score function and similarity measure enable reliable ranking and classification of patterns under uncertainty.