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    Applied optimization problems
    (Elsevier, 2024) Rahmaniperchkolaei, Bijan; Taeeb, Zohreh; Shahriari, Mohammadreza; Lotfi, Farhad Hosseinzadeh; Saati, Saber
    Applied Optimization, a pivotal discipline in various fields, involves the strategic utilization of mathematical techniques to enhance decision-making, resource allocation, and problem-solving across diverse domains. This abstract highlights the significance of Applied Optimization by delving into its multifaceted importance. In an era marked by intricate challenges and resource constraints, Applied Optimization emerges as a potent tool to streamline complex processes. Its ability to identify optimal solutions within the constraints of real-world scenarios empowers organizations and individuals to maximize efficiency, minimize costs, and achieve desired outcomes. From industrial engineering and supply chain management to finance, healthcare, and beyond, Applied Optimization offers tailored solutions that resonate with specific challenges. This abstract underlines that the true essence of Applied Optimization lies not just in mathematical elegance but in its tangible impact. By optimizing processes, decisions, and strategies, Applied Optimization accelerates progress, propelling businesses toward competitive advantage and societal sectors toward sustainable development. This chapter, dedicated to exploring the realm of Applied Optimization, delves into its methodologies, models, and practical applications. It underscores the interconnectedness of optimization with the modern world, emphasizing that its impact extends far beyond theoretical constructs. Through real-world case studies and in-depth analyses, readers gain insights into how Applied Optimization reshapes industries and transforms societies. In conclusion, Applied Optimization stands as an indispensable tool that transcends disciplines and permeates every facet of our lives. This abstract encapsulates its importance as an enabler of efficient resource utilization, strategic decision-making, and the attainment of optimal outcomes in an ever-evolving world. © 2024 Elsevier Inc. All rights reserved.
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    Bipolar fuzzy Fourier transform for bipolar fuzzy solution of the bipolar fuzzy heat equation
    (University of Sistan and Baluchestan, 2022) Akram, Muhammad Saeed; Bilal, Muhammad Hamza; Shahriari, Mohammadreza; Allahviranloo, Tofigh
    This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology’s liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposed methodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics. © 2024, University of Sistan and Baluchestan. All rights reserved.
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    Bipolar fuzzy Fourier transform for bipolar fuzzy solution of the bipolar fuzzy heat equation
    (University of sistan & baluchestan, 2024) Akram, M.; Bilal, M.; Shahriari, Mohammadreza; Allahviranloo, Tofigh
    This article presents the exact solution of a bipolar fuzzy heat equation based on bipolar fuzzy Fourier transform under generalized Hukuhara partial (gH-p) differentiability. A bipolar fuzzy Fourier transform is defined, and the related key propositions and fundamental characteristics are discussed. Further, a bipolar fuzzy heat equation model is constructed using gH-differentiability, and the analytical solution of a bipolar fuzzy heat equation with bipolar fuzzy Fourier transform approach is examined. Some illustrative examples are provided to check the suggested methodology's liability and efficiency. The type of differentiability and the solution of the bipolar fuzzy heat equation are shown graphically, demonstrating the versatility of the proposed methodology and elucidating the impact of differentiability types on the solution behavior of the bipolar fuzzy heat equation. Additionally, the impact of different parameters on the solution behavior is analyzed, revealing insights into the underlying dynamics.
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    Data optimization and analysis
    (Elsevier, 2024) Shahriari, Mohammadreza; Hosseinzadeh Lotfi, Farhad; Rahmaniperchkolaei, Bijan; Taeeb, Zohreh; Saati, Saber
    Efficient decision-making within any organization is not just a possibility, but a reality, thanks to the practicality of meticulous data analysis. This chapter delves deeply into an array of data analysis methods that prove to be invaluable in this pursuit. The central focus is directed toward the data envelopment analysis (DEA) technique. This potent tool, which serves as a cornerstone in evaluating the performance of a cluster of analogous decision-making units (DMUs), is not just a theoretical concept, but a practical solution. Throughout the chapter's course, we delve into a diverse range of models that encompass efficiency assessment, benchmarking, ranking, and advancement. Additionally, regression analysis is explored for each DMU. These models inherently accommodate multiple inputs and outputs, thereby facilitating a comprehensive evaluation. It becomes distinctly apparent that intricate DMUs or those governed by specific indicator conditions necessitate the employment of sophisticated models, as classical paradigms might fall short in such intricate scenarios. Furthermore, the chapter casts a spotlight on the support vector machine (SVM) method. SVM, a versatile approach for the classification of data points into discrete sets, is not just a single-use tool, but a versatile solution. It produces a set of rules that enable precise predictions regarding the categorization of a new data point within one of these predefined sets. By harnessing the power of SVM, organizations are not just limited to one type of data analysis, but can proficiently classify incoming data and derive informed decisions rooted in these discerning categorizations. This chapter provides readers with a profound understanding of the methodologies that underlie DEA and SVMs. These instrumental tools empower organizations to extract profound insights from their data reservoirs, thereby equipping them to navigate intricate decision terrains with unwavering assurance. © 2024 Elsevier Inc. All rights reserved.
