Linguistic Quantifiers Research Articles

Product selection by consumers utilizing the membership values

Assessment and assortment of the most favorable, competent, and trustworthy products is getting to be more and more important for businesses in the current scenario, so the majority of the production industries do their utmost to achieve the requirements, standards, and expenditure patterns of the consumer to attain their expectations. Approaches are made to fulfill the needs of the consumer, as shown by the creation of diverse technologies for improving the capability to manage complex optimizations regarding decision attributes that involve uncertainty. The procedure of detecting the best alternative from all the feasible options is the basis of the decision-making problem. This article recommended two approaches: (a) multi-objective decision making by utilizing fuzzy technique and (b) fuzzy TOPSIS (Technique for Ordering Preferences by Similarity to Ideal Solution) method for choosing the best product while many products with many attributes are present in the marketplace. As per the need of the customer priority and their satisfaction level, this paper used linguistic quantifiers to evaluate the weight of the objective that is represented in triangular or trapezoidal fuzzy numbers. To demonstrate the technique used for the suggested approaches a case study was conducted. The simulation result shows a specific path that fuzzy logic can evolve in the problem of decision making as well as in the planning process in the product selection practice. Solutions obtained by employing both techniques were compared, which urges that the fuzzy TOPSIS approach provides more accurate information than the fuzzy MODM (multi-objective decision making) approach to find the best product from among many available products. This work helps to assist the managers to adopt suitable techniques while planning to design the product according to the customer requirements so that the consumer can get the best product as per their objectives.

Mitigating impact of risks on economic integration between entities in agrifood supply chain

The paper aims to assess and reduce the risks associated with infrastructure, financial, natural and environmental, farm management, and political changes among smallholders in tomato supply chain entities. Uncertainties related to the producer, buyer, infrastructure, finance, natural and environmental, management, and political changes in STSC take into account risk levels' assessment. These threats were assessed using Fuzzy Linguistic Quantifier Order Weighted Aggregation (FLQOWA) model. The obtained results showed the level of risk arising in production, cooperation, infrastructure, and financial issues. At the same time, measures to reduce risk levels were taken in the study. According to the results, applying "written contract" and "insurance" to collaborative relationships to reduce risk levels has been shown to reduce risks to 0.6 coefficients. The results obtained from this investigation will have a positive effect if policymakers use the applications to increase the economic cooperation between the subjects in STSC.

Risk Mitigation Strategies in the Tomato Supply Chain

Tomatoes produced by smallholders in the summer season in Uzbekistan provide a significant part of the population’s demand for tomato products. However, tomato production in smallholders is based on the principles of the free market economy and is operating at high risk. The paper aims to assess and reduce the level of risks associated with infrastructure, financial, natural and environmental, farm management and political changes among entities in the smallholder tomato supply chain. Uncertainties related to producer, buyer, infrastructure, finance, natural and environmental, management and political changes are taken into account in the assessment of risk levels. These threats were assessed using Fuzzy Linguistic Quantifier Order Weighted Aggregation (FLQOWA) model. The obtained results showed that the level of risk arising in production, cooperation, infrastructure and financial issues was high. At the same time, measures to reduce risk levels were taken in the study. According to the results, application “written contract” and “insurance” to collaborative relationships to reduce risk levels has been shown to reduce risks until 0.6 coefficients. The results obtained from this investigation will have a positive effect if policy makers use the applications to increase the economic cooperation between the subjects in STSC.

Clustering using ordered weighted averaging operator and 2-tuple linguistic model for hotel segmentation: The case of TripAdvisor

With the growth of online tourism, it is important to analyze the reviews left by numerous customers on social networks to improve the hotel's online reputation. Hotel segmentation based on online reviews has attracted an increasing interest from many academics. The problem is that many hotel segmentation models overlook the fact that some customers focus on positive reviews when choosing a hotel, while others focus on negative ones. To address this shortcoming, this paper develops a novel approach to classify hotels using the ordered weighted averaging (OWA) operator, the 2-tuple linguistic model, and K-means clustering. The proposed approach has been evaluated with a real dataset from TripAdvisor, which contains more than 50 million customer online reviews on eight aspects of the hotel. The results show that the proposed model can produce denser and more separated clusters than the model without linguistic quantifiers. From a business point of view, this model enables hotels to distinguish customers' perceptions (from the less demanding to the most demanding) about their eight aspects, allowing them to specify which of them need to be improved and develop strategies more quickly. At the same time, it introduces a new way of ranking hotels online, allowing customers to create personalized rankings of hotels based on their degree of demand for various hotel aspects (better location, cleaner rooms, etc.) rather than the average ratings, so that they can select the most suitable hotels more quickly.

