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2. An overview of generalized basic logic algebras
- Creator:
- Jipsen, Peter
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- basic logic, residuated lattices, full Lambek calculus, triangular norms, and categorical equivalences
- Language:
- English
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
3. Migrativity properties of 2-uninorms over semi-t-operators
- Creator:
- Li-Jun, Ying and Feng, Qin
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- 2-uninorms, uninorms, semi-t-operators, triangular norms, and triangular conorms
- Language:
- English
- Description:
- In this paper, we analyze and characterize all solutions about α-migrativity properties of the five subclasses of 2-uninorms, i. e. Ck, C0k, C1k, C01, C10, over semi-t-operators. We give the sufficient and necessary conditions that make these α-migrativity equations hold for all possible combinations of 2-uninorms over semi-t-operators. The results obtained show that for G∈Ck, the α-migrativity of G over a semi-t-operator Fμ,ν is closely related to the α-section of Fμ,ν or the ordinal sum representation of t-norm and t-conorm corresponding to Fμ,ν. But for the other four categories, the α-migrativity over a semi-t-operator Fμ,ν is fully determined by the α-section of Fμ,ν.
- Rights:
- http://creativecommons.org/licenses/by-nc-sa/4.0/ and policy:public
4. On the hyperspace of bounded closed sets under a generalized Hausdorff stationary fuzzy metric
- Creator:
- Qiu, Dong, Lu, Chongxia, Deng, Shuai, and Wang, Liang
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Hausdorff metric, hyperspace, triangular norms, and stationary fuzzy metric
- Language:
- English
- Description:
- In this paper, we generalize the classical Hausdorff metric with t-norms and obtain its basic properties. Furthermore, for a given stationary fuzzy metric space with a t-norm without zero divisors, we propose a method for constructing a generalized Hausdorff fuzzy metric on the set of the nonempty bounded closed subsets. Finally we discuss several important properties as completeness, completion and precompactness.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
5. Preservation of properties of fuzzy relations during aggregation processes
- Creator:
- Drewniak, Józef and Dudziak, Urszula
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- fuzzy relation, fuzzy relation properties, fuzzy relation classes, ∗-transitivity, transitivity, aggregation functions, relation aggregation, and triangular norms
- Language:
- English
- Description:
- Diverse classes of fuzzy relations such as reflexive, irreflexive, symmetric, asymmetric, antisymmetric, connected, and transitive fuzzy relations are studied. Moreover, intersections of basic relation classes such as tolerances, tournaments, equivalences, and orders are regarded and the problem of preservation of these properties by n-ary operations is considered. Namely, with the use of fuzzy relations R1,…,Rn and n-argument operation F on the interval [0,1], a new fuzzy relation RF=F(R1,…,Rn) is created. Characterization theorems concerning the problem of preservation of fuzzy relations properties are given. Some conditions on aggregation functions are weakened in comparison to those previously given by other authors.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public
6. Some properties of B-operations
- Creator:
- Butkiewicz, Bohdan
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- fuzzy system, connectives, weak operations, and triangular norms
- Language:
- English
- Description:
- In the paper the problem of mathematical properties of B-operations and weak WB-operations introduced by the author for interpretation of connectives "and'', "or'', and "also'' in fuzzy rules is considered. In previous author's papers some interesting properties of fuzzy systems with these operations were shown. These operations are weaker than triangular norms used commonly for a fuzzy system described by set of rules of the type if - then. Monotonicity condition, required for triangular norms, is replaced by condition of positivity (negativity), i. e. operations must be only positively (negatively) defined. Weak B-operations may not fulfill associativity condition.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public