**
APPROXIMATE REASONING, ROUGH SETS, RANKING AND PAIRWISE COMPARISONS**

When dealing with big data approximate reasoning is a necessity as
obtaining exact results or analyzing
all data is often not feasible.

Consider the following problem: we have a set of data that have been
obtained in an empirical manner. From the nature of the problem we know that the
set should have some structure and desired properties, for example, it should be partially ordered, but because the data are empirical it is not. In general case
this might be just an arbitrary set without the desired structure and
properties. What is the “*best*”
approximation that
has the desired structure and properties and how it can be
computed? In general, we cannot assume
the
existence of any obvious numerical metric
which is a substantial theoretical and practical obstacle.

While ‘*Rough Sets*’ (Pawlak
1982) handle lower and upper approximations very well, ‘*optimal*’ and ‘*structural*’
(i.e. having desired special properties) approximations are much less developed.
While some frameworks for structural (Yao 1996,
Janicki 2010) and optimal
(Janicki-Lenarcic 2016) Rough Sets approximations exist, they are far from being
universal and satisfactory. Usually, it is not clear how ‘*optimal*’
approximation should be defined (Janicki 2018), and what kind of ‘*similarity*’
should be chosen (Tversky 1977). It also turns out that even for very simple
similarity measures and rather simple desired properties the problems often may
become NP-complete, so some second level of approximation might be needed
(Janicki 2018).

Current research involves two orthogonal approaches.
The first is to develop
a family of abstract metrics that can be used for various classes of sets,
relational structures, and properties. The second approach is to simulate the
concept of a metric by a sequence of ‘lower’ and ‘upper’ approximations that
preserve the desired properties (in both the standard theory of relations and
rough sets settings). In both cases finding some efficient algorithms and
supporting software is a long term ultimate goal.

There are plenty of potential applications of
approximate reasoning (in a sense described above) in Knowledge Engineering,
Classification Theory, Clustering, etc.

One obvious important application and a good testbed is pairwise
comparisons based *non-numerical*
ranking (Janicki 2009, which provided the main motivation for this general
problem).

Most of
the
ranking theories either assumes some numerical
(quantitative) metrics or uses rather very specific assumptions. The
*pairwise comparisons* method is based
on the observation that it is much easier to rank the importance of two objects
than it is to rank the importance of several objects. While
*non-numerical* (or
*qualitative*) ranking was informally used for a very long time, its
strict formalization
started with (Janicki-Koczkodaj 1996). A comprehensive
theory of non-numerical pairwise comparisons based ranking where the binary
relationship between objects is characterized
by five relations interpreted as
‘indifference’, ‘slightly in favour’, ‘in favor’, ‘strongly better’ and
‘extremely better’ (including a *thorough analysis of consistency*), was
provided by (Janicki 2009,
Janicki-Zhai 2012).

A combined version of pairwise comparisons that
involves both quantitative and qualitative techniques has been proposed by
(Janicki-Soudkhah 2015,
Janicki 2018a) and applied in areas not typical for using
pairwise comparisons paradigm, namely software evaluation, and data
classification.

Current research involves
a
formal relationship between
qualitative and quantitative models, especially between concepts of consistency
in both models, and a thorough study of the role of consistency scales. The
combined model could be a good alternative for the popular numerical pairwise
comparisons based technique called Analytical Hierarchy Process (Saaty 1977).

**2022**

**
IPMU’2022 (19th International Conference on Information Processing and
Management of Uncertainty in Knowledge-Based Systems)**,

** Proc. of
17th Conference on Computer Science and Intelligent Systems FedCSIS 2022, Sofia,
Bulgaria, Sept. 4-7 2022, pp. 247-251**.

**
2019**

3. X. Xie, X. Qin, Q. Zhou, Y. Zhou, T. Zhang, R. Janicki, W. Zhao, A
novel test-cost-sensitive attribute reduction approach using the binary bat
algorithm, *
Knowledge Based Systems*

4.
X. Xie,
R. Janicki, X. Qin, W. Zhao,
G. Huang, Local search for attribute reduction,
**IJCRS’2019 (International
Joint Conference on Rough Sets), ****Lecture Notes in Artificial Intelligence****
11499, Springer 2019, 102-117**

**2018**

5.
R. Janicki*,**
*
Approximations
of Arbitrary Relations by Partial Orders,
*
International Journal of Approximate Reasoning*,
98 (2018) 177-195.

