Parameterized fuzzy operators in fuzzy decision making

Abstract

The basic operations of fuzzy sets, such as negation, intersection, and union, usually are computed by applying the one-complement, minimum, and maximum operators to the membership functions of fuzzy sets. However, different decision agents may have different perceptions for these fuzzy operations. In this article, the concept of parameterized fuzzy operators will be introduced. A parameter ␣ will be used to represent the degree of softness. The variance of ␣ captures the differences of decision agents' subjective attitudes and characteristics, which result in their differing perceptions. The defined parameterized fuzzy operators also should satisfy the axiomatic requirements for the traditional fuzzy operators. A learning algorithm will be proposed to obtain the parameter ␣ given a set of training data for each agent. In this article, the proposed parameterized fuzzy operators will be used in individual decision-making problems. An example is given to show the concept and application of the parameterized fuzzy operators.

Hybrid Decision-Making Frameworks under Complex Spherical Fuzzy N -Soft Sets

“…Step 6: the complex spherical fuzzy normalized Euclidean distance of each alternative is given in Table 49 and computed by the formula [16], from CSF-PIS: (4, (0.85e i1.66π , 0.021e i0.042π , 0.23e i0.52π )) (2, (0.22e i0.44π , 0.027e i0.058π , 0.91e i1.74π )) z 2 (4, (0.88e i1.76π , 0.021e i0.042π , 0.174e i0.038π )) (2, (0.31e i0.66π , 0.029e i0.06π , 0.87e i1.74π )) z 3 (3, (0.601e i1.22π , 0.019e i0.034π , 0.53e i1.1π )) (2, (0.2e i0.4π , 0.019e i0.034π , 0.91e 1.82π )) z 4 (3, (0.47e i0.96π , 0.028e i0.056π , 0.73e 1.42π )) (2, (0.15e i0.318π , 0.025e i0.052π , 0.89e 1.8π )) z 5 (2, (0.19e i0.38π , 0.035e i0.068π , 0.95e i1.9π )) (2, (0.5e iπ , 0.023e i0.046π , 0.67e i1.36π ))…”

“…is means an extension of binary valuations, which is, henceforth, referred to as crisp evaluations. Concerning its use for solving MADM and MAGDM problems in fuzzy environments, Song et al [4] gave an algorithm based on arithmetic operators, and Chen [5] built up a theory for a fuzzy-TOPSIS method. No doubt, FS theory produced a turn of direction in the field of decision-making.…”

Parameterized continuous models of fuzzy reasoning

“…However, generally fuzzy sets express humanity's knowledge and experience whose main character is flexibility. Many decisions must be made under imprecision and uncertainty, which cannot be represented easily by the crisp intersection, union, and negation of fuzzy sets [2]. References [2][3][4][5][6] have taken notice of this flaw of the basic operations of fuzzy sets and proposed many schemes to soften these operations.…”

“…Many decisions must be made under imprecision and uncertainty, which cannot be represented easily by the crisp intersection, union, and negation of fuzzy sets [2]. References [2][3][4][5][6] have taken notice of this flaw of the basic operations of fuzzy sets and proposed many schemes to soften these operations. One typical scheme is to use Schweizer-Sklar t-norms to soften crisp intersection^; the other soft basic operations can be induced by this softened intersection.…”

A fuzzy logic system based on Schweizer-Sklar t-norm

“…By giving a reasonable explanation to the parameters in the parametric t-norms, the flexibility in fuzzy reasoning is reflected (in fact, many scholars are studying the parametric fuzzy logic controls, as seen in refs. [13][14][15][16]), this may provide a new way to combine fuzzy logic with fuzzy reasoning.…”