Mining diatom algae fossil data for discovering past lake salinity

Abstract

Climate changes around a large body of water have an intertwined relationship with the salinity of the water and diatom algae growing within it. One may use the diatom algae fossils obtained from bottom of an inland lake to conclude the historical climate changes around the lake and by extension the historical salinity of the water. The discovery of the historical quantified salinity of inland lakes is extremely important to understanding climate change, carbon dioxide levels, and global warming. In this research effort, the past salinity levels for Santa Fe Lake located in New Mexico, USA, were discovered by mining the data of diatom algae fossils. Modified Rough Sets as the first component of the proposed hybrid system were used to establish the relationships between diatom algae data, expressed in linguistic values, and the climate changes. The established relationships were extended to embrace the linguistic values of water salinity. The outcome was a set of fuzzy patterns. Fuzzy Logic as the second component of the proposed hybrid system was employed to: (i) provide the membership functions for the different linguistic values of the salinity and (ii) produce a crisp value for the salinity of the water related to each slice of diatom fossil using the crisp values of algae abundance indices in each slice. The validity of the findings was tested which revealed 72% of accuracy for the produced results.

Full text

IADIS International Journal on Computer Science and Information Systems
Vol. 12, No. 2, pp. 102-114
ISSN: 1646-3692
102
MINING DIATOM ALGAE FOSSIL DATA FOR
DISCOVERING PAST LAKE SALINITY
Ray R. Hashemi1, Azita A. Bahrami2, Jeffrey A. Young1, Nicholas R. Tyler3
and Jay Y. S. Hodgson4
1Department of Computer Science, Armstrong State University, Savannah, GA, USA
2IT Consultation, Savannah, GA, USA
3School of Pharmacy, University of Georgia, Athens, GA, USA
4Department of Biology, Armstrong State University, Savannah, GA, USA
ABSTRACT
Climate changes around a large body of water have an intertwined relationship with the salinity of the
water and diatom algae growing within it. One may use the diatom algae fossils obtained from bottom of
an inland lake to conclude the historical climate changes around the lake and by extension the historical
salinity of the water. The discovery of the historical quantified salinity of inland lakes is extremely
important to understanding climate change, carbon dioxide levels, and global warming. In this research
effort, the past salinity levels for Santa Fe Lake located in New Mexico, USA, were discovered by
mining the data of diatom algae fossils. Modified Rough Sets as the first component of the proposed
hybrid system were used to establish the relationships between diatom algae data, expressed in linguistic
values, and the climate changes. The established relationships were extended to embrace the linguistic
values of water salinity. The outcome was a set of fuzzy patterns. Fuzzy Logic as the second component
of the proposed hybrid system was employed to: (i) provide the membership functions for the different
linguistic values of the salinity and (ii) produce a crisp value for the salinity of the water related to each
slice of diatom fossil using the crisp values of algae abundance indices in each slice. The validity of the
findings was tested which revealed 72% of accuracy for the produced results.
KEYWORDS
Data Mining, Past Salinity Levels Extraction, Diatom Algae Fossils, Modified Rough Sets, Fuzzy Logic,
and Feature Extraction
1. INTRODUCTION
For a given inland body of water, any two of the three elements of the climate change, diatom
algae growth, and salinity level of the water have a highly intertwined relationship. To explain
it further, diatom algae are considered as one of the most robust climate proxies collected from

