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Fuzzy set theory has been developed to solve problems where the descriptions of activities and observations are imprecise, vague, or uncertain. The term “fuzzy” refers to a situation in where there are no well defined boundaries of the set of activities or observations to which the descriptions apply. For example, one can easily assign a person 180cm tall to the “class of tall men”. But it would be...
The fuzzy programming approach [194, 410, 412] is useful and efficient for treating a programming problem under uncertainty. While a classical and stochastic programming approach may cost a lot to obtain the exact coefficient value or distribution, fuzzy programming approach does not [411]. From this fact, fuzzy programming approach can be very advantageous when the coefficients are not known exactly...
Since the fuzzy set was initialized by Zadeh[9], the possibility theory has been developed Dubios and Prade[48], and it has been applied in many fields. Later, many scholars proposed the concept of two-fold uncertain variables, combined fuzzy variables with fuzzy and random variables. The concept of the fuzzy random variable was first defined by Kwakernaak [215]. There are further scholars who defined...
When we dig into the uncertainty of a fuzzy set, there are two cases: the memberships are also fuzzy, and the elements are also fuzzy. So there exists a level-2 fuzzy set and type-2 fuzzy set which originally proposed by Zadeh. Then some scholars elaborated these two concepts, respectively.
The concept of a rough set was first raised by Pawlak [340]. Then Liu [226] proposed the fuzzy rough (Fu-Ro) variable by combining the fuzzy variable and rough variable. Xu and Zhao [343] discussed the properties of Fu-Ro variable, and introduced the Fu- Ro multi-objective decision making models and the ways to deal with them, some crisp equivalent models are given and relative algorithms are proposed...
Fuzzy-like multiple objective decision making (FLMODM) considers multiple objective decision making under fuzzy-like environments. In this book, we focus on fuzzy-like uncertainty, and develop a series of multiple objective decision making problems: - Multiple objective decision making under a fuzzy random environment; - Multiple objective decision making under a bifuzzy environment; ...
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