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Solar Panel Selection using Extended WASPAS with Disc Intuitionistic Fuzzy Choquet Integral Operators: CASPAS Methodology

Mahmut Can Bozyiğit, Mehmet Ünver

TL;DR

This paper addresses solar panel selection where multiple criteria interact in complex ways. It develops CASPAS, a Choquet integral-based extension of WASPAS that leverages disc intuitionistic fuzzy sets with a radius function to model interdependencies among criteria. The framework introduces disc intuitionistic fuzzy Choquet integral operators and provides a full methodological pipeline—from expert linguistic inputs to fuzzy measures and significance degrees—to produce robust rankings. Empirical analyses show CASPAS can yield more accurate and consistent decisions than additive approaches, with results aligning with C-IF TOPSIS and C-IF VIKOR under various conditions, advancing decision support for renewable energy applications.

Abstract

Renewable energy is crucial for addressing the growing energy demands of modern society while mitigating the adverse effects of climate change. Unlike fossil fuels, renewable energy sources such as solar, wind, hydro, geothermal, and biomass are abundant, sustainable, and environmentally friendly. This study focuses on addressing a critical challenge in renewable energy decision-making by developing a novel framework for optimal solar panel selection, a key component of sustainable energy solutions. Solar panel selection involves evaluating multiple interdependent criteria, such as efficiency, cost, durability, and environmental impact. Traditional multi-criteria decision-making (MCDM) methods often fail to account for the interdependencies among these criteria, leading to suboptimal outcomes. To overcome this limitation, the study introduces the Choquet Aggregated Sum Product Assessment (CASPAS) method, a Choquet integral-based MCDM approach that incorporates fuzzy measures to model interactions among criteria. CASPAS generalizes the Weighted Aggregated Sum Product Assessment (WASPAS) method, thereby enhancing decision-making accuracy and reliability. This study also introduces the concept of disc intuitionistic fuzzy set (D-IFS), a generalization of the concept of circular intuitionistic fuzzy set, which employ a radius function capable of assigning varying values to individual elements instead of relying on a fixed radius. Recognizing that traditional weighted aggregation operators neglect the interaction among criteria, this study proposes disc intuitionistic fuzzy Choquet integral operators by incorporating the concept of fuzzy measures, which are effective in modeling such interactions. The proposed method is applied to a renewable energy problem on selecting optimal solar panels.

Solar Panel Selection using Extended WASPAS with Disc Intuitionistic Fuzzy Choquet Integral Operators: CASPAS Methodology

TL;DR

This paper addresses solar panel selection where multiple criteria interact in complex ways. It develops CASPAS, a Choquet integral-based extension of WASPAS that leverages disc intuitionistic fuzzy sets with a radius function to model interdependencies among criteria. The framework introduces disc intuitionistic fuzzy Choquet integral operators and provides a full methodological pipeline—from expert linguistic inputs to fuzzy measures and significance degrees—to produce robust rankings. Empirical analyses show CASPAS can yield more accurate and consistent decisions than additive approaches, with results aligning with C-IF TOPSIS and C-IF VIKOR under various conditions, advancing decision support for renewable energy applications.

Abstract

Renewable energy is crucial for addressing the growing energy demands of modern society while mitigating the adverse effects of climate change. Unlike fossil fuels, renewable energy sources such as solar, wind, hydro, geothermal, and biomass are abundant, sustainable, and environmentally friendly. This study focuses on addressing a critical challenge in renewable energy decision-making by developing a novel framework for optimal solar panel selection, a key component of sustainable energy solutions. Solar panel selection involves evaluating multiple interdependent criteria, such as efficiency, cost, durability, and environmental impact. Traditional multi-criteria decision-making (MCDM) methods often fail to account for the interdependencies among these criteria, leading to suboptimal outcomes. To overcome this limitation, the study introduces the Choquet Aggregated Sum Product Assessment (CASPAS) method, a Choquet integral-based MCDM approach that incorporates fuzzy measures to model interactions among criteria. CASPAS generalizes the Weighted Aggregated Sum Product Assessment (WASPAS) method, thereby enhancing decision-making accuracy and reliability. This study also introduces the concept of disc intuitionistic fuzzy set (D-IFS), a generalization of the concept of circular intuitionistic fuzzy set, which employ a radius function capable of assigning varying values to individual elements instead of relying on a fixed radius. Recognizing that traditional weighted aggregation operators neglect the interaction among criteria, this study proposes disc intuitionistic fuzzy Choquet integral operators by incorporating the concept of fuzzy measures, which are effective in modeling such interactions. The proposed method is applied to a renewable energy problem on selecting optimal solar panels.
Paper Structure (19 sections, 3 theorems, 48 equations, 8 figures, 7 tables)

This paper contains 19 sections, 3 theorems, 48 equations, 8 figures, 7 tables.

Table of Contents

  1. Intruduction
  2. Literature research
  3. A comparison of C-IFSs and D-IFSs
  4. A comparison of WASPAS and CASPAS approaches
  5. Types of solar panels
  6. Disc Intuitionistic Fuzzy Sets
  7. Disc Intuitionistic fuzzy Choquet integral operator
  8. An Application to Solar Panels
  9. An assessment of the types of solar panels
  10. CASPAS approach
  11. A numerical example
  12. Assessment of performance
  13. Sensitivity analysis
  14. Validity analysis
  15. Comparative Analysis
  16. ...and 4 more sections

Key Result

Theorem 1

Consider a collection of D-IFVs denoted as $\{\theta_k=\langle (\mu_{\theta_k},\nu_{\phi_k});r_{\theta_k}\rangle:k=1,\ldots,m\}$. $\hbox{D-IFCAIO}_q^\tau(\theta_1,\ldots,\theta_m)$ and $\hbox{D-IFCAIO}_p^\tau(\theta_1,\ldots,\theta_m)$ are also a D-IFV and can be expressed by and respectively where the sequence $\{\theta_{(k)}\}_{k=0}^m$ indicates the indices permuted such that $\theta_{(1)}\pre

Figures (8)

  • Figure 1: Types of renewable energy
  • Figure 2: Global solar photovoltaic production data by region between 2014 and 2022
  • Figure 3: Timeline of the development of solar panels
  • Figure 4: Comparison of C-IFSs and D-IFSs
  • Figure 5: Flowchart of CASPAS method
  • ...and 3 more figures

Theorems & Definitions (23)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Remark 1
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • ...and 13 more