MINING DIATOM ALGAE FOSSIL DATA FOR DISCOVERING PAST LAKE SALINITY
103
lakes (Battarbee 1986). Since they are extremely fastidious to climate changes, their
emergence, decline, presence, and absence in lakes are highly indicative of climate changes.
When there is a drought, the evaporation of the water accelerates and the salinity level of the
water concomitantly increases. An extended drought causes a decline in some species of the
diatom algae and a bloom of some other species in the water. Many species of diatom algae
have a very narrow range of salinity tolerance and simply cannot live if values become too
high or too low.
Climate change entails more than temperature differences alone. For example, since the
atmosphere is coupled with the oceans, their combined circulation systems have caused some
areas to warm, others to not warm, some to experience drought, and a few to receive more
precipitation than before (Jones et al. 2001, Cook et al. 2004). Deciphering these patterns has
cast uncertainty on models predicting future climate (Von Storch et al. 2004). Therefore,
records of historical climate from areas sensitive to changes are needed to understand potential
impacts of future global warming (Mann 2002).
The American southwest is such an area very prone to climate change, particularly drought
(Cook et al. 2004). Tree rings (Grissino-Mayer 1996) and lakes studies have suggested that the
climate in this region has gone through drought cycles in the past and will likely continue into
the future (Hodgson et al. 2013). Using data from inland lakes in this area will be useful in
linking the diatom algae to climate and climate to lake salinity and setting the template for our
data mining approach.
As we mentioned, algae are extremely sensitive to changes in climate (Smol and Cumming
2000) and, therefore, diatom algae fossils retrieved from the lake’s bottom inherently carry the
indications for historical climate changes around the lake. The abundance of different types of
algae in a given slice of fossil may be expressed in linguistic values of “Low”, “High”, and
“Medium”. (A linguistic value, in contrast with a crisp value, is fuzzy. Therefore, we use
linguistic value and fuzzy value interchangeably in this paper). The abundance indices may be
used by experts to calculate a climate value of “Rain” or “Drought” for the period of time
(identified by Carbon 14 dating) represented by the slice of diatom fossil. Observing the
generated data, we are intrigued by the following question. Can the same data be used to
discover the past salinity level of the Lake’s water? An answer to this question is the goal of
this research effort. To be more specific, the goal is to mine a crisp salinity value for each slice
of a Diatom algae fossil for which the algae abundance is expressed in fuzzy values.
The significance of such mining stems from the fact that the salinities of bodies of water
are closely related to the global climate system (Adkins et al. 2002, Durack and Wijffels 2010,
Mendelsohn et al. 1994, Durack et al. 2012). Specifically, climate changes such as freezing
(ice ages), melting (global warming), and evaporation (droughts) that change water levels will
alter the concentration of dissolved substances within the water (Verschuren et al. 2000)
including salinity level of the water. In turn, changes in salinity will affect how well
atmospheric carbon dioxide dissolves in water (Sigman and Boyle 2000). Carbon dioxide is
undoubtedly one of the leading causes of global warming because it is a very powerful
greenhouse agent, trapping large quantities of heat on the planet’s surface (Barry and Chorley
1999). As salinity increases from reductions in water level, the ability of the waterbody to
dissolve carbon dioxide decreases and the atmospheric carbon dioxide increases, resulting in
greenhouse gas accumulation and global warming (Adkins et al. 2002). As temperatures rise,
the lake begins to evaporate, which increases salinity and will then release more carbon
dioxide to the atmosphere. Subsequently, the added carbon dioxide will cause additional
warming, driving more lake evaporation. Furthermore, since climate change affects

IADIS International Journal on Computer Science and Information Systems
104
precipitation and consequently lake levels, discovering historical lake salinity is paramount to
understanding climate. Ultimately, understanding historical salinities over millennia are
important when reconstructing past climates for predicting future changes.
To meet the goal, we (i) identify a set of patterns representing the relationship between
linguistic values of the algae indices and climate using Modified Rough Sets, (ii) extend the
patterns to represent the relationship between linguistic values of the algae and linguistic
values of the water salinity level, and (iii) find a crisp value for the salinity level of each slice
of the fossil using Fuzzy Logic.
The organization of the rest of the paper is as follows. The Previous Works is the subject
of Section two. The Methodology is presented in Section three. The Empirical Results are
discussed in Section four. The Conclusions and Future Research are covered in Section five.
2. PREVIOUS WORKS
The salinity of a body of water and climate changes have an intertwined relationship. The
investigation of the historical quantified salinity level of a body of water definitely will shed
light on the history of the climate change and provides for a more precise analysis of global
warming and human contribution to the problem.
However, past salinities cannot be directly measured and must be interpreted from proxy
data. Much attention has been paid to oceanic studies using chemical isotopes (Adkins et al.
2002, Henderson 2002, Emiliani 1955), but researchers are now increasingly using inland
lakes as sources of historical salinity (Laird et al. 1998, Wilson et al. 1994). Majority of lakes
have greater levels of carbon dioxide than the atmosphere, thus becoming potential major
sources of greenhouse gasses (Cole et al. 1994, Jansson et al. 2012). Algal fossils collected
from the bottom of lakes have emerged as reliable indicators of past salinity (Wilson et al.
1994). Many of these types of studies have relied on constructing weighted-averaging models,
maximum likelihood, bootstrapping, and transfer functions from large datasets of multiple
lakes.
One common obstacle challenging all these methodologies is the inherent uncertainty in
the data. Here, we present a new method of extracting the historical salinity using a hybrid
system of Modified Rough Sets and Fuzzy Logic for a single lake. This hybrid system is more
adoptive to the uncertainty nature of data. To the best of our knowledge such a hybrid system
has not been reported in the literature.
3. METHODOLOGY
A dataset, F, is given and each record, Ri, of the dataset represents a slice of diatom algae
fossils retrieved from bottom of a lake, Figure 1. Ri contains the abundance indices for a set of
algae in linguistic values of “Low”, “Medium” and “High”. Ri also contains an age value and
a climate value representing the age of the fossil slice and climate around the lake for the slice.
Subtraction of ages of the n-th slice and (n-1)-th slice of the fossils represents the number of
years that algae of the slice n survived the climate assigned to the slice. The climate values are
“Rain” and “Drought”.

