Proposing a hierarchical group compromise method can be regarded as a one of major multi-attributes decision-making tool that can be introduced to rank the possible alternatives among conflict criteria. Decision makers’ (DMs’) judgments are considered as imprecise or fuzzy in complex and hesitant situations. In the group decision making, an aggregation of DMs’ judgments and fuzzy group compromi...

The description of the error dynamics (30) in our paper [1] contains an omission that leads to some bounds used in the conditions of Theorem 8 and Corollary 2 in the paper to be incorrectly defined. In what follows, the correct error dynamics and the corresponding conditions are given. Instead of (30) in [1], the error dynamics are actually given by ė = m ∑ i=1 wi(z)[(Ai − LiC +MiAδi)e +Mi(Āδix̂...

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then,the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature ...

This paper is a brief summary of “M.Takahashi, T.Murofushi, S.Asahina, A new necessary and sufficient condition for the Egoroff theorem in non-additive measure theory, Fuzzy Sets and Systems, to appear.” This paper states that a newly defined condition, called condition (M), is a necessary and sufficient condition for the Egoroff theorem in non-additive measure theory. The existing necessary an...

Probabilistic hesitant fuzzy set (PHFS) is a fruitful concept that adds to hesitant fuzzy set (HFS) the term of probability which is able to retain more information than the usual HFS. Here, we demonstrate that the existing definitions of PHFS are not still reasonable, and therefore, we first improve the PHFS definition. By endowing the set and algebraic operations with a new re-definition of P...

Abstract. This paper proposes the concept of an interval neutrosophic hesitant fuzzy set (INHFS) and the operational relations of INHFSs. Then, we develop correlation coefficients of INHFSs and investigate the relation between the similarity measures and the correlation coefficients. Furthermore, a multiple attribute decision making method based on the correlation coefficients is established un...

The concept of upper and lower semicontinuity of fuzzy mappings introduced by Bao and Wu [Y.E. Bao, C.X. Wu, Convexity and semicontinuity of fuzzy mappings, Comput. Math. Appl., 51 (2006) 1809–1816] is redefined by using the concept of parameterized triples of fuzzy numbers. On the basis of the linear ordering of fuzzy numbers proposed by Goetschel and Voxman [R. Goetschel, W. Voxman, Elementar...

In (Fuzzy Sets and Systems 97 (1998) 33), we presented a fuzzy multipurpose decision making model integrating di4erent preference representations based on additive reciprocal fuzzy preference relations. The main aim of this paper is to complete the decision model studying conditions under which reciprocity property is maintained when aggregating preference relations using an OWA operator guided...