A Hierarchical Approach to Interpretability of TS Rule-Based Models

Interpretability of fuzzy rule-based models has always been of significant interest to the research community and the research in this area led to a number of far-reaching results. In this study, we briefly revisit the methodology and concepts of interpretability of Takagi–Sugeno (T-S) rule-based models and develop a conceptual framework involving several levels at which rules are interpreted. The layers at which interpretability is positioned are structured hierarchically by starting with the initial fuzzy set level (originating from the design of the rules), moving to information granules of finite support (where interval calculus is engaged) and finally ending up with symbols built at the higher level. As T-S rule-based models are endowed with local functions forming the conclusion parts of the rules, with the use of the principle of justifiable granularity, we develop a way of forming an interpretable conclusion in the form of information granule. To facilitate interpretability of conditions of the rules, multidimensional fuzzy sets (coming as a result of clustering) are decomposed into a Cartesian product of 1-D fuzzy sets and the quality of the resulting decomposition is evaluated. The quality of granular rules is assessed by analyzing the relationship between specificity of condition and conclusion information granules. The rules emerging at the level of symbols are further interpreted by engaging linguistic approximation, which helps approximate a collection of linguistic terms of subconditions producing a linguistic summarization in the form <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">τ</i> (inputs are <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">A</i> ) consisting of a certain linguistic quantifier <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">τ</i> . The performance of summarization is provided in the form of ranking of the relevance of the rules. Experimental studies using publicly available data are completed and analyzed.

Multiple Scenarios of Quality of Life Index Using Fuzzy Linguistic Quantifiers: The Case of 85 Countries in Numbeo

In economic development, in addition to comparing the gross domestic product (GDP) between nations, it is critical to assess the quality of life to gain a holistic perspective of their different aspects. However, the quality of life index (QOLI) is a subjective term that can be difficult to quantify. Although this composite index is typically calculated using universal weights proposed by experts to aggregate indicators, such as safety indexes, healthcare indexes, pollution indexes, and housing indicators, it is complicated to balance multiple dimensions whose weights are adjusted to account for different countries’ circumstances. Therefore, this paper aims to construct various scenarios of the QOLI, using linguistic quantifiers of the ordered weighted averaging (OWA) operator, and the 2-tuple linguistic model. Numbeo, one of the largest quality of life information databases, was used in this paper to estimate the QOLI in 85 countries. Uncertainty and sensitivity analyses were employed to assess the robustness of the QOLI. The results of the proposed model are compared with those obtained using the Numbeo formulation. The results show that the proposed model increases the linguistic interpretability of the QOLI, and obtains different QOLIs, based on diverse country contexts.

Symmetric weights for OWA operators prioritizing intermediate values. The EVR-OWA operator

One of the most widely adopted approaches to define weights for Ordered Weighting Averaging (OWA) operators consists of using biparametric linear increasing fuzzy linguistic quantifiers. However, several shortcomings appear when using these quantifiers because depending on the values of these parameters, the aggregations could be biased or the extreme values might be completely ignored. In this contribution, the use of Extreme Values Reductions (EVRs) as fuzzy linguistic quantifiers is proposed to define weights for OWA operators in order to provide more realistic aggregations. First, the impact of the parameters of these linear fuzzy linguistic quantifiers in the OWA aggregations is studied. After that, EVR-OWA operators are introduced as those OWA operators whose weights are computed by using an EVR as fuzzy linguistic quantifier. It will be shown that when using EVR-OWA operators to fuse information, the aggregations are non-biased, take into account more information and the intermediate values are prioritized before the extreme ones. After proposing several families of EVRs, the generalising potential of the EVR-OWA operators is shown by proving that every family of symmetric weights for OWA operators that prioritize the intermediate information are the weights obtained from a certain EVR. Finally, an illustrative example is provided.