MINING DIATOM ALGAE FOSSIL DATA FOR DISCOVERING PAST LAKE SALINITY
105
Figure 1. A slice of diatom algae fossil
We take the following three steps to achieve our goal.
1. Use Modified Rough Sets (Hashemi et al. 2008) to identify a set of patterns representing
the relationships between linguistic values of the algae and climate values.
2. Extend the patterns to embrace the linguistic values of water salinity.
3. Build the membership function for the linguistic values of algae abundance and water
salinity level (Zimmermann 2001) using the reported data in literature.
Apply the process of defuzzification to derive a crisp value for the lake’s water salinity
level at the time associated with the age of the slice using the crisp values of algae indices
along with the extended patterns (Biacino and Gerla 2002).
The details of each step are discussed in the following three sub-sections.
One may ask why the hybrid system of Modified Rough Sets and Fuzzy Logic is chosen
to act as the methodology in this research effort. The answer lies on two facts: (i) The
presence of the linguistic values in the fossil data and (ii) the expression of the possible
tolerance level of salinity for algae, in literature, as a range that also differs from one citation
to the next. The Modified Rough Sets approach easily lends itself to extraction of fuzzy
patterns from data with linguistic values and the use of Fuzzy Logic is the best way, if not the
only way, to extract the crisp salinity levels from the patterns.
3.1 Modified Rough Sets and Pattern Extraction
In a nutshell, member of a rough set (in contrast with a traditional set) is either totally inside
the set or partially inside the set. A modified rough set is a version of rough set for which
those members that are partially inside the set are moved to be totally inside the set with an
assigned confidence level (CL) and a dominant decision that both are determined by a
Bayesian model. For details consult Hashemi et al. (2008).
As a brief description of rough set and modified rough set, we start with a few essential
definitions as follows.
Diatom Algae
(The rest of the
objects in the
slice are debris
and/or bubbles)

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Def. 1: An approximation space P is an ordered pair, P = (U, R) where, U is a set called the
universe and R is a binary equivalence relation on U.
Def. 2: Let A  U and let E* be a family of equivalence classes of R. The set A is definable in
P if for some G  E*, set A is equal to the union of all the sets in G; Otherwise, A is a
non-definable or a rough set.
Def. 3: A rough set A is represented by its upper and lower approximations.
Upper(A) = {a  U | [a]R  A  Ø} and
Lower(A) = {a  U | [a]R  A}, where, [a]R is the equivalence class of relation R
containing a. The set Ms(A) = Upper(A) – Lower (A) is called a boundary of A in P.
To find the rough sets for a given dataset, the dataset is considered as an information
system (a rough Sets terminology) and it is defined as follows:
Def. 4: An information system, S, is a quadruple (U, Q, V, d) Where,
U is a non-empty finite set of objects, u;
Q is a finite set of attributes, q;
V = qQVq, and Vq is the domain of attribute q.
d is a mapping function such that d (a,q)Vq for every q  Q and a  U.
As an example, Table 1 presents an information system. The information system is
reduced vertically and horizontally. In vertical reduction process, all the duplicated records are
collapsed into one. This reduced information system has an internal configuration which
simply says all the records are unique considering the Q attributes. In horizontal reductions,
those condition attributes that their removal does not change the configuration of the system
are removed, Table 2.
Table 1. An information system with linguistic values of L: low, M: medium, and H: high
U
Q
Condition
Attributes
Decision
Attribute
C1
C2
C3
a1
L
H
L
1
a2
M
L
M
2
a3
L
L
M
2
a4
M
M
H
1
a5
L
H
L
1
a6
M
M
H
2
a7
M
L
M
2
a8
M
L
M
1
a9
L
M
M
2
Table 2. Reduced information system of Table 1
U
Q
Condition
Attributes
Decision
Attribute
C1
C2
z1={a1, a5}
L
H
1
z2={a2, a7}
M
L
2
z3={a3}
L
L
2
z4={a4}
M
M
1
z5={a6}
M
M
2
z6={a8}
M
L
1
z7={a9}
L
M
2