6.
R.
Janicki,
Finding
Consistent Weights Assignments with Combined Pairwise Comparisons,
* International Journal of Management and Decision Making,
*17, 3 (2018)
322-247

**
2017**

7.
R. Janicki, Yet Another Kind of Rough Sets Induced by Coverings, Proc. of
**IJCRS’2017 (International Joint Conference on Rough Sets),
****Lecture Notes
in Artificial Intelligence 10313****, Springer 2017, 140-153**.

**
2016**

8.
R.
Janicki,
A. Lenarcic,
Optimal Approximations with Rough Sets and Similarities in Measure Spaces,
**International Journal of Approximate Reasoning****, 71
(2016) 1-14**.

9.
R. Janicki, On
Optimal Approximations of Arbitrary Relations by Partial Orders, Proc. of
**IJCRS’2016 (International Joint Conference on Rough Sets),
****Lecture Notes in
Artificial Intelligence**** 9920, Springer 2016, 107-119**.

10.
A. D. Bogobowicz, R. Janicki, On Approximation of Relations by Generalized
Closures
and Generalized Kernels,
**Proc. of IJCRS (International Joint Conference on
Rough Sets), ****Lecture Notes in Artificial Intelligence**** 9920, Springer
2016, 120-130**,

2015

11.
R. Janicki,
M. H. Soudkhah,
On Classification with Pairwise Comparisons, Support Vector Machines and Feature
Domain Overlapping,
*The Computer Journal** *
58, 3 (2015).

12. R. Janicki, On Qualitative and Quantitative Pairwise Comparisons, Proc. of ICAT’15 (International Conference on Advanced Technology & Sciences), Antalya, Turkey, August 4-7, 2015, pp. 21-28.

13. A. Mirdad, R. Janicki, Applications of Mixed Pairwise Comparisons, Proc. of ICAI’2015 (International Conference on Artificial Intelligence), Las Vegas, Nevada, USA, July 27-30, 2015, pp. 414-420, CSREA Press

**
2013**

14.
R.
Janicki, Property-Driven Rough Sets Approximations of Relations, In A.
Skowron, Z. Suraj (eds.), *Rough Sets
and Intelligent Systems - Professor Zdzisław Pawlak in Memoriam (Series:
Intelligence Systems Reference
Laboratory Vol. 42)*, pp. 333-357, Springer 2013.

15.
R.
Janicki, A. Lenarcic, Optimal
Approximations with Rough Sets, Proc. of *RSKT’2013* (7^{th}
Int. Conf. on Rough Sets and Knowledge Technology), *Lecture Notes in
Artificial Intelligence *8171, Springer 2013, 87-98.

16.
M. H. Soudkhah,
R. Janicki, Weighted Features Classification with Pairwise Comparisons,
Support Vector Machines and Feature Domain Overlapping, 22^{nd} IEEE
WETICE (Workshops on Enabling Technologies: Infrastructure for Collaborative
Enterprises) Conference, 4^{th} Track on Cooperative Knowledge
Discovery & Data Mining, Hammamet, Tunisia 2013, pp. 172-177, IEEE Publ.

17.
A.
Bogobowicz, R. Janicki, On pairwise comparisons based internal and external
measures for software
evaluation, 22^{nd} IEEE WETICE (Workshops on Enabling Technologies:
Infrastructure for Collaborative Enterprises) Conference, 1^{st}
Track on Validating Software for Critical Systems, Hammamet, Tunisia 2013,
pp. 371-376, IEEE Publ.

2012

18.
R.
Janicki, Y. Zhai, On a
Pairwise Comparison Based Consistent Non-Numerical Ranking,
**Logic
Journal of IGPL**** 20, 4 (2012), 667-676**.

