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The concept of perceptual map is introduced in this paper to capture the semantics of linguistic assessments of an individual in a qualitative reasoning scenario, concretely in hesitant fuzzy linguistic term sets. In addition, the projected perceptual map is considered to provide a space to aggregate different perceptual maps. Qualitative distances and measures of centrality and agreement or consensus are revised based on this projected perceptual map. This research has been partially supported by the PERCEPTIONS R. P. (PID2020-114247GB-I00), funded by the Spanish Ministry of Science and Information Technology.

Vies Braves (Sea Swimming Lanes) is a pioneer company in designing, promoting, and revitalizing open water and marine itineraries which are protected by buoys, and dedicated to health, leisure, educa- tional and environmental protection activities. The management team's strategic priority is the implementation of new Vies Braves in new coastal locations. In this paper, we propose a fuzzy decision-aiding ap- proach, using hesitant linguistic term sets to study the viability of new potential coastal locations. The proposed approach considers main eco- nomic, political, environmental and social criteria to nd similarities between each new alternative and existing ones. This research was supported partly by the INVITE research project (TIN201680049-C2-1-R and TIN2016-80049-C2-2-R), funded by the Spanish Ministry of Economy and Competitiveness. In addition, the authors gratefully acknowledge the encouraging support of Mr. Miquel Sunyer, CEO of Vies Braves.

When searching for recommendations online, users are often presented with similar items all having the same ratings. It is left to the user to discern which rated item is best from other information. In order to facilitate this process, we propose a new methodology to associate a measure of consensus to the ratings derived from a group of reviewers. The opinion of reviewers are considered not only from rating values but from written reviews. This allows us to express reviewer opinions as interval ratings by means of hesitant fuzzy linguistic term sets and compute a consensus. A real case example is provided to show the potential of the proposed methodology. The example provided is based on 966 TripAdvisor reviews of the twenty most reviewed hotels during 2017 in Rome at the time the data was taken. The consensus measure allows us to better understand hotel reviews. This research has been partially supported by the Secretary of Universities and Research of the Department of Enterprise and Knowledge of the Generalitat de Catalunya (2017 DI 086) and by the INVITE Research Project (TIN2016- 80049-C2-1-R and TIN2016-80049-C2-2-R (AEI/FEDER, UE)), funded by the Spanish Ministry of Science and Information Technology.

This paper offers a new method inspired by classic importance-performance analysis (IPA) that provides a global index of importance versus performance for firms together with a new version of the IPA diagram. The index compares two rankings of the same set of features regarding importance and performance, taking into account under-performing features. The marginal contribution of each feature to the proposed global index defines a set of isocurves that represents an improvement in the IPA diagram. The defined index, together with the new version of the diagram, enables, by means of qualitative reasoning techniques, the assessment of a firm’s overall performance and therefore enhance decision making in the allocation of resources. The proposed method has been applied to a Taiwanese multi-format retailer and managerial perceptions of performance and importance are compared to assess the firm’s overall performance.

Hesitant fuzzy linguistic term sets were introduced to grasp the uncertainty existing in human reasoning. In this paper, inspired by absolute order-of-magnitude qualitative reasoning techniques, an extension of the set of hesitant fuzzy linguistic term sets is presented to capture differences between non-compatible preferences. In addition, an order relation and two closed operations over this set are also introduced to provide a lattice structure to the extended set of hesitant fuzzy linguistic term sets. Based on this lattice structure a distance between hesitant fuzzy linguistic term sets is defined.

Given a finite totally ordered set of linguistic descriptions, the extended set of qualitative labels with different levels of precision L is constructed. In this framework, qualitative descriptions of a given set are L-fuzzy sets. A distance between L-fuzzy sets is introduced based on the properties of the lattice L. An illustrative example in the retail sector applied to assess a firm’s overall performance using perceptions of managers in the firm’s different departments is presented. Given a finite totally ordered set of linguistic descriptions, the extended set of qualitative labels with different levels of precision L is constructed. In this framework, quali- tative descriptions of a given set are L -fuzzy sets. A distance between L -fuzzy sets is introduced based on the properties of the lattice L . An illustrative example in the retail sector applied to assess a firm’s overall performance using perceptions of managers in the firm’s different departments is presented.

