Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy mo...Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).展开更多
The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measur...The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt.展开更多
This paper demonstrates knowledge-guided fuzzy logic modeling of regional-scale surficial uranium(U)prospectivity in British Columbia(Canada).The deposits/occurrences of surficial U in this region vary from those in W...This paper demonstrates knowledge-guided fuzzy logic modeling of regional-scale surficial uranium(U)prospectivity in British Columbia(Canada).The deposits/occurrences of surficial U in this region vary from those in Western Australia and Namibia;thus,requiring innovative and carefully-thought techniques of spatial evidence generation and integration.As novelty,this papers introduces a new weighted fuzzy algebraic sum operator to combine certain spatial evidence layers.The analysis trialed several layers of spatial evidence based on conceptual mineral system model of surficial U in British Columbia(Canada)as well as tested various models of evidence integration.Non-linear weighted functions of(a)spatial closeness to U-enriched felsic igneous rocks was employed as U-source spatial evidence,(b)spatial closeness to paleochannels as fluid pathways spatial evidence,and(c)surface water U content as chemical trap spatial evidence.The best models of prospectivity created by integrating the layers of spatial evidence for U-source,pathways and traps predicted at least 85%of the known surficial U deposits/occurrences in>10%of the study region with the highest prospectivity fuzzy scores.The results of analyses demonstrate that,employing the known deposits/occurrences of surficial U for scrutinizing the spatial evidence layers and the final models of prospectivity can pinpoint the most suitable critical processes and models of data integration to reduce bias in the analysis of mineral prospectivity.展开更多
In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T...In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).展开更多
How to verify that a given fuzzy set A∈F(X *) is a fuzzy code? In this paper, an algorithm of test has been introduced and studied with the example of test. The measure notion for a fuzzy code and a precise form...How to verify that a given fuzzy set A∈F(X *) is a fuzzy code? In this paper, an algorithm of test has been introduced and studied with the example of test. The measure notion for a fuzzy code and a precise formulation of fuzzy codes and words have been discussed. sification:90K20,94D05.展开更多
A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famo...A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved.展开更多
文摘Triangular norm is a powerful tool in the theory research and application development of fuzzy sets. In this paper, using the triang norm, we introduce some concepts such as fuzzy algebra, fuzzy a algebra and fuzzy monotone class, and discuss the relations among them,obtaining the following main conclusions:Theorem 1: Let (I,S,T,C) be a norm spetem, S and T be dual norm,(Ⅰ) If is a fuzzy σ algebra, then is also a fuzzy monotooe class;(Ⅱ ) If a fuzzy algebra is a fuzzy monotone class, then is also a fuzzy σ algebra.Theorem 2: If φ(X) is a fuzzy algebra, then m (φ) =σ(φ).
文摘The ideas of ambiguous bipolar skepticism under algebra and closed skepticism ambiguous bipolar ideals and related features have been developed.The fuzzy measure ideal is described in terms of bipolar ambiguous measure algebra and bipolar skepticism,and the linkages between bipolar fuzzy measure algebra are determined.A bipolar misty ideal’s skepticism is examined.InBCW andBCL-measure algebra,homogeneous ideas and dubious pictures of fuzzy bipolar measure ideas are examined.Also,we gave the relationship between these concepts.Finally,it is given the perfect terms for an occult bipolar doubt to be a measure of ideal fuzzy bipolar closed doubt.
文摘This paper demonstrates knowledge-guided fuzzy logic modeling of regional-scale surficial uranium(U)prospectivity in British Columbia(Canada).The deposits/occurrences of surficial U in this region vary from those in Western Australia and Namibia;thus,requiring innovative and carefully-thought techniques of spatial evidence generation and integration.As novelty,this papers introduces a new weighted fuzzy algebraic sum operator to combine certain spatial evidence layers.The analysis trialed several layers of spatial evidence based on conceptual mineral system model of surficial U in British Columbia(Canada)as well as tested various models of evidence integration.Non-linear weighted functions of(a)spatial closeness to U-enriched felsic igneous rocks was employed as U-source spatial evidence,(b)spatial closeness to paleochannels as fluid pathways spatial evidence,and(c)surface water U content as chemical trap spatial evidence.The best models of prospectivity created by integrating the layers of spatial evidence for U-source,pathways and traps predicted at least 85%of the known surficial U deposits/occurrences in>10%of the study region with the highest prospectivity fuzzy scores.The results of analyses demonstrate that,employing the known deposits/occurrences of surficial U for scrutinizing the spatial evidence layers and the final models of prospectivity can pinpoint the most suitable critical processes and models of data integration to reduce bias in the analysis of mineral prospectivity.
基金Supported by the NSF of China(10371106,60774073)
文摘In this paper,the topological space(PF_(MP)(X),T) based on prime MP-filters of a lattice FI-algebra X is constructed firstly and we proved that it is a compact T_0-space if X with condition(P).Secondly,we restricted T to the set of all maximal MP-filters MF_(MP)(X) of X and concluded that(PF_(MP)(X),T |_(PF_(MP)(X)) )is a compact T_2 space if X with conditions(P) and(S).
基金Supported by National Natural Science Foundation of China(6980 30 0 7)
文摘How to verify that a given fuzzy set A∈F(X *) is a fuzzy code? In this paper, an algorithm of test has been introduced and studied with the example of test. The measure notion for a fuzzy code and a precise formulation of fuzzy codes and words have been discussed. sification:90K20,94D05.
文摘A great disturbance was raised by the report of Elkan entitled 'The Paradoxical Success of Fuzzy Logic' at the llth Annual Conference on Artificial Intelligence held in the United States in July, 1993. 15 famous experts working in artificial intelligence and fuzzy systems refuted the opinion. Elkan then gave another report entitled 'The Paradoxical Controversy over Fuzzy Logic' as a reply to the refutations mentioned above. Prof. Wu gave a detailed analysis on the controversy (see ref. [3]). This shows that there is no rigid logic foundation for fuzzy propositional calculus. In this note we first point out that it is impossible to keep all classical theorems as tautologies in the field of fuzzy propositional calculus. Then we introduce a formal deductive system in fuzzy propositional calculus by giving up certain classical axioms, and the corresponding soundness theorem is proved.
