A Fuzzy Representation for the Semantics of Hesitant Fuzzy Linguistic Term Sets
Recently, a concept of hesitant fuzzy linguistic term sets (HFLTS) to facilitate elicitation of linguistic information when experts hesitate among several linguistic terms to express their preferences in linguistic decision problems was presented. To carr
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Abstract Recently, a concept of hesitant fuzzy linguistic term sets (HFLTS) to facilitate elicitation of linguistic information when experts hesitate among several linguistic terms to express their preferences in linguistic decision problems was presented. To carry out computations with such type of information, it was introduced the concept of envelope of an HFLTS. This envelope is represented by a symbolic linguistic interval, hence the results do not keep the fuzzy representation. Therefore, this contribution proposes a new fuzzy envelope to represent HFLTS by means of a fuzzy membership function that keeps the fuzzy representation in computational processes with HFLTS.
1 Introduction Decision-making problems are usually defined under uncertain and imprecise situations. There are different approaches to deal with this type of uncertainty, such as, evidential reasoning approach [11], type-2 fuzzy sets [2], fuzzy linguistic approach [12], etc. The use of linguistic information implies to carry out computing with words (CWW), processes [6, 13] that can be accomplished by different computational models [6]. Usually, in decision-making problems defined in qualitative settings with vague and imprecise information, experts hesitate among R. M. Rodríguez (&) L. Martínez Computer Science Department, University of Jaén, 23071 Jaén, Spain e-mail: [email protected] L. Martínez e-mail: [email protected] H. Liu School of Management, Northwestern Polytechnical University, 710129 Xi’an, China e-mail: [email protected]
Z. Wen and T. Li (eds.), Foundations of Intelligent Systems, Advances in Intelligent Systems and Computing 277, DOI: 10.1007/978-3-642-54924-3_70, Springer-Verlag Berlin Heidelberg 2014
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different linguistic terms and need more flexible and richer expressions than single linguistic terms to express their preferences. Recently, Rodríguez et al. proposed the concept of hesitant fuzzy linguistic term sets (HFLTS) [7] to improve the elicitation of linguistic information in decision making when experts hesitate among several linguistic terms to express their preferences. This approach allows experts to express their preferences by means of comparative linguistic expressions close to human beings’ cognitive model by using context-free grammars that formalize the generation of linguistic expressions. The use of comparative linguistic expressions and HFLTS has been applied in different decision-making problems [7, 8] where computational processes are carried out by the envelope of the HFLTS which is a linguistic interval. This envelope manages in a symbolic way the HFLTS, thus the results obtained lose the initial fuzzy representation. In this contribution, we propose a new fuzzy envelope for HFLTS that represents the comparative linguistic expressions by means of a fuzzy membership function obtained by aggregating the multiple linguistic terms of the HFLTS with the OWA operator [10]. This fuzzy envelope facilitates the CWW processes in fuzzy decision models [1] that manage HFLTS. Th
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