MINING DIATOM ALGAE FOSSIL DATA FOR DISCOVERING PAST LAKE SALINITY
107
The partition of the reduced information system using the decision values produce the
elementary sets of L1 = {z1, z4, z6} and L2 = {z2, z3, z5, z7} for D = 1 and D = 2, respectively.
The elementary sets for the condition attributes in C are: R1 = {z1}, R2 = {z2, z6}, R3 = {z3}, R4
= {z4, z5}, and R5 = {z7}.
The lower approximation spaces for D = 1 and D =2 are: Lower (L1) = {z1} and Lower
(L2) = {z3, z7}. The upper approximation spaces for D = 1 and D = 2 are: Upper (L1) = {z4, z5,
z2, z6} and Upper (L2) = {z4, z5, z2, z6}.
We extract patterns from the lower approximation spaces of the decisions in form of if . . .
Then rules. These patterns are known as the local certain rules and they are:
If C1 = L ^ C2 = H then D = 1, If C1 = L ^ C2 = L then D = 2,
If C1 = L ^ C2 = M then D = 2.
We also extract patterns from the upper approximation spaces of the decisions and they are
known as the local possible rules:
If (C1 = M ^ C2 = M) then D = 1, If (C2 = M ^ C2 = M) then D = 2,
If (C1 = M ^ C2 = L) then D = 2, If (C1 = M ^ C2 = L) then D = 1.
The set of objects in Upper(L1) is the same of the set of objects in Upper (L2). The
Bayesian model suggests D = 2 as the dominant decision with the confidence level of 3/5 =
0.6. One can change the decisions for the objects in Upper (L1) to the dominant decision by
introducing a confidence level to the decision values of all objects in the information system.
As a result, the previous local possible rules change into two new local certain rules with
confidence level of 60%. Since the local possible rules no longer exist, we refer to local
certain rules simply the Local rules. The list of all extracted local rules is shown in Table 3.a.
Basically, for each rough set the lower approximation space has been expanded to make
sure all the members are totally inside the set (with assigned confidence levels) and the upper
approximation space no longer exist. Enforcing the expansion of the lower approximation
space and, therefore, generation of local rules constitutes Modified Rough Sets methodology.
Table 3. Extracted patterns using Modified Rough Sets: (a) Local rules and (b) Global rules.
The set of conditions in each local rule is unique throughout the entire set. The local rules
can be turned into the global rules by minimizing the number of conditions in each local rule
while preserving its uniqueness. The list of global rules produced from the local rules of Table
3 is shown in Table 3.b.
3.2 Extension of Patterns
Let us assume that an attribute of interest (AOI) exist such that a domain expert can generate
linguistic values for it using a set of global rules. For example, let the water salinity level be
an AOI for the dataset F. If decision D = 1 means “Drought” in a given global rule then, the
Local Rules:
If (C1=L ^ C2=H) then D=1 (CL=100%)
If (C1=L ^ C2=L) then D=2 (CL=100%)
If (C1=L ^ C2=M) then D=2 (CL=100%)
If (C1=M^ C2=M) then D=2 (CL=60%)
If (C1=M^ C2=L) Then D=2 (CL=60%)
Global Rules
If (C2=H) then D=1 (CL=100%)
If (C1=L ^ C2=L) then D=2 (CL=100%)
If (C1=L ^ C2=M) then D=2 (CL=100%)
If (C1=M^ C2=M) then D=2 (CL=60%)
If (C1=M^ C2=L) Then D=2 (CL=60%)
(a) (b)

