In this original article, there are several editing errors and it is given below:

  • In section 2. The Problem of Axiomatisation of the Concept of Grey, Axioms 1 to 4 are incorrect. It should be:

    Axiom 1. \(G^{^\circ }\) (\(A_{i}\)) ≥ 0 for any \(A_{i} \in { }{\mathcal{F}}\)

    Axiom 2. \(G^{^\circ }\) (\(A_{i}\)) = 0 ⇔ \(A_{i}\) = \(\left\{ {a_{i} } \right\}\), with \(A_{i}\) = \(\left\{ {a_{i} } \right\}\) denotes any one-element set belonging to the \({\mathcal{F}}\)

    Axiom 3. \( G^{^\circ }\) (Ω) = 1

    Axiom 4. \(G^{^\circ }\) (\(\bigcup\nolimits_{i \in N} {A_{i} }\)) = \(\mathop \sum \limits_{i \in N} G^{^\circ } {(}A_{i} {)}\), where: \(A_{i} \cap A_{j} = {\text{\O }}\) ˄ \(A_{i}\) ≠ {\(a_{i}\)}

  • In section 2. The Problem of Axiomatisation of the Concept of Grey, Definition 1 is incorrect. It should be:

    Definition 1. If \(\left\{ {{\Omega },{\mathcal{F}},G^{^\circ } } \right\}\), is a grey space and \({\Omega } \subset {\mathcal{R}}\) and \(A \subset {\mathcal{F}},\) then a continuous grey number is called an unknown number \(d^{*} \in {\mathcal{R}},\) about which we can only say that: \(\underline {a} \le d^{*} \le \overline{a}\), whereby: \(\underline {a} = \inf (A)\), \(\overline{a} = \sup (A)\).

  • In section 2. The Problem of Axiomatisation of the Concept of Grey, the following text is editorially incorrect:

    Since the Numbers Mentioned are sets of One Element, the Following Axiom Applies to them.

    It should be:

    Since the numbers mentioned are sets of one Element, the following axiom applies to them.

  • In section 4. The Category of Quality and its Relevance to Methodological Issues in Grey Systems Theory and Other Approaches to Data Analysis Definition 12 is incorrect. It should be:

    Definition 12. Quality is called a set of characteristics.

    $$ Q = \left\{ {a_{1} ,a_{2} ,a_{3} \ldots } \right\}\;{\text{or}}\;Q = \left\{ {a_{1} ,a_{2} ,a_{3} \ldots ,a_{n} } \right\}\;{\text{or}}\;Q = \emptyset $$

  • In section 4. The Category of Quality and its Relevance to Methodological Issues in Grey Systems Theory and Other Approaches to Data Analysis Definition 12 is incorrect. It should be:

    Definition 14. A quality state is called a set of state of a feature

    $$ Q_{s} = \{ s_{a1} ,s_{a2} , \ldots \} \;{\text{or}}\;Q_{s} = \left\{ {s_{a1} ,s_{a2} , \ldots s_{an} } \right\}\;{\text{or}}\;Q_{s} = \emptyset $$

  • In section 4. The Category of Quality and its Relevance to Methodological Issues in Grey Systems Theory and Other Approaches to Data Analysis, the following text is to be corrected:

    $$ Q^{FUZZY} = \left\{ {\left( {a_{i} ,\mu_{Q} \left( {a_{i} } \right)} \right)|a_{i} \in Q} \right\};\mu_{Q} : Q \to \left[ {0,1} \right]; i \in N $$
    (1.5)

    It should be:

    $$Q^{FUZZY} = \left\{ {\left( {a_{i} ,\mu_{Q} \left( {a_{i} } \right)} \right)|a_{i} \in Q} \right\};\mu_{Q} :{ }Q \to { }\left[ {0,1} \right];{ }i \in N$$

  • In section 4. The Category of Quality and its Relevance to Methodological Issues in Grey Systems Theory and Other Approaches to Data Analysis, the following text is to be corrected:

    In an analogous way, the grey quality state of an object can be determined by using the concept of feature state and quality state (1.8)

    $$ Q_{s}^{GREY} = \left\{ {\left( {S_{ai} ,G_{s}^{^\circ } \left( {S_{ai} } \right)} \right)|Q_{s} \subset {\Omega }_{s} ,{ }S_{ai} \subset {\mathcal{F}}\left( {{\Omega }_{s} } \right), s_{ai} \in S_{ai} } \right\};G_{s}^{^\circ } :{\mathcal{F}}\left( {{\Omega }_{s} } \right) \to \left[ {0,1} \right];i \in N $$
    (1.8)

    It should be:

    In an analogous way, the grey quality state of an object can be determined by using the concept of feature state and quality state

    $$ Q_{s}^{GREY} = \left\{ {\left( {S_{ai} ,G_{s}^{^\circ } \left( {S_{ai} } \right)} \right)|Q_{s} \subset {\Omega }_{s} ,{ }S_{ai} \subset {\mathcal{F}}\left( {{\Omega }_{s} } \right), s_{ai} \in S_{ai} } \right\};G_{s}^{^\circ } :{\mathcal{F}}\left( {{\Omega }_{s} } \right) \to \left[ {0,1} \right];i \in N $$

  • In section 4. The Category of Quality and its Relevance to Methodological Issues in Grey Systems Theory and Other Approaches to Data Analysis, the following text is to be corrected:

    Q? the quality of the item in question

    It should be:

    Q - the quality of the item in question

  • There are the following typographical errors in the References section:

    First, there is:

    Boris, T. (1984). Quality category in comparative statistical analysis. University Press of the Wroclaw University of Economics. (in Polish).

    It should be:

    Borys, T. (1984). Quality category in comparative statistical analysis. University Press of the Wroclaw University of Economics. (in Polish).

    Secondly, there is:

    Mazur, M. (1987). The Concept of a system and the Rigours of its application. Advances in Cybernetics, 10, 21–29. (in Polish).

    It should be:

    Mazur, M. (1987). The Concept of a system and the rigours of its application. Advances in Cybernetics, 10, 21–29. (in Polish).

    Thirdly, there is:

    Mantura, W. (2010). Introduction to qualitology. Publishing House of Poznan University of Technology

    It should be:

    Mantura, W. (2020). Overview of qualitology. Publishing House of Poznan University of Technology

The Original article has been corrected