## The Weighting Issue in Fuzzy Logic (1997)

Venue: | Informatica: An International Journal of Computing and Informatica |

Citations: | 6 - 2 self |

### BibTeX

@ARTICLE{Luo97theweighting,

author = {Xudong Luo and Chengqi Zhang and J. Cai and Jingqiu Cai},

title = {The Weighting Issue in Fuzzy Logic},

journal = {Informatica: An International Journal of Computing and Informatica},

year = {1997},

volume = {21},

pages = {255--262}

}

### OpenURL

### Abstract

this paper is to establish a class of models for solving the weight problem in fuzzy logic. First, some constraints that weighted fuzzy logic should satisfy are given based on Triangular norms and conorms. Then, based on these constraints, a class of models (referred to as relative weighted models) are established for handling weights in fuzzy logic. These models are novel in three aspects: (1) they include non-weighted models as their special cases, (2) the weighted conjunction and weighted disjunction can be distinguished from each other, and (3) the information from all sub-propositions can be sufficiently considered. In addition, this paper proposes principles for selecting proper weighted models. 1 Introduction

### Citations

555 |
On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decision Making
- Yager
- 1988
(Show Context)
Citation Context ...sitions are usually assumed to carry equal importance in traditional knowledge-based systems. However, this is not true when experts are interviewed [4, 8, 9, 12], or the decision process is analyzed =-=[6, 10, 14]-=-. In fact, different sub-propositions may have different (even quite different) influences on a composite proposition. Such a case is often encountered in practical applications. In order to take acco... |

95 |
The role of fuzzy logic in the management of uncertainty in expert systems
- Zadeh
- 1983
(Show Context)
Citation Context ...xxx--yyy X. Luo et al. weighted fuzzy logic should degenerate into a nonweighted fuzzy logic. For a non-weighted conjunctionsA = A 1s\Delta \Delta \Delta A n , its fuzzy truth value T (A) is given by =-=[15]-=-: T (A) = minfT (A 1 ); \Delta \Delta \Delta ; T (A n )g (3) On the other hand, in the weighted averaging model, when w 1 = \Delta \Delta \Delta = w n = 1 n , formula (2) becomes: T (A) = P n i=1 T (A... |

64 | A class of fuzzy measures based on triangular norms - Dubois, Prade - 1982 |

41 | On a general class of fuzzy connectives - Yager - 1980 |

34 |
Criteria aggregation and ranking of alternatives in the framework of fuzzy set theory
- Dubois, Prade
- 1984
(Show Context)
Citation Context ... other kinds of operators can consider information comprehensively from all sub-propositions. In fact, the above operators are some typical pairs of T-norms and their dual T-conorms. Dubois and Prade =-=[3]-=- have shown that T-norms and T-conorms are the most general families of binary functions, which respectively satisfy the requirements of the conjunction and disjunction operators. The axiomatic defini... |

13 |
Importance in knowledge systems
- Sanchez
- 1989
(Show Context)
Citation Context ...sitions are usually assumed to carry equal importance in traditional knowledge-based systems. However, this is not true when experts are interviewed [4, 8, 9, 12], or the decision process is analyzed =-=[6, 10, 14]-=-. In fact, different sub-propositions may have different (even quite different) influences on a composite proposition. Such a case is often encountered in practical applications. In order to take acco... |

4 | A Unified Algebraic Structure for Uncertain Reasonings - Luo, Zhang - 1996 |

3 | NLPM: an approach for non-monotonic reasoning based on linguistic probability - Shi, Luo - 1992 |

1 |
Selection Uncertainty Calculi and Granularity: An Experiment Trading-off Precision and Complexity
- Bonisssone
- 1986
(Show Context)
Citation Context ...roblem in fuzzy logic. The weighted averaging model can be described as follows: Suppose that there are n sub-propositions. Let A i denote a sub-proposition of the composite proposition A, T (A i ) 2 =-=[0; 1]-=- denote the fuzzy truth value of A i , and w i denote the weight of A i , which satisfies P n i=1 w i = 1. If a composite proposition in the form of weighted conjunction is A = A 1 (w 1 )s\Delta \Delt... |

1 |
The Fuzzy Logic of a Text Understanding
- Rocha
- 1987
(Show Context)
Citation Context ...f multiple subpropositions, the different sub-propositions are usually assumed to carry equal importance in traditional knowledge-based systems. However, this is not true when experts are interviewed =-=[4, 8, 9, 12]-=-, or the decision process is analyzed [6, 10, 14]. In fact, different sub-propositions may have different (even quite different) influences on a composite proposition. Such a case is often encountered... |

1 |
Knowledge Processing and Expert Systems. National Defence Industry
- He
- 1990
(Show Context)
Citation Context ...th value of the composite proposition using the truth value of every sub-proposition and its corresponding weight. In this paper, we discuss this issue in the context of fuzzy logic. Some researchers =-=[5, 14]-=- have tried to exploit the weighted averaging model to cope with the weight problem in fuzzy logic. The weighted averaging model can be described as follows: Suppose that there are n sub-propositions.... |

1 |
Zadeh's Commonsense Knowledge. Approximate Reasoning in Expert Systems
- Kacprzick
- 1985
(Show Context)
Citation Context ...sitions are usually assumed to carry equal importance in traditional knowledge-based systems. However, this is not true when experts are interviewed [4, 8, 9, 12], or the decision process is analyzed =-=[6, 10, 14]-=-. In fact, different sub-propositions may have different (even quite different) influences on a composite proposition. Such a case is often encountered in practical applications. In order to take acco... |

1 |
Handling Uncertainty
- Rocha, Theoto, et al.
- 1989
(Show Context)
Citation Context ...f multiple subpropositions, the different sub-propositions are usually assumed to carry equal importance in traditional knowledge-based systems. However, this is not true when experts are interviewed =-=[4, 8, 9, 12]-=-, or the decision process is analyzed [6, 10, 14]. In fact, different sub-propositions may have different (even quite different) influences on a composite proposition. Such a case is often encountered... |

1 |
Declarative and Procedural Knowledge: Two Complimentary Tools for Expertise. Approximate Reasoning Tools for Artificial Intelligence, Verlag Tuv Rheinland
- Rocha, Laginha, et al.
- 1990
(Show Context)
Citation Context ...f multiple subpropositions, the different sub-propositions are usually assumed to carry equal importance in traditional knowledge-based systems. However, this is not true when experts are interviewed =-=[4, 8, 9, 12]-=-, or the decision process is analyzed [6, 10, 14]. In fact, different sub-propositions may have different (even quite different) influences on a composite proposition. Such a case is often encountered... |

1 |
Fuzzy Belief and Text Understanding
- Theoto
- 1990
(Show Context)
Citation Context |