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    Discrete and combinatorial optimization
    (Elsevier, 2024) Rahmaniperchkolaei, Bijan; Taeeb, Zohreh; Shahriari, Mohammadreza; Lotfi, Farhad Hosseinzadeh; Saati, Saber
    In the realm of practical scenarios, numerous complex situations inherently align with the framework of integer programming (IP). These real-life challenges emerge when the linear programming assumption of divisibility proves inapplicable. An integer programming problem manifests as an extension of linear programming (LP), wherein some or all decision variables are constrained to non-negative integer values. However, the unfortunate reality is that solving integer programming problems tends to be considerably more intricate than addressing standard linear programming challenges. A plethora of vital optimization problems within diverse domains find their most fitting representation through either graphical or grid-based models. These models offer an intuitive approach to understanding and solving intricate optimization quandaries. The focus of this chapter lies in the exploration of integer programming problems and the transportation problem, which emerges as a distinct facet of linear programming. The transportation problem stands as one among the specialized structures of linear programming, garnering extensive applicability in real-world scenarios. It serves as a pivotal tool for efficiently allocating resources, optimizing supply chains, and devising strategies for distribution and logistics. This chapter embarks on a journey to decipher the intricacies of integer programming, uncovering its significance in encapsulating real-life dilemmas where discrete decision-making is fundamental. By delving into the nuances of the transportation problem, we gain insights into a practical manifestation of linear programming's potential, further enriching our understanding of optimization techniques in the context of real-world complexities. © 2024 Elsevier Inc. All rights reserved.
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    An interval-valued Pythagorean fuzzy group AHP-PROMETHEE approach for organizational behavior assessment and ranking in higher education of Iran considering environmental criteria
    (Springer, 2023) Torkzadeh, Jafar; Niroomand, Sadegh; Shahzadi, Sundas; Allahviranloo, Tofigh; Shahriari, Mohammadreza
    In this paper, we aim to apply the environmental criteria and to assess and rank various higher education institutes of Iran based on the impact of the environmental criteria on their organizational behavior. This is a new aspect of organizational behavior of higher education sector that, to the best of our knowledge, has not been considered earlier in the literature. For this aim, a set of experts of the field is selected and are asked to compare the criteria pair wisely using linguistic terms and also evaluate the impact of each criterion on each of the considered higher education institutes of Iran. Then, to respect the uncertain nature of such evaluations, the linguistic terms are converted to the form of interval-valued Pythagorean fuzzy values. An interval-valued Pythagorean fuzzy AHP approach is used to obtain the importance weight of each criterion. Then an interval-valued Pythagorean fuzzy group PROMETHEE approach is developed to assess and rank various higher education institutes of Iran. According to the obtained results from the proposed approach and the approaches of the literature in comparison study, the organizational behavior of the public universities of Iran is more affected by the considered set of environmental criteria.
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    Mathematical programming
    (Elsevier, 2024) Hosseinzadeh Lotfi, Farhad; Saati, Saber; Shahriari, Mohammadreza; Rahmaniperchkolaei, Bijan; Taeeb, Zohreh
    Optimization stands as an exceptional cornerstone, harnessed extensively and with a resounding impact to confront the multifaceted challenges of the tangible world. Its expansive repertoire of applications, complemented by its innate ability to unfurl optimal solutions, has bestowed upon it an inherent allure, captivating a diverse spectrum of enthusiasts traversing the intricate landscape of research. Spanning domains as varied as the fundamental sciences, engineering marvels, strategic management paradigms, agricultural landscapes, and the ecological tapestry of environmental studies, optimization resonates as a unifying force in problem-solving endeavors. Nestled within the confines of this chapter is a captivating odyssey, a journey that navigates through the bedrock of optimization's essence. We embark upon this voyage by peeling back the layers of fundamental concepts that lay the groundwork for this dynamic field. From this foundational standpoint, we plunge headfirst into the realm of optimization problems, where two distinctive categories beckon: the structured world of linear programming and the intricate enigma of nonlinear programming. As we unravel the mysteries that enshroud these two archetypes, we simultaneously unveil the symphony of solution algorithms meticulously tailored to navigate each unique category's labyrinthine complexities. In our pursuit to instill a comprehensive comprehension, we seamlessly weave tangible examples throughout the narrative tapestry. These instances of real-world conundrums serve as eloquent companions to the theoretical frameworks, acting as guiding beacons to illuminate the path for readers. Through this harmonious marriage of theory and application, we aspire to bestow upon our readers the twin gifts of knowledge and proficiency—a twin that empowers them to not only navigate the intricate terrain of optimization but also to rise as adept problem solvers, armed with the analytical acumen and innovative strategies requisite to surmount the most formidable challenges that reality presents. © 2024 Elsevier Inc. All rights reserved.
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    Uncertain optimization (with a special focus on data envelopment analysis)
    (Elsevier, 2024) Amirteimoori, Alireza; Allahviranloo, Tofigh; Shahriari, Mohammadreza
    Uncertain optimization refers to contexts where there is uncertainty in models and data. It potentially has various applications in different domains such as portfolio selection, inventory management, pollution reduction, sustainable development, resource allocation and reallocation, and performance analysis. In real life, decisions often need to be made under unknown scenarios. In our terminology, uncertainty refers to the variability of data and optimization refers to the analysis and solution of a problem that involves optimizing an objective, given a set of constraints. This chapter deals with uncertain optimization problems with a special emphasis on data envelopment analysis (DEA). Since many books discuss fuzzy optimization problems, only the stochastic type of uncertainty in data and models is considered here.