A type-1 OWA operator for Extended Comparative Linguistic Expressions with Symbolic Translation

Recently, a new representation model has been proposed to improve the interpretability and accuracy of Computing with Words (CW) processes, the so-called Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT). It extends the concept of comparative linguistic expressions based on hesitant fuzzy linguistic term sets into a continuous domain by means of the symbolic translation used in the linguistic 2-tuple model. The aggregation of this kind of information is vital when solving decision making problems, but as the field of ELICIT information is still quite new, not many aggregation operators have been defined for it. Therefore, taking into account the need to deal with the fuzzy representation of ELICIT information for its aggregation, we propose the ELICIT type-1 OWA (ELICIT-t1-OWA) operator based on the equivalent α−level type-1 OWA operator to simplify the CW processes by using ELICIT trapezoidal fuzzy representations. The ELICIT-t1-OWA operator will use interval weights induced by an interval-valued linguistic quantifier to aggregate ELICIT expressions and then its properties will be studied. Additionally, a way to deal with both the weights and arguments of the ELICIT-t1-OWA operator is provided in the form of fuzzy numbers. Finally, a decision making model dealing with ELICIT information that carries out the aggregation by using the proposed ELICIT-t1-OWA operator is developed and a numerical example to show its effectiveness is introduced.

Induced OWA Operator for Group Decision Making Dealing with Extended Comparative Linguistic Expressions with Symbolic Translation

Nowadays, decision making problems have increased their complexity and a single decision maker cannot handle these problems, with a more diverse and comprehensive view of them being necessary, which results in group decision making (GDM) schemes. The complexity of GDM problems is often due to their inherent uncertainty that is not solved just by using a group. Consequently, different methodologies has been proposed to handle it, in which, the use of the fuzzy linguistic approach stands out. Among the multiple fuzzy linguistic modeling approaches, Extended Comparative Linguistic Expressions with Symbolic Translation (ELICIT) information has been recently introduced, which enhances classical linguistic modeling that is based on single terms by providing linguistic expressions in a continuous linguistic domain. Its application to decision making is quite promising, but it is necessary to develop enough operators to accomplish aggregation processes in the decision solving scheme. So far, just a small number of aggregation operators have been defined for ELICIT information. Hence, this paper aims at providing new aggregation operators for ELICIT information by developing novel OWA based operators, such as the Induced OWA (IOWA) operator in order to avoid the OWA operator needs of reordering its arguments, because ELICIT information does not have an inherent order due to its fuzzy representation. Our proposal not only consists of extending the definition of an IOWA operator for ELICIT information with crisp weights, but it is also proposed a type-1 IOWA operator for ELICIT information in which both weights and arguments are fuzzy as well as the use of ELICIT information constructing the order inducing variable to reorder the arguments. Additionally, the use of ELICIT information in GDM demands the ability to manage majority based decisions that are better represented in the IOWA operator by linguistic quantifiers. Hence, a majority-driven GDM process for ELICIT information is proposed, which it is the first proposal for fulfilling the majority solving process for GDM while using ELICIT information. Eventually, an illustrative example and a brief comparative analysis are presented in order to show the performance of the proposal and its feasibility.

Agriculture supply chain risks and COVID-19: mitigation strategies and implications for the practitioners

ABSTRACT The agricultural supply chains (ASCs) are exposed to unprecedented risks following COVID-19. It is necessary to investigate the impact of risks and to create resilient ASC organisations. In this study, we have identified and assessed the ASC risks caused by disruptions. These threats were assessed using Fuzzy Linguistic Quantifier Order Weighted Aggregation (FLQ-OWA). The findings reveal that supply risks, demand risks, financial risks, logistics and infrastructure risks, management and operational, policy and regulation, and biological and environmental risks have a significant impact in ASC depending upon the organisations scope and scale. Various strategies such as adoption of industry 4.0 technologies, supply chain collaboration and shared responsibility is identified for sustainable future. Theoretical and managerial implications are provided based on the outcomes of the study.

