In the realm of decision-making, the delineation of uncertainty and ambiguity within data is a pivotal challenge. This study introduces a novel approach through complex intuitive hesitant fuzzy sets (CIHFS), which offers a unique multidimensional perspective for data analysis. The CIHFS framework is predicated on the concept that membership degrees reside within the unit disc of the complex plane, thereby providing a more nuanced representation of data. This method stands apart in its ability to simultaneously process and analyze data in a two-dimensional format, incorporating additional descriptive elements known as phase terms into the membership degrees. The study is bifurcated into two primary phases. Initially, a possibility degree measure is proposed, facilitating the ranking of numerical values within the CIHFS context. Subsequently, the development of innovative operational rules and aggregation operators (AOs) is undertaken. These AOs are instrumental in amalgamating diverse options within a CIHFS framework. The research dissects and deliberates on various AOs, including weighted average (WA), ordered weighted average (OWA), weighted geometric (WG), ordered weighted geometric (OWG), hybrid average (HA), and hybrid geometric (HG). Furthermore, the study extends to the realm of multi-criteria decision making (MCDM), where it proposes a methodology utilizing intricate intuitive and fuzzy information. This methodology emphasizes the objective management of weights, thereby enhancing the decision-making process. The study's findings hold significant implications for the optimization of resources and decision-making strategies, providing a robust framework for the application of CIHFS in practical scenarios.

This investigation delves into the critical challenges of urban development and management, employing a comprehensive evaluation of four strategic alternatives: transit-oriented development, green infrastructure investment, smart city technologies, and community-based development. These alternatives are rigorously assessed against a set of eight meticulously chosen criteria. Distinct from conventional analyses, the study adopts the sophisticated Criteria Importance Through Inter-criteria Correlation (CRITIC)-Weighted Aggregated Sum Product Assessment (WASPAS) methodology, utilizing spherical fuzzy sets (SFS). This approach mitigates uncertainties inherent in decision-making processes, thereby refining the accuracy of the evaluation. The CRITIC-WASPAS method, with its innovative application in this context, augments the precision of the assessments, yielding a detailed appraisal of each alternative's merits and limitations. Through assigning weighted criteria and systematically ranking these alternatives, the study furnishes pivotal insights for urban planners and policymakers. This contribution is instrumental in guiding decisions that promote resilience, equity, and environmental sustainability in urban environments. The novel integration of the CRITIC-WASPAS method in this domain not only propels the field forward but also lays a robust foundation for informed and effective decision-making. The outcomes of this research are poised to significantly impact the discourse on sustainable urban development, offering a data-driven framework that is essential for sculpting the future of cities amidst evolving urban challenges.

The present work is concerned with a traction-free thermoelastic half-space subjected to a known axisymmetric temperature distribution. The thermoelastic interactions inside the medium are investigated by employing the fractional order theory of thermoelasticity. The problem is solved by using Laplace's and Hankel's transforms. The inverse transforms are computed numerically. The variations of temperature, displacements, and stresses inside the half-space are investigated. The field variables for a particular material are graphically presented. Comparisons are made within the theory in the presence and absence of fractional order parameter.

In the realm of sustainable urban development, a paramount focus is placed on the amalgamation of environmental conservation, the integration of smart technology, and the promotion of social inclusivity. This approach advocates for transit-oriented development, the establishment of resilient infrastructure, and the active engagement of communities. A critical balance is sought between economic viability and adaptive governance, aiming to cultivate cities that are simultaneously environmentally conscious, economically vibrant, and socially equitable. Within this context, Multiple Attribute Decision Making (MADM) emerges as a pivotal tool, streamlining decision processes through the quantitative evaluation of alternatives against criteria such as environmental impact and social inclusivity. MADM plays an instrumental role in ensuring effective resource allocation, thereby fostering resilient infrastructure and optimizing the equilibrium between economic growth and sustainability in urban planning. This study delves into an advanced methodology for addressing uncertainties in decision-making, employing Picture Fuzzy Sets (PFSs), articulated through the meticulous application of the Measurement Alternatives and Ranking according to Compromise Solution (MARCOS). The utilization of the MARCOS strategy in decision-making is underscored by its proven robustness as a tool for pinpointing the optimal objective. This method integrates diverse aggregation strategies to adeptly navigate complex decision scenarios characterized by multiple criteria. To illustrate the adaptability and efficacy of the proposed methodology, a numerical case study is presented, offering a vivid demonstration of its practical application in the field of urban development.

This article introduces magneto-thermoelastic exchanges in an unbounded medium with a spherical cavity. A refined multi-time-derivative dual-phase-lag thermoelasticity model is applied for this reason. The surface of the spherical hole is considered traction-free and under both constant heating and external magnetic field. A generalized magneto-thermoelastic coupled solution is developed utilizing Laplace’s transform. The field variables are shown graphically and examined to demonstrate the impacts of the magnetic field, phase-lags, and other parameters on the field quantities. The present theory is examined to assess its validity including comparison with the existing literature.

The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.