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confidence level of 100% suggests the water salinity (the AOI) has a linguistic value of
“high”. Whereas the decision D = 2 (i.e. Rain) with the confidence level of 100% for the same
rule suggests the linguistic value of “low” for the AOI. The same suggestions may be
extended to the confidence levels of CL   where,  is close to 100% and it is selected by the
domain experts. A threshold value for confidence level, TCL, is also selected by the domain
experts and any global rule with the confidence level less than or equal to TCL is dismissed.
Those confidence levels that fall in the interval of (TCL, ) are categorized based on the
number of selecting subintervals that is dictated by the desired granularity of the linguistic
values. For example, if the desired granularity of the linguistic values are coarse (e.g. “Low”,
“Medium”, and “High”) then, the interval of (TCL, ) may be divided into two subintervals
(not necessarily of the same width) to categorize the confidence levels into “low” and
“medium. If the desired granularity of the linguistic values are finer (e.g. “low”,
“medium-low”, “medium”, “medium-high”, and “high”) then, the interval of (TCL, ) may be
divided into four subintervals to categorize the confidence levels of every global rule. The
number of subintervals and the width of each subinterval are decided by the domain experts.
We refer to the above mentioned process as the extension of patterns (the global rules) in
reference to an AOI. The result of such extension for global rules of Table 3.b and for the AOI
of the water salinity level is shown in Table 4.
Table 4. Extended patterns for global rules of Table 3.b and water salinity level(S) as an AOI
Patterns: (For  = 90, coarse linguistic values, and TCL = 57%)
P1: If (C2 = H) then S= H,
P2: If (C1 = L ^ C2 = L) then S= L
P3: If (C1 = L ^ C2 = M) then S= L
P4: If (C1 = M^ C2 = M) then S= M
P5:If (C1 = M^ C2 = L) then S= M
3.3 Membership Functions and Defuzzification Process
Let P be the set of patterns in Table 4 in which the conditions C1 and C2 stand for two algae
abundances—Alga1 and Alga2. The Alga1, Alga2, and salinity level have values of “low”,
“medium”, and “high”. Each fuzzy value has its own membership function. To define these
functions, we have collected the possible tolerance level of salinity for algae from the
literature (Hodgson et al. 2013, Borton 2005, Round et al. 1990, Melack et al. 2001) and two
domain experts used the data to conclude the membership functions for the fuzzy values of
algae indices and the salinity levels. The results are shown in Figure 2.
Figure 2. Membership functions for: (a) the alga index values and (b) the salinity levels
0 .1 .2 .3 1 4 4.3 8.0 14.1 46
Salinity Level mS/cm
0 .015 .03 .04 .05 .3 .4 .5 1.00
Alga Index
Low Medium High
Membe
rship
Degree
0
1
Low Medium High
0
1
(a)
(b)