Fuzzy Optimization Algorithm for Software Cost Estimation

Estimation of a software cost depends on a probabilistic model and thus it doesn't create precise values. In any case, accessibility of good chronicled information combined with a efficient technique can create improved outcomes. This paper, we have displayed a Software Effort Estimation Model utilizing PSO and Fuzzy Logic. Fuzzy sets have been utilized for displaying uncertainty and imprecision in estimation of effort while PSO has been utilized for tuning parameters. This has been seen from the outcomes that Fuzzy-PSO intelligence gives precise outcomes when compared through its different partners. This system relies upon thinking by linguistic quantifiers and fuzzy logic. This kind of model holds well, when the product plans are communicated by absolute or potentially arithmetical data. Along these lines, this projected methodology improves the old style correlation process that doesn't think about clear cut data. In the fuzzy correlation model, fuzzy sets are used to describe both the clear cut and the arithmetical data.

Attitude quantifier based possibility distribution generation method for hesitant fuzzy linguistic group decision making

The possibility distribution-based approach is one of the powerful tools available to manage hesitant fuzzy linguistic term set (HFLTS) information. However, existing possibility distribution studies have not considered the experts’ satisfied preference for HFLTSs in the process of generating the possibility distribution. This paper aims at filling this research gap. To achieve this goal, a novel possibility distribution generation method based on the concept of linguistic quantifier is proposed. This is accomplished by defining a new attitude linguistic quantifier, which is supported with theoretical results to analyze the relationship between the proposed attitude linguistic quantifier with the original linguistic quantifier, attitude indices and the expected linguistic term. The new possibility distribution generation method is proved to be (1) more general than the two main existing approaches, which are particular cases for specific linguistic quantifiers; and (2) useful to implement the concept of soft majority in the resolution process of the decision making situation. Additionally, a new two stages feedback mechanism of attitude adjustment and assessment adjustment is devised to guarantee the convergence of the consensus reaching process. Finally, a framework of group decision making with HFLTSs information is presented and an illustrative example is conducted to verify the proposed method.

The theory of intermediate quantifiers in fuzzy natural logic revisited and the model of “Many”

The fuzzy natural logic (FNL) is a formal theory whose goal is to provide a mathematical model of natural human reasoning whose typical feature is the use of natural language. One of its tasks is to develop a mathematical model of a special class of linguistic quantifiers called intermediate ones. In our previous papers, we introduced a general principle of how intermediate quantifiers can be formed and suggested generalized definitions of the relations of contrary, contradictory, subcontrary, and subalterns between these quantifiers. Based on these relations and following Peterson's book [62], we were able to suggest a formal model of the 5-square of opposition with intermediate quantifiers. This paper picks up the threads of this work and has the following goals: it contributes to the development of the theory of fuzzy natural logic. First, it gets back to some concepts of the theory of evaluative linguistic expressions, introduces slight modifications, and proves some not yet presented properties. Furthermore, it improves the formal theory of intermediate quantifiers; some definitions are made more precise, and some new theorems are proved. Finally, it contributes to the theory of the intermediate quantifier “Many” and the analysis of its position in the mentioned 5-square. We will show that “Many” manifests an ambiguous relation towards the other quantifiers.

Multiattribute Spatial Decision-Making for Qualitative Information Processing as Applied to the Renewable Energy Generating Sites Prospection

The objective of this research is to develop methodological tools to consider qualitative information in solving spatial problems with their particular application to the determination of generating sites for renewable energy systems. This locational problem has a complex nature and its solution has to be capable to take into account a wide range of considerations, as well as evaluations of a qualitative character. In this sense, the proposed process of elaborating decisions starts with studies related to the spatial criteria, which are modeled and processed within the Spatial Multicriteria Analysis. The relative importance of the spatial criteria is established by the involved experts on the basis of the construction, transformation, and processing of preference relations within the framework of the Analytic Hierarchy Process. The resulting decision maps are generated by aggregating the spatial criteria, applying the Ordered Weighted Averaging operator and the linguistic quantifiers. These maps permit one to highlight rational solution alternatives, which, if necessary, are evaluated, compared, chosen, prioritized, and/or ordered, applying additional spatial criteria (of quantitative as well as qualitative character), by means of techniques for preference modeling in a fuzzy environment (within the framework of so-called $ $ models). The corresponding decision process permits one to take into account and process quantitative and qualitative spatial criteria as well as preferences and judgments of the experts. The paper results are illustrated by a Case Study related to the determination of the most suitable locational alternatives for renewable power plants in the Minas Gerais state, Brazil.

