On clarifying some definitions and notations used for type-2 fuzzy sets as well as some recommended changes

Mendel, Jerry M.; Rajati, Mohammad Reza; Sussner, Peter

doi:10.1016/j.ins.2016.01.015

Cited by 135 publications

(48 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, we sumarize the relevant concepts of fuzzy sets of type-1, and fuzzy sets of type-2, which details can be found in [2,5,6]. Given a universe set, X , the set…”

Section: Fuzzy Background For the Electric Circuit Modelmentioning

confidence: 99%

See 1 more Smart Citation

Fuzzy Linear Programming: Optimization of an Electric Circuit Model

Bertone

Jafelice

Câmara

2018

Tend. Mat. Apl. Comput.

View full text Add to dashboard Cite

ABSTRACT.A problem of a voltage division circuit is modeled in order to determine the values of the resistors centered, in a way that the impedance of the resistance voltage divider is minimal. This problem is equivalent to maximizing the admittance, associated to the resistance, which is defined as the quotient of the electric current and its voltage, measured in Siemens. Three cases are analyzed for the components of the linear programming: real numbers, fuzzy numbers of type-1, and fuzzy sets of type-2. The first case is considered in order to validate the other two cases. The optimal solution in the fuzzy linear programming of type-1 is obtained through a linear defuzzification function, defined in the trapezoidal fuzzy numbers subspace of fuzzy numbers vector space, which allows to solve the corresponding linear programming problem with real components. A study upon the parameter for linear defuzzification is accomplished to determine the best representative of the family of parameters. The α−levels representation theorem is the method to obtain the optimal solution of type-2. For each α−level is solved a fuzzy linear programming problem of type-1, using the previous methodology. Numerical simulations illustrate the results in the three cases.

show abstract

“…In this section, we sumarize the relevant concepts of fuzzy sets of type-1, and fuzzy sets of type-2, which details can be found in [2,5,6]. Given a universe set, X , the set…”

Section: Fuzzy Background For the Electric Circuit Modelmentioning

confidence: 99%

“…It is solved for each α a PL problem of type-1, the method used in case 2. The solution is obtained by applying the representation theorem of α−levels of the sets of type-2 [6].…”

mentioning

confidence: 99%

Fuzzy Linear Programming: Optimization of an Electric Circuit Model

Bertone

Jafelice

Câmara

2018

Tend. Mat. Apl. Comput.

View full text Add to dashboard Cite

show abstract

“…Definition [8]. In the universe of discourse X, a T2FSs Ã can be characterized by μ Ã , the type-2 membership function , expressed as follows:…”

Section: The Concepts Of T2fss and It2fssmentioning

confidence: 99%

“…Calculate the values of S k , R k and Q k by using Eqs. (7)(8)(9), values are presented in Table 6: Table 6 Values of S k , R k and Q k Step 4. Propose the compromise solution Rank the alternative locations, sorting by the values S k , R k and Q k in ascending order.…”

Section: Numerical Examplementioning

confidence: 99%

Type-2 Fuzzy VIKOR Method and Its Application in Facility Location Selection

Liu¹,

Liu²,

Jiang³

2017

Proceedings of 3rd International Symposium on Social Science (ISSS 2017)

View full text Add to dashboard Cite

Abstract. This study presents a multi-criteria group decision making (MCGDM) approach named interval type-2 fuzzy VIKOR method, which aims to help new enterprises determine facility locations in a more reliable way. Initially, decision makers (DMs) describe the alternative locations within the context of linguistic variables. Moreover, this paper models the values of these variables with interval type-2 fuzzy sets (IT2FSs). Finally, a compromise solution which is the 'closet' one to the ideal solution can be obtained through computing by VIKOR method under IT2FSs environment. A numerical example is given to demonstrate the validity of the presented method.

show abstract

“…Index Terms-Interval type-2 fuzzy sets, interval valued fuzzy sets, type-2 fuzzy sets YPE-2 fuzzy sets (T2 FSs) have been beset with some unfortunate notation, although, as is explained in [9], this has not prevented their use nor has it led to any theoretically incorrect results. The work presented in [1] addressed the many facets of the notational problems and there are many useful recommendations in [1] to remedy them.…”

mentioning

confidence: 99%