MINING DIATOM ALGAE FOSSIL DATA FOR DISCOVERING PAST LAKE SALINITY
109
There are five patterns in Table 4 and each pattern has a set of conditions and a consequent
which are expressed in fuzzy values. Calculation of a crisp value for the consequent given
crisp values for the conditions is done through a defuzzification process. The following steps
are involved in this process:
Step 1: Calculating degree of membership for conditions’ crisp values.
Step 2: Inferring degree of membership for the consequent using P and the results
delivered by step 1. The outcome is a set of membership degrees for the
consequent (one membership degree per pattern).
Step 3: Grouping the set of membership degrees into m groups in reference to the m fuzzy
values for the consequent and find the minimum value in each group as the
composed value for the group.
Step 4: Determine the areas under the membership function curves for the fuzzy values of
the consequent using the results obtained in step 3. Calculate the coordinates of
the overall centroid of the areas. The x coordinate of the overall centroid is the
crisp value for the consequent.
The following subsection covers the detailed explanation of each step.
3.3.1 Detailed Explanations
Let us assume that the abundance crisp values of algae for a record, R, are obtained in the lab,
and they are: Alga1 = 0.03 and Alga2 = 0.35. The explanation of each step in reference to the
crisp values of Aga1 and Alga2 are cited below.
Step 1: The crisp value of Alga1 = 0.03 has membership degrees of 1, 0.5 and 0 in the
“low”, “medium”, and “high”, respectively, Figure 3.a. The degree of membership for Alga2 =
0.35 in the three fuzzy values are 0, 0.4, and 0.2., Figure 3.a.
Figure 3. Degree of memberships for: (a) crisp values of Alga1 = 0.03 and Alga2 = 0.35 and (b) The
boundary of the area under curves for the record R
Step 2: Let us first look at the pattern P2: If (Alga1 = L ^ Alga2 = L) then S= L.
The condition (Alga1 = Low) is replaced by the membership degree of Alga1 in the “low”
fuzzy value (i.e. 1) and condition (Alga2 = Low) is replaced by value of zero (UNC-Charlotte
2016). The value for the condition (S = Low) is the Min(1, 0) = 0. Following the same
process, the inferred degrees of membership for the Salinity Level using the rest of the five
patterns of Table 4 are:
0 .015 .03 .04 .05 .3 .4 .5 1.00
Alga Index
(a)
Low Medium High
Memb
ership
Degree
0
.4 .5
1
0 .1 .2 .3 1 4 4.3 8.0 14.1 46
Salinity Level mS/cm
(b)
Low Medium High
0
.2
.4
1

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P1: High(S) = Min[High (Alga2)] = 0.2
P3: Low(S) = Min[Low(Alga1), Med(Alga2)] = 0.4
P4: Med(S) = Min[Med(Alga1), Med(Alga2)] = 0.4
P5: Med(S) = Min[Med(Alga1), Low(Alga2)] = 0
Step 3: Compose one crisp value out of the several crisp values produced for the
membership degree of salinity level for a given fuzzy value by choosing the maximum crisp
value among all the membership degree for the sanity level. As an example, for the salinity
level of “low”, P2 delivers the crisp value of zero for Low(S) and P3 delivers the crisp value of
0.4 for the same fuzzy value of salinity. Thus, the composed crisp value for: Low(S) = Max(0,
0.4) = 0.4. Using the same analogy, the rest of the composed values are: Med(S) = Max(0.4, 0)
= 0.4 and High(S) = Max(0.2) = 0.2.
Step 4: Find separately the area under the curves for the membership functions of the
sanity level “Low” “Medium”, and “High” for Low(S) = 0.4, Med(S) = 0.4 and High (S) =
0.2, respectively. The result is three under the curve areas in shape of trapezoids and the
boundary of each area under curves, for the record R, is shown by different types of thick
broken lines in Figure 3.b.
Finding the overall centroid for the identified areas is done by, first, finding the centroids
of the three trapezoids separately and then, finding the centroid of the triangle that its vertices
are the centroids of the three trapezoids. To find the centroid of a trapezoid, consider the
trapezoid of Figure 4, that its larger parallel side is on X axis (Efunda 2016).
Figure 4. A typical under the curve area
The coordinates of the centroid for a trapezoid are:
x =  
󰇛󰇜   and y = 󰇛󰇜
󰇛󰇜 (1)
Where, a =(x2-x1), b=(x3-x2), c=(x4-x1), and h = y1.
The coordinates of the centroid for a triangle are:
x = 
y = 
 (2)
Where, xi and yi are the x and y coordinates of the i-th vertex of the triangle.
Using the above formulas deliver the x= 10.97 and y = 0.15 for the coordinates of the
overall centroid. The value of x is the crisp value for the water salinity level of the given
record.
(x1, y1) (x2, y1) (x3, y1)
(x1, y2) (x4, y2)
h