On Link Stability Metric and Fuzzy Quantification for Service Selection in Mobile Vehicular Cloud

Vehicular cloud (VC) is a promising environment, where intelligent transport applications can be developed relying on mobile vehicles, which can be both cloud users and cloud service providers. It enables vehicles that have sufficient resources to act as mobile cloud servers by offering a variety of services to users’ vehicles. In this context, to consume a cloud service on the move, a user vehicle must first identify the most stable vehicles, relative to his/her motion, which are able to provide the service, and then select the most suitable service according to his/her preferences, while both provider vehicles and their services are described by attributes or quality constraints. Therefore, we introduce a generic relative motion model, as a generic link stability metric, upon which vehicles can form a stable cloud, and we address the VC service selection by using linguistic quantifiers and fuzzy quantified propositions, to define our flexible quantified service selection (FQSS) scheme, which aggregates efficiently both user preferences and service constraints and ranks service providers from the most to the least satisfactory. To break ties among the top-ranked service providers, we make use of our parameters for ranking refinement, called least satisfactory proportion (lsp) and greatest satisfactory proportion (gsp). The simulation results show that our link stability achieves generic motion, by modeling a wider range of vehicle motion types, and our FQSS scheme allows a good successful service consumption rate while reducing latency.

A method for fuzzy quantified querying over fuzzy Resource Description Framework graph

Vagueness (or imprecision) naturally arises in real-world Resource Description Framework (RDF) data. The way we query RDF data is a crucial subject because of the vagueness and the wide connectivity of such data. Fuzzy quantified queries have been studied over several types of data and allow to sum up large volumes of data in a very intuitive manner. However, there are a few works that have been led on RDF graph database. In this study, we dealt with a specific type of fuzzy quantified queries in the context of a (fuzzy) RDF graph database. We first show how these queries can be expressed and interpreted in a quantified graph pattern, which is an extension of graph patterns by supporting linguistic quantifier on edges. A query processing strategy based on subgraph matching queries is also proposed. Then, we develop an algorithm for evaluating quantified RDF graph patterns, that is, enumerating all RDF isomorphism from the given RDF graph patterns into the data graph. The algorithm is based on a backtracking strategy, which incrementally finds partial solutions by adding joinable candidate vertices or abandoning them when it determines they cannot be completed. Finally, we perform some experiments to study its performances. The results of these experiments show that the method of dealing with fuzzy quantification in a query is feasible.

Risk-Based Analysis in Mineral Potential Mapping: Application of Quantifier-Guided Ordered Weighted Averaging Method

In this work, a quantifier-guided ordered weighted averaging (OWA) method was employed for mineral potential mapping (MPM) in Nowchun Cu–Mo prospect, SE Iran. The proposed knowledge-driven method has the capability of incorporating the geologists’ preference (weight) and attitude toward risk analysis during MPM. Since quantitative determination of OWA parameters is a tough task, employing linguistic quantifiers aid geologists to simply define their desired strategy for MPM. To implement the method, eight weighted criteria spatially associated with mineralization were derived from geological, geochemical and geophysical datasets. The evidential layer integration was implemented using various OWA operators, which is generated by employing seven linguistic quantifiers. As a result, seven mineral potential maps, which report favorability index from 0 to 1, were produced in a spectrum range of risk from extremely optimistic to extremely pessimistic. According to results, the western and southeastern part of the study area were detected as regions with the lowest and highest mineral favorability. For validation, the results of subsequent geological field works and 106 drilled boreholes were taken into account. The evaluation indicated that the mineral potential map based on the “Some” quantifier has the highest correspondence with underground 3D mineralization zones of Cu and Mo. The mineral potential map based on the “Some” quantifier delineated two main prospective zones in the eastern and central-north parts of the study area. The former zone was recently investigated by drilling, but the latter zone was proposed for new drilling operation. Applying the proposed method in each scale of target delineation (a) generates various continuum favorability maps; (b) reveals mineralization patterns in the study area; and (c) provides an opportunity in exploration to select the optimal mineral potential map for detailed exploration tasks regarding the geologists’ attitudes toward risk and project budget.

