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The fuzzy order convergence in fuzzy Riesz spaces is defined only for fuzzy order bounded nets. The aim of this paper is to define and study unbounded fuzzy order convergence and some of its applications. Furthermore, some theoretical concepts like the fuzzy weak order unit and fuzzy ideals are studied in relation to unbounded fuzzy order convergence.

Preference of an alternative over another alternative is a useful way to express the opinion of decision maker. In the process of group decision making, preference relations are used in preference modelling of the alternatives under given criteria. The probability is an important tool to deal with uncertainty; in many scenarios of decision making probabilities of different events affect the decision making process directly. In order to deal with this issue, in this paper, hesitant probabilistic fuzzy preference relation (HPFPR) is defined. Furthermore, consistency of HPFPR and consensus among decision makers are studied in the hesitant probabilistic fuzzy environment. In this respect, many novel algorithms are developed to achieve consistency of HPFPRs and reasonable consensus between decision makers and a final algorithm is proposed comprehending all other algorithms, presenting a complete decision support model for group decision making. Lastly, we present a case study with complete illustration of the proposed model and discussed the effects of probabilities on decision making validating the importance of the introduction of probability in hesitant fuzzy preference relation.

The fuzzy Riesz space is an attempt to study vector spaces with fuzzy ordering to model scenarios of more vague nature. The aim of this paper is to prove the existence of fuzzy Dedekind completion, whereas to achieve this goal, other related concepts like fuzzy order convergence, fuzzy positive operators, and their related results are also explored to enrich the theory of fuzzy Riesz spaces.

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