# An Intuitionistic Extension of the Simple WISP Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Preliminaries

#### 2.1. The Basic Elements of Intuitionistic Fuzzy Sets

**Definition**

**1.**

**Definition**

**2.**

**Definition**

**3.**

**Definition**

**4.**

_{(i)}of i is as follows [54]:

**Definition**

**5.**

_{j}is as follows [55]:

_{j}denotes the weight of element j of the collection A

_{j}, ${w}_{j}\in \left[0,1\right],$and ${{\displaystyle \sum}}_{j=1}^{n}{w}_{j}$= 1.

**Definition**

**6.**

_{j}is as follows [55]:

_{j}denotes the weight of element j of the collection A

_{j}, ${w}_{j}\in \left[0,1\right]$and ${{\displaystyle \sum}}_{j=1}^{n}{w}_{j}$= 1.

#### 2.2. Deintuitionistification

## 3. The Simple Weighted Sum-Product Method

_{i}is the most preferable.

## 4. An Intuitionistic Extension of the WISP Method

_{i}.

## 5. A Numerical Example

_{1}), financial position (C

_{2}), standards and relevant certificates (C

_{3}), commercial strength (C

_{4}), performance (C

_{5}), and delivery price (C

_{6}).

_{3}is the most appropriate alternative.

## 6. A Comparison of the Proposed Extension with Similar Extensions of Some MCDM Methods

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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C_{1} | C_{2} | C_{3} | C_{4} | C_{5} | C_{6} | |
---|---|---|---|---|---|---|

w_{j} | 0.210 | 0.137 | 0.137 | 0.131 | 0.175 | 0.210 |

Optimization | max | max | max | max | max | min |

A_{1} | <0.9, 0.0> | <0.7, 0.0> | <0.9, 0.0> | <1.0, 0.1> | <1.0, 0.0> | <1.0, 0.1> |

A_{2} | <0.9, 0.1> | <0.8, 0.1> | <1.0, 0.1> | <0.9, 0.0> | <0.8, 0.0> | <0.9, 0.1> |

A_{3} | <0.7, 0.0> | <1.0, 0.0> | <1.0, 0.0> | <1.0, 0.0> | <0.9, 1.0> | <0.9, 0.0> |

A_{4} | <0.8, 0.0> | <0.8, 0.1> | <0.9, 0.1> | <1.0, 0.0> | <1.0, 0.0> | <1.0, 0.2> |

${\mathit{S}}_{\mathit{i}}^{+}$ | ${\mathit{S}}_{\mathit{i}}^{-}$ | ${\mathit{P}}_{\mathit{i}}^{+}$ | ${\mathit{P}}_{\mathit{i}}^{-}$ | |
---|---|---|---|---|

A_{1} | <0.08, 0.00> | <0.00, 0.62> | <0.92, 1.00> | <1.00, 0.38> |

A_{2} | <0.10, 0.00> | <0.02, 0.62> | <0.90, 1.00> | <0.98, 0.38> |

A_{3} | <0.09, 0.00> | <0.02, 0.00> | <0.91, 1.00> | <0.98, 1.00> |

A_{4} | <0.09, 0.00> | <0.00, 0.71> | <0.91, 1.00> | <1.00, 0.29> |

${\mathit{S}}_{\mathit{i}}^{+}$ | ${\mathit{S}}_{\mathit{i}}^{-}$ | ${\mathit{P}}_{\mathit{i}}^{+}$ | ${\mathit{P}}_{\mathit{i}}^{-}$ | ${\mathit{u}}_{\mathit{i}}^{\mathit{s}\mathit{d}}$ | ${\mathit{u}}_{\mathit{i}}^{\mathit{p}\mathit{d}}$ | ${\mathit{u}}_{\mathit{i}}^{\mathit{s}\mathit{r}}$ | ${\mathit{u}}_{\mathit{i}}^{\mathit{p}\mathit{r}}$ | |
---|---|---|---|---|---|---|---|---|

A_{1} | 0.08 | −0.62 | −0.08 | 0.62 | 0.70 | −0.70 | −0.13 | −0.13 |

A_{2} | 0.10 | −0.59 | −0.10 | 0.59 | 0.69 | −0.69 | −0.17 | −0.17 |

A_{3} | 0.09 | 0.02 | −0.09 | −0.02 | 0.07 | −0.07 | 4.07 | 4.07 |

A_{4} | 0.09 | −0.71 | −0.09 | 0.71 | 0.80 | −0.80 | −0.12 | −0.12 |

**Table 4.**The recalculated values of four utility measures, overall utility measures, and ranking order of alternatives.