This paper compares two multi-criteria decision making (MCDM) approaches based on linguistic label assessment. The first approach consists of a modified fuzzy TOPSIS methodology introduced by Kaya and Kahraman in 2011. The second approach, introduced by Agell et al. in 2012, is based on qualitative reasoning techniques for ranking multi-attribute alternatives in group decision-making with linguistic labels. Both approaches are applied to a case of assessment and selection of the most suitable types of energy in a geographical area.

This paper presents the foundation for a new methodology for a collaborative recommender system (RS). This methodology is based on the degree of consensus of a group of users stating their preferences via qualitative orders-of-magnitude. The structure of distributive lattice is considered in defining the distance between users and the RSs new users. This proposed methodology incorporates incomplete or partial knowledge into the recommendation process using qualitative reasoning techniques to obtain consensus of its users for recommendations.

This paper presents a mathematical framework to assess the consensus found among different evaluators who use ordinal scales in group decision-making and evaluation processes. This framework is developed on the basis of the absolute order-of-magnitude qualitative model through the use of qualitative entropy. As such, we study the algebraic structure induced in the set of qualitative descriptions given by evaluators. Our results demonstrate a weak, partial and semi lattice structure that in some conditions takes the form of a distributive lattice. We then define the entropy of a qualitatively-described system. This enables us, on the one hand, to measure the amount of information provided by each evaluator and, on the other hand, to consider a degree of consensus among the evaluation committee. This new approach is capable of managing situations where the assessment given by experts involves different levels of precision. In addition, when there is no consensus regarding the group decision, an automatic process assesses the effort required to achieve said consensus.

Ordinal scales are commonly used in rating and evaluation processes. These processes usually involve group decision making by means of an experts’ committee. In this paper a mathematical framework based on the qualitative model of the absolute orders of magnitude is considered. The entropy of a qualitatively described system is defined in this framework. On the one hand, this enables us to measure the amount of information provided by each evaluator and, on the other hand, the coherence of the evaluation committee. The new approach is capable of managing situations where the assessment given by experts involves different levels of precision. The use of the proposed measures within an automatic system for group decision making will contribute towards avoiding the potential subjectivity caused by conflicts of interests of the evaluators in the group.