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111
4. EMPIRICAL RESULTS
The given historical dataset is based on the data collected by Hodgson et al. (2013) and it is
representative of the diatom algae fossils and climate change for nearly 2000 years in the
Santa Fe Lake region, New Mexico, USA. The dataset has 75 records and 84 attributes. One
attribute represents the climate as the dependent variable with possible values of “Drought”
and “Rain”. The other 83 attributes represent the abundance of 83 species of algae (algae
indices) as independent variables expressed in linguistic values of “Low”, “Medium” and
“High”. Each record represents a slice of the retrieved Diatom fossils (one cm in height) from
the bottom of the lake.
A pre-processing step was completed to identify and remove the redundant independent
variables using the entropy approach (Natt et al. 2012). The final cleaned dataset had 75
records and seven attributes: climate and six non-redundant algae species of Achnanthes
lanceolata var. lanceolata, Cyclotella meneghiniana, Fragilaria construens var. venter,
Fragilaria pinnata var. pinnata, Navicula laevissima, and Pinnularia abaujensis var.
subundulata. (The membership functions of Figure 2 are derived only for the non-redundant
algae).
Our hybrid methodology of Modified Rough Sets and Fuzzy Logic was applied on the
dataset and salinity level of each slice of the diatom fossils was calculated. The calculation
was completed under the following parameters: TCL = 67%,  = 90%,  = 74%, and desired
level of granularity = coarse. It is crucial to determine the validity of the calculated historical
salinity results. The process for measuring the validity of the results is the subject of the
following subsection.
4.1 Validity Measurement
To measure the validity of results produced by the proposed hybrid system, we have generated
seven pairs of training and test sets out of the fossil dataset (in linguistic values) such that the
records of one test set do not appear in any of the other test sets and each test set contains ten
records (roughly 13% of the total records) that are chosen randomly. The crisp values of the
algae for the test records along with the climate value of “drought/rain” were borrowed from
the data reported in (Hodgson et al. 2013).
Figure 5. The regions of interest in the membership functions of salinity
F
B
D
A
C
0 .1 .2 .3 1 4 4.3 8.0 14.1 46 50
Salinity Level mS/cm
Low Medium High
Members
hip
Degree
0
1
E

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The following two steps were applied separately on every training set and the salinity level
for each record of the corresponding test set was produced:
1. The proposed hybrid system was applied on the training set to get the global rules
and identify the extended patterns in reference to water salinity level.
2. For every record in the test set, the crisp values of the conditions were used to derive
a crisp salinity level for the record using the membership functions and
defuzzification process.
The produced salinity level for each test record suggests a climate for the test record based
on Figure 5. There are six specific regions of interest under the curves of the salinity
membership functions of Figure 5, named A, B, C, D, E, and F. If the overall centroid appears
in areas of A, B, C, D, E, and F, the suggested climates are “rain, “rain”, “unknown”, “rain”,
“drought”, and “drought”, respectively. For our example, the overall centroid is located in area
F which means climate = “drought”.
The suggested climate value may be in agreement or disagreement with the actual climate
value of the record. In either case the results are recorded. The percentage of the agreement
between the suggested climate by the salinity level and the actual climate value for each test
set is shown in Table 5 which suggests that the mined historical salinity levels have a high
average degree of validity—72%.
Table 5. The results of validity checking of the calculated salinity
Test Sets
1
2
3
4
5
6
7
Average
Validity (%)
60
70
80
82
70
80
60
72
5. CONCLUSIONS AND FUTURE RESEARCH
The data used in this research represented the diatom algae fossils and climate change for
nearly 2000 years in an alpine region of New Mexico, USA. The drought/rain cycles of the
past for the region were established by Hodgson et al. (2013). During a drought cycle water
was evaporated in a larger scale causing increase in the salinity of the water, which in turn
eliminated some type of algae while some other types flourished. During a rain cycle, the
water level increased causing a decrease in the salinity level of the water, which in turn those
algae flourished with lower levels of tolerance for the saltier water. Therefore, it seems
logical to use the diatom algae fossils to discover the salinity level of water in which the algae
lived. In addition, the expression of the fossil data in linguistic values and disagreement about
the reported range of tolerance level of salinity for different algae in literature suggest the use
of Modified Rough Sets and Fuzzy Logic as the best way (if not the only way) to extract the
historical water salinity levels.
The results revealed that our methodology has a great potential in mining of the historical
salinity level for a body of water using diatom algae fossils. Discovery of the historical
salinity of inland lakes is extremely important to understanding climate change, carbon
dioxide levels, and global warming.
Investigation of the relationships among the three entities of historical salinity, solar
intensity, and Human contribution to the global warming is in progress as the future research.

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113
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