${\overline{\mathit{u}}}_{\mathit{i}}^{\mathit{s}\mathit{d}}$ | ${\overline{\mathit{u}}}_{\mathit{i}}^{\mathit{p}\mathit{d}}$ | ${\overline{\mathit{u}}}_{\mathit{i}}^{\mathit{s}\mathit{r}}$ | ${\overline{\mathit{u}}}_{\mathit{i}}^{\mathit{p}\mathit{r}}$ | ${\mathit{u}}_{\mathit{i}}$ | Rank | |
---|---|---|---|---|---|---|

A_{1} | 0.94 | 0.32 | 0.17 | 0.17 | 0.402 | 2 |

A_{2} | 0.94 | 0.33 | 0.16 | 0.16 | 0.399 | 3 |

A_{3} | 0.59 | 1.00 | 1.00 | 1.00 | 0.898 | 1 |

A_{4} | 1.00 | 0.21 | 0.17 | 0.17 | 0.390 | 4 |

λ | 0.01 | 0.25 | 0.5 | 0.75 | 0.999 | |||||
---|---|---|---|---|---|---|---|---|---|---|

${\mathit{u}}_{\mathit{i}}$ | Rank | ${\mathit{u}}_{\mathit{i}}$ | Rank | ${\mathit{u}}_{\mathit{i}}$ | Rank | ${\mathit{u}}_{\mathit{i}}$ | Rank | ${\mathit{u}}_{\mathit{i}}$ | Rank | |

A_{1} | 0.581 | 3 | 0.666 | 2 | 0.494 | 2 | 0.700 | 2 | −5.021 | 4 |

A_{2} | 0.581 | 3 | 0.638 | 3 | 0.491 | 3 | 0.693 | 4 | 0.993 | 1 |

A_{3} | 0.755 | 1 | 0.697 | 1 | 0.934 | 1 | 0.961 | 1 | 0.967 | 2 |

A_{4} | 0.622 | 2 | 0.175 | 4 | 0.491 | 3 | 0.696 | 3 | −4.596 | 3 |

C_{1} | C_{2} | C_{3} | C_{4} | |
---|---|---|---|---|

En | Co | Gr | Au | |

w_{j} | 0.28 | 0.25 | 0.24 | 0.23 |

Optimization | max | max | max | max |

A_{1} | <0.742, 0.125> | <0.625, 0.375> | <0.590, 0.250> | <0.375, 0.250> |

A_{2} | <0.595, 0.327> | <0.750, 0.158> | <0.590, 0.125> | <0.500, 0.250> |

A_{3} | <0.717, 0.155> | <0.500, 0.125> | <0.586, 0.327> | <0.339, 0.176> |

**Table 7.**The overall utility measures and ranking order of alternatives obtained using intuitionistic extensions of some MCDM methods.

WASPAS | Rank | CoCoSo | Rank | SAW | Rank | WISP | Rank | |
---|---|---|---|---|---|---|---|---|

A_{1} | 0.325 | 3 | 1.884 | 3 | 0.380 | 3 | 0.963 | 3 |

A_{2} | 0.300 | 1 | 2.164 | 1 | 0.419 | 1 | 1.000 | 1 |

A_{3} | 0.323 | 2 | 1.902 | 2 | 0.381 | 2 | 0.966 | 2 |

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**MDPI and ACS Style**

Zavadskas, E.K.; Stanujkic, D.; Turskis, Z.; Karabasevic, D. An Intuitionistic Extension of the Simple WISP Method. *Entropy* **2022**, *24*, 218.
https://doi.org/10.3390/e24020218

**AMA Style**

Zavadskas EK, Stanujkic D, Turskis Z, Karabasevic D. An Intuitionistic Extension of the Simple WISP Method. *Entropy*. 2022; 24(2):218.
https://doi.org/10.3390/e24020218

**Chicago/Turabian Style**

Zavadskas, Edmundas Kazimieras, Dragisa Stanujkic, Zenonas Turskis, and Darjan Karabasevic. 2022. "An Intuitionistic Extension of the Simple WISP Method" *Entropy* 24, no. 2: 218.
https://doi.org/10.3390/e24020218