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Several practical problems incorporate uncertainty and erroneous information within its framework of definition. Many distinguished models have already been developed to manage such unreliability, like probabilistic models, and so forth. However, to revitalize the problems where uncertainty is not probabilistic, or the information is vaguely accessible, other tools like fuzzy logic and fuzzy linguistic-based approach have emerged. The efficacy of a linguistic-based approach pertains to a problem of decision making involving qualitative information where precise numerical modeling appears to be inappropriate. The 2-tuple linguistic model formalized by Herrera and Martínez in year 2000, has upgraded several linguistic processes for solving complex decision-making issues. Its successful application in different fields has impelled several researchers to work in its extension. This study aims to offer a systematic literature review on a 2-tuple linguistic model as well as discuss its extensions. The manuscript lays out a brief review of 188 articles published between 2000 and 2019. Based on the 188 selected articles, the following questions can be justified: (1) What is the fuzzy linguistic approach? (2) What is the linguistic model based on the 2-tuples and its foundation? (3) Why the 2-tuple model preferred over other existing classical linguistic models? (4) What are the extensions of the 2-tuple model? Moreover, (5) What are the major applications of a 2-tuple model witnessed in varied disciplines, specifically decision analysis? Therefore, seeking answers to these questions indicate current trends in research. Further, it provides the direction for scholars to work in this field and overcome the challenges associated with the prevailing 2-tuple model. [ABSTRACT FROM AUTHOR]

Several real-world problems employ linguistic-based approaches to handle qualitative data. The set of linguistic terms that is utilized in the problems are mostly alleged to be symmetrically distributed. However, with the advent of time, as the complexity of the problem increases, the equidistant linguistic term set seems improper. Consequently, in such cases, experts often prefer to use the set of the unbalanced linguistic term to direct the appraisal for the problems. In this article, we tend to propose a method that is newly designed to deal with a set of unbalanced linguistic terms. In this direction, we initially propose an algorithm to represent unbalanced linguistic information via a multiplicative linguistic label set that has a global inconsistent linguistic term distribution. Furthermore, in light of the Herrera and Martínez, “2-tuple linguistic model,” we develop a novel 2-tuple approach for the unbalanced linguistic set, which is based on the notion of minimum distance measure. Finally, to validate the proposed model in the physical realm and to demonstrate the functioning of the method, a numerical example is being elucidated. The proposed methodology seeks to indicate a reduction in the computation time and also enhances the decision-makers’ evaluations. [ABSTRACT FROM AUTHOR]

Interferometry is one of the central organizing principles of optics. Key to interferometry is the concept of optical delay, which facilitates spectral analysis in terms of time-harmonics. In contrast, when analyzing a beam in a Hilbert space spanned by spatial modes - a critical task for spatial-mode multiplexing and quantum communication - basis-specific principles are invoked that are altogether distinct from that of 'delay'. Here, we extend the traditional concept of temporal delay to the spatial domain, thereby enabling the analysis of a beam in an arbitrary spatial-mode basis - exemplified using Hermite-Gaussian and radial Laguerre-Gaussian modes. Such generalized delays correspond to optical implementations of fractional transforms; for example, the fractional Hankel transform is the generalized delay associated with the space of Laguerre-Gaussian modes, and an interferometer incorporating such a 'delay' obtains modal weights in the associated Hilbert space. By implementing an inherently stable, reconfigurable spatial-light-modulator-based polarization-interferometer, we have constructed a 'Hilbert-space analyzer' capable of projecting optical beams onto any modal basis. [ABSTRACT FROM AUTHOR]

We have discovered a new domain of optical coherence, and show that it is the third and last member of a previously unreported fundamental triad of coherences. These are unified by our derivation of a parallel triad of coherence constraints that take the form of complementarity relations. We have been able to enter this new coherence domain experimentally and we describe the novel tomographic approach devised for that purpose. [ABSTRACT FROM AUTHOR]

Developing a richer understanding of the various properties of light is central to the field of photonics. One often neglected degree of freedom (DOF) is the second-order correlation of the light field, known as coherence. To make proper use of this DOF, one needs to first obtain information about the field's coherence, which may be characterized through the cross spectral density (CSD) function. We present a measurement of the CSD of a ubiquitous, partially coherent source: a multiple quantum well device in its near-field region, where a photonic structure would commonly encounter the emitted field. We show a departure from the coherence area that is expected from an incoherent source and demonstrate the application of coherent mode decomposition as a way to further analyze the measured results.

A spatial mode analyzer based on a Michelson interferometer with a bucket detector is experimentally implemented. The delay line in the interferometer is an optical implementation of the fractional Fourier transform (fFT) which enables the spatial mode analysis of a given input field in the Hermite-Gaussian (HG) mode basis. Modal weights for both 1D and 2D input fields are experimentally measured. Results for input fields comprising of multiple HG modes are also presented.

Modal analysis of an optical field via generalized interferometry (GI) is a novel technique that treats said field as a linear superposition of transverse modes and recovers the amplitudes of modal weighting coefficients. We use phase retrieval by nonlinear optimization to recover the phase of these modal weighting coefficients. Information diversity increases the robustness of the algorithm by better constraining the solution. Additionally, multiple sets of random starting phase values assist the algorithm in overcoming local minima. The algorithm was able to recover nearly all coefficient phases for simulated fields consisting of up to 21 superpositioned Hermite Gaussian modes from simulated data and proved to be resilient to shot noise.

We have discovered a new domain of optical coherence, and show that it is the third and last member of a previously unreported fundamental triad of coherences. These are unified by our derivation of a parallel triad of coherence constraints that take the form of complementarity relations. We have been able to enter this new coherence domain experimentally and we describe the novel tomographic approach devised for that purpose.