19.
R.
Janicki, Y. Zhai, Rank
Reversals and Testing of Pairwise Comparisons Based Non-Numerical
Rankings, Proc. of 10^{th} Int. FLINS Conf. On
Uncertainty Modeling in Knowledge Engineering and Decision Making, Istanbul,
Turkey 2012, pp.374-381.

**2011**

20.
R.
Janicki, Y. Zhai, Remarks on
Pairwise Comparison Numerical and Non-Numerical Rankings, Proc. of *RSKT’2011
*(Rough Sets and Knowledge Technology), *Lecture Notes in
Artificial Intelligence* 6954, Springer 2011, 290-300.

21.
R.
Janicki, Y. Zhai, On Testing
Pairwise Comparisons Based Non-Numerical Rankings, Proc. of
ICAAA’2011 (International Conference on
Applied Analysis and Algebra), pp. 45-49, Istanbul, Turkey 2011.

2010

22.
R. Janicki, Approximation of Arbitrary Binary Relations by Partial Orders.
Classical and Rough Set Models,
**Transactions on Rough Sets**
13 (2010), 17-38.

23.
R.
Janicki, Y. Zhai, On a
Consistency Driven Pairwise Comparison Based Non-numerical Ranking, Proc. of
CMMSE’2010 (Computational and Mathematical
Methods in Science and Engineering), Vol. 2, pp. 566-576, Almeria, Spain,
2010.

2009

24.
R.
Janicki, Pairwise Comparisons Based Non-Numerical Ranking,
**Fundamenta
Informaticae** 94 (2009), 1-21.

25.
P.
Adamic, V. Babiy, R. Janicki,
T. Kakiashvili, W. W.
Koczkodaj, R. Tadeusiewicz, Pairwaise Comparisons and Visual Perceptions of
Equal Area Polygons,
**Perceptual and Motor Skills**,
108, 1 (2009), 37-42.

26.
R.
Janicki, On Rough Sets with Structures and Properties, 12^{th}
RSFDGrC’2009 (Rough Sets, Fuzzy Sets, Data Mining and Granular Computing),
*Lecture Notes in Artificial Intelligence* 5958, Springer 2009,
109-116.

27.
R.
Janicki, Some Remarks on Approximations of Arbitrary Binary Relations by
Partial Orders, Proc. of RSCTC’2008 (Rough
Sets and Current Trends in Computing), Lecture
Notes in Artificial Intelligence 5306, Springer 2008, 81-91.

28.
R. Janicki, Ranking with Partial
Orders and Pairwise Comparisons,
Proc. of
*RSKT’2008 *(Rough Sets and
Knowledge Technology), *Lecture Notes in Artificial Intelligence* 5009,
Springer 2008, 442-451.

29.
R.
Janicki, W. W. Koczkodaj, V. Babiy,
Pairwise Comparisons and Ranking, ICSS’08
(Int. Conference on Social Sciences), Izmir, Turkey 2008.

2007

30. R. Janicki, Pairwise Comparisons,
Incomparability and Partial Orders, ICEIS’2007
( 9^{th} Int. Conference on Enterprise Information
Systems), Volume 2 (Artificial Intelligence and Decision Support Systems),
pp. 297-302, Funchal, Portugal 2007.

1998

31.
R.
Janicki, W. Koczkodaj, "A Weak Order Solution to a Group Ranking and
Consistency-Driven Pairwise Comparisons",
** Applied Mathematics and
Computation**,

1997

32.
R.
Janicki, "Pairwise Comparisons Revisited",
*6th Symposium on Intelligent
Information Systems*,

1996

33.
R.
Janicki, W. Koczkodaj, "A Weak Order Approach to Group Ranking",
** Computers and Mathematics with
Applications**, 32, 2 (1996), 51-59.

34.
R.
Janicki, W. Koczkodaj, "Consistency-Driven Approach to Knowledge Acquisition
for Expert Systems", *Proceedings of
CESA'96 (Computational Engineering in System Applications)*,

**
1994**

35.
R.
Janicki, "On Non-Numerical Ranking", *Proceedings of the 3rd International Workshop on Rough Sets and Soft
Computing (RSSC'94)*, San Jose, California, 1994, 190-197.