Multiple-criteria or multiple-attribute group decision-making is a sub-field of operations research that seek to find a common and representative solution given the preferences elicited by a pre-defined group, over a set of alternatives and with respect to a set of coherent criteria (or attributes). Recently, the modelling of natural language in these processes has captured the attention of many researchers. Most of the evaluations in a group-decision making context are inherently imprecise, incomplete or vague, and therefore, experts feel more comfortable using their language rather than numerical values. The use of hesitant fuzzy linguistic term sets is one of the recent tools that enables the modelling of linguistic assessments in multiple-criteria decision-making. Nonetheless, advances in hesitant linguistic multi-attribute group decision making require the development of structures flexible enough to deal with unbalanced and multi-granular linguistic information. More tools are needed in order to really grasp the differences in the qualitative reasoning processes of each individual. This thesis, firstly, introduces a perceptual-based distance able to capture differences between unbalanced linguistic assessments, which is based on a lattice structure of hesitant fuzzy linguistic terms. Secondly, this distance is used to define a perceptual-based centroid or central opinion which, in turn, is used to define a consensus measure or degree of agreement within the group. Thirdly, with the aim to deal with multi-perceptual group decision-making contexts, where each decision maker has its own qualitative reasoning approach, a perceptual-based transformation function and a projected algebraic structure are defined. The developed tools can deal with different multi-granularity linguistic environments. Two applications are presented to demonstrate the utility, relevancy and feasibility of the methods. On the one hand, a specific perceptual-based classification and ranking method is introduced and applied to a real group decision making problem in an educational setting. This framework is used to classify and rank a set of secondary students according to their degree of entrepreneurial competency, which is based on real data provided by the Andorra Government. On the other hand, an extended fuzzy multi-perceptual linguistic TOPSIS is designed and applied to a real group decision making problem in the context of smart city governance. This perceptual extension is used to assess the criteria governing the strategic decision making process of energy multinational companies when deciding where to expand its sustainable services and products. El multiple-criteria o bé multi-attributte group decision-making (MCGDM / MAGDM) és una branca del camp de OR (operations research) l'objectiu del qual és buscar solucions comunes i representatives donades unes preferències d'un grup d'experts definit, sobre un conjunt d'alternatives i en relació a un conjunt coherent de criteris o atributs. L'objectiu d'aquesta tesis és contribuir específicament en l'àrea lingüística de MCGDM / MAGDM millorant les metodologies i marcs matemàtics existents amb l'objectiu de poder modelar qualsevol tipus de situació de presa de decisions en grup que impliqui multi-granularitat i raonament qualitatiu molt heterogeni entre el grup (ús d'etiquetes lingüístiques no balancejades). En concret, la tesis es basa en l'ús de l'eina dels hesitant fuzzy lingüístic term sets (HFLTSs) que fou introduïda per Rodriguez et al (2012) amb l'objectiu de permetre als experts poder donar opinions i preferències lingüístiques usant el seu llenguatge habitual (i no, números) capturant també la incertesa, ambigüitat i manca d'informació característica en aquest tipus de decisions. La majoria d'estructures matemàtiques existents basades en l'ús de HFLTSs en problemes de MCGDM/MAGDM fan la hipòtesis que tots els experts han d'expressar-se usant el mateix set d'etiquetes lingüístiques i/o bé el pes que cada expert dona a cadascuna de les etiquetes ha de ser el mateix. Aquests estructures no són suficientment flexibles per modelar situacions de GDM de multi-granularitat que també incloguin diversitat de raonament qualitatiu amb etiquetes lingüístiques no balancejades de forma simultània. En primer lloc, la present tesis desenvolupa un nou concepte, el perceptual-map, definit sobre l'estructura algebraica de HFLTSs no balancejats i introdueix una nova distància basada en aquesta mètrica. Aquesta distància és utilitzada per definir un centroide (opinió central) i una mesura de consens per a qualsevol situació de MAGDM que necessiti de l'ús d'un set d'etiquetes lingüístiques no balancejat. En segon lloc, una funció de transformació basada en el perceptual-map es defineix per tal de poder modelar simultàniament situacions lingüístiques amb multi-granularitat i poder així, realitzar operacions en un espai projectat. A nivell pràctic, la tesis presenta dos aplicacions reals per demostrar la utilitat i rellevància de les eines matemàtiques desenvolupades. D'una banda, la tesis introdueix un nou mètode de classificació i rànquing, que és aplicat en l'àmbit de l'educació. El nou mètode és utilitzat per classificar i ranquejar els alumnes de secundària de l'escola Andorrana d'acord amb el seu grau de desenvolupament de la competència emprenedora. D'altra banda, s'ha desenvolupat un nou model de TOPSIS anomenat fuzzy multi-perceptual lingüístic TOPSIS, que s'ha aplicat en el context d'avaluació de smart cities. La nova versió de TOPSIS s'ha aplicat amb èxit per avaluar els criteris que governen la decisió estratègica de localització, en el context de ciutats europees, de les multinacionals del sector energètic. Matemàtica aplicada

Decision-making is an active field of research. Specifically, in recent times, a lot of contributions have been presented on decision-making under linguistic assessments. To tackle this kind of processes, hesitant fuzzy linguistic term sets have been introduced to grasp the uncertainty inherent in human reasoning when expressing preferences. This thesis introduces an extension of the set of hesitant fuzzy linguistic term sets to capture differences between non-compatible assessments. Based on this extension, a distance between linguistic assessments is defined to quantify differences between several opinions. This distance is used in turn to present a representative opinion from a group in a decision-making process. In addition, different consensus measures are introduced to determine the level of agreement or disagreement within a decision-making group and are used to define a decision maker’s profile to keep track of their dissension with respect to the group as well as their level of hesitancy. Furthermore, with the aim of allowing decision makers to choose the linguistic terms that they feel more comfortable with, the concept of free double hierarchy hesitant fuzzy linguistic term set is developed in this thesis. Finally, a new approach of the TOPSIS methodology for processes in which the assessments are given by means of free double hierarchy hesitant fuzzy information is presented to rank alternatives under these circumstances.