Multiple criteria decision making for linguistic judgments with importance quantifier guided ordered weighted averaging operator

In this paper, an importance quantifier-guided Ordered Weighted Averaging (OWA) Operator for linguistic decision judgments is developed. To create a ‘softer’ decision aggregation task, the decision criteria are associated with the degree of importance in aggregation. The importance quantifier-guided OWA operator is extended from Yager’s OWA using linguistic quantifiers. These interval type 2 fuzzy sets are used to map the linguistic quantifiers. The first stage of applying the importance quantifier-guided OWA operator is to rank a set of interval type 2 fuzzy sets. A new interval type 2 fuzzy set ranking methodology is proposed. Such ranking methodology is concerned with two newly defined type 2 fuzzy set characteristics, the extended level set (alpha-cut) and the parametric generalized graded mean integration representation. The partial ordering set properties of the ranking methodology are rigorously discussed. The framework of multiple criteria decision making with linguistic judgments is constructed using the importance quantifier-guided OWA operator. The optimal importance quantifier-guided OWA type 2 fuzzy weights for decision criteria, and the overall decision fuzzy rates for alternatives are obtained. The mixed integer linear programming models are created specifically for solving the optimal importance quantifier-guided type 2 fuzzy weights. The piecewise linear and the general non-linear quantifier models are developed. The overall procedure for interval type 2 fuzzy sets multiple criteria decision making with the optimal importance quantifier-guided OWA weights is formulated. A multiple criteria decision making problem, New Product Development Project Screening, is used to demonstrate the proposed methodology.

An Entropy-Based Approach to Fuzzy Multi-objective Optimization of Reservoir Water Quality Monitoring Networks Considering Uncertainties

In this study, a new fuzzy methodology for a multi-objective optimization of reservoir Water Quality Monitoring Stations (WQMS) was developed, based on Transinformation Entropy (TE), the IRanian Water Quality Index (IRWQI), and fuzzy social choice considering uncertainties. The approach was utilized in the Karkheh Dam reservoir in Iran. The objective functions were: 1) minimizing costs, 2) minimizing redundant information and uncertainties, and 3) maximizing the spatial coverage of the network. A CE-QUAL-W2 model was used for the simulation of water quality variables. The IRWQI was computed to reveal a complete picture of the reservoir water quality. The TE quantities were calculated for each pair of potential stations. The TE values were plotted against the spatial distances among potential WQMS to obtain the TE–Distance (TE–D) curve, and minimize redundant information among stations, while providing coverage of the entire network. A multi-objective Genetic Algorithm (NSGA-II) was applied to obtain Pareto-optimal solutions taking stakeholder preference into account. The most preferred solution was then obtained using fuzzy social choice approaches to achieve a consensus. The fuzziness embedded in the decision-making procedure, the uncertainty in the value of mutual information, and the uncertainty in identifying the optimal distance among WQMS were also investigated. Results indicated that the three fuzzy social choice approaches (Borda Count, Minimax, and Approval Voting) led to the same number of optimized WQMS in each fuzzy alpha-cut. Based on the fuzzy linguistic quantifiers method, the number of optimized WQMS was increased.

Application of ‘most’ fuzzy linguistic quantifier to filter impulse noise

Median filter is one of the established filters to de-noised impulse noise. Median filter determine median of a predefine mask. Sometimes estimated intensity of median filter again produces noise. Consider a pixel with 8-connected neighbors (255, 255, 255, 150, 255, 255, 100, 10, 90). If median filter is applied, then estimated intensity will be 255 i.e. 5th largest elements which is again noise. Hence in proposed work ‘at least half’, ‘as many as possible’, and ‘most’ fuzzy linguistic quantifier are used to de-noise images corrupted by impulse noise. In proposed work infrared image of ship with impulse noise is used as input. The impulse noise is inserted with a probability of 0.01. The ‘most’ quantifier produces more promising results than other two quantifiers. SNR ratio of proposed filter is much closer to original image as compare to median filter. Moreover, performance is verified for different types of images. Nevertheless, the performance of proposed method is found satisfactory.