56
B. Uzun et al.
(e) Bounded- Product:
˜
A ˜
B ⇔ μ ˜
A ˜
B = 0 ∨ (μ ˜
A + μ ˜
B − 1)
(36)
where the following symbols; ∨, ,, +, − denote the max, min, arithmetic sum and
arithmetic difference, respectively.
However, the extension of the multi criteria decision analysis method in a fuzzy
environment can be achieved by expressing the importance weights of the criteria
and ratings for the linguistic variables or fuzzy variables. A linguistic variable is
a variable whose meanings are considered linguistic definitions. The concept of a
linguistic variable can be quite useful in cases that are very complex or very badly
assigned so that they can reasonably be described in classical quantitative expressions
(Balioti et al. 2018). However by applying one of the defuzzification technique, the
decision maker could apply to one of the multi criteria decision making techniques
to solve the problem under the fuzzy condition.
References
Balioti V, Tzimopoulos C, Evangelides C (2018) Multi-criteria decision making using topsis method
under fuzzy environment. Appl Spillway Select Proc 2(11):637. https://doi.org/10.3390/procee
dings2110637
Ibarra L, Webb J (2016) Advantages of fuzzy control while dealing with complex/ unknown model
dynamics: a quadcopter example
Kiral E (2018) Modeling brent oil price with markov chain process of the fuzzy states. Pressacademia
5(1):79–83. https://doi.org/10.17261/pressacademia.2018.785
Kiral E, Uzun B (2017) Forecasting closing returns of borsa istanbul index with markov chain
process of fuzzy states. Pressacademia 4(1):15–24. https://doi.org/10.17261/pressacademia.201
7.362
Ozsahin DU, Uzun B, Ozsahin I, Mubarak MT, Musa MS (2020) Fuzzy logic in medicine biomedical
signal processing and artificial intelligence in healthcare Academic Press. In: Zgallai W (ed) Series
developments in biomedical engineering and bioelectronics 153–182
Uzun B, Kıral E (2017) Application of markov chains-fuzzy states to gold price. Proc Comput Sci
120:365–371. Available https://doi.org/10.1016/j.procs.2017.11.251
Uzun B, Kıral E (2019) Evaluating US dollar index movements using markov chains-fuzzy states
approach. In: Aliev R, Kacprzyk J, Pedrycz W, Jamshidi M, Sadikoglu F (eds) 13th International
conference on theory and application of fuzzy systems and soft computing—ICAFS-2018, ICAFS
2018 Advances in intelligent systems and computing, vol 896, Springer, Cham
Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353. Available: https://doi.org/10.1016/s00199958(65)90241-x
Zadeh L (1973) Outline of a new approach to the analysis of complex systems and decision processes.
IEEE Trans Syst Man Cybernet 3(1):28–44. Available https://doi.org/10.1109/tsmc.1973.540
8575
Zadeh L (1968) Fuzzy algorithms. Inf Control 12(2):94–102. Available https://doi.org/10.1016/
s0019-9958(68)90211-8
B. Uzun et al.
(e) Bounded- Product:
˜
A ˜
B ⇔ μ ˜
A ˜
B = 0 ∨ (μ ˜
A + μ ˜
B − 1)
(36)
where the following symbols; ∨, ,, +, − denote the max, min, arithmetic sum and
arithmetic difference, respectively.
However, the extension of the multi criteria decision analysis method in a fuzzy
environment can be achieved by expressing the importance weights of the criteria
and ratings for the linguistic variables or fuzzy variables. A linguistic variable is
a variable whose meanings are considered linguistic definitions. The concept of a
linguistic variable can be quite useful in cases that are very complex or very badly
assigned so that they can reasonably be described in classical quantitative expressions
(Balioti et al. 2018). However by applying one of the defuzzification technique, the
decision maker could apply to one of the multi criteria decision making techniques
to solve the problem under the fuzzy condition.
References
Balioti V, Tzimopoulos C, Evangelides C (2018) Multi-criteria decision making using topsis method
under fuzzy environment. Appl Spillway Select Proc 2(11):637. https://doi.org/10.3390/procee
dings2110637
Ibarra L, Webb J (2016) Advantages of fuzzy control while dealing with complex/ unknown model
dynamics: a quadcopter example
Kiral E (2018) Modeling brent oil price with markov chain process of the fuzzy states. Pressacademia
5(1):79–83. https://doi.org/10.17261/pressacademia.2018.785
Kiral E, Uzun B (2017) Forecasting closing returns of borsa istanbul index with markov chain
process of fuzzy states. Pressacademia 4(1):15–24. https://doi.org/10.17261/pressacademia.201
7.362
Ozsahin DU, Uzun B, Ozsahin I, Mubarak MT, Musa MS (2020) Fuzzy logic in medicine biomedical
signal processing and artificial intelligence in healthcare Academic Press. In: Zgallai W (ed) Series
developments in biomedical engineering and bioelectronics 153–182
Uzun B, Kıral E (2017) Application of markov chains-fuzzy states to gold price. Proc Comput Sci
120:365–371. Available https://doi.org/10.1016/j.procs.2017.11.251
Uzun B, Kıral E (2019) Evaluating US dollar index movements using markov chains-fuzzy states
approach. In: Aliev R, Kacprzyk J, Pedrycz W, Jamshidi M, Sadikoglu F (eds) 13th International
conference on theory and application of fuzzy systems and soft computing—ICAFS-2018, ICAFS
2018 Advances in intelligent systems and computing, vol 896, Springer, Cham
Zadeh L (1965) Fuzzy sets. Inf Control 8(3):338–353. Available: https://doi.org/10.1016/s00199958(65)90241-x
Zadeh L (1973) Outline of a new approach to the analysis of complex systems and decision processes.
IEEE Trans Syst Man Cybernet 3(1):28–44. Available https://doi.org/10.1109/tsmc.1973.540
8575
Zadeh L (1968) Fuzzy algorithms. Inf Control 12(2):94–102. Available https://doi.org/10.1016/
s0019-9958(68)90211-8