By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results...By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results are intuitional and realizable for computer.展开更多
Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of ...Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of a postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing fuzzy truth values and fuzzy set membership functions to re-capture the human knowledge and subjectivity structure in membership function evaluations. We formulate a fractal multi-modal logic of Kabbalah which integrates the cognitive, emotional and behavioral levels of humanistic systems into epistemic and modal, deontic and doxastic and dynamic multi-modal logic. This is done by creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke model type. The Kabbalah possible worlds semantic frame integrates together both the multi-modal logic aspects and their Kripke possible worlds model. We will not focus here on modal operators and axiom sets. We constructively define a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the postmodern fuzzy set theory based on Kabbalah logic and semantics.展开更多
Driven by market requirements, software services organizations have adopted various software engineering process models （such as capability maturity model （CMM）, capability maturity model integration （CMMI）, ISO ...Driven by market requirements, software services organizations have adopted various software engineering process models （such as capability maturity model （CMM）, capability maturity model integration （CMMI）, ISO 9001：2000, etc.） and practice of the project management concepts defined in the project management body of knowledge. While this has definitely helped organizations to bring some methods into the software development madness, there always exists a demand for comparing various groups within the organization in terms of the practice of these defined process models. Even though there exist many metrics for comparison, considering the variety of projects in terms of technology, life cycle, etc., finding a single metric that caters to this is a difficult task. This paper proposes a model for arriving at a rating on group maturity within the organization. Considering the linguistic or imprecise and uncertain nature of software measurements, fuzzy logic approach is used for the proposed model. Without the barriers like technology or life cycle difference, the proposed model helps the organization to compare different groups within it with reasonable precision.展开更多
Objective Due to the incompleteness and complexity of fault diagnosis for power transformers,a comprehensive rough-fuzzy scheme for solving fault diagnosis problems is presented.Fuzzy set theory is used both for repre...Objective Due to the incompleteness and complexity of fault diagnosis for power transformers,a comprehensive rough-fuzzy scheme for solving fault diagnosis problems is presented.Fuzzy set theory is used both for representation of incipient faults' indications and producing a fuzzy granulation of the feature space.Rough set theory is used to obtain dependency rules that model indicative regions in the granulated feature space.The fuzzy membership functions corresponding to the indicative regions,modelled by rules,are stored as cases.Results Diagnostic conclusions are made using a similarity measure based on these membership functions.Each case involves only a reduced number of relevant features making this scheme suitable for fault diagnosis.Conclusion Superiority of this method in terms of classification accuracy and case generation is demonstrated.展开更多
Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. I...Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. In this paper, we introduce a pair of nonmonotonic aggregation connectives on fuzzy sets-soft intersection and soft union, in the light of Zadeh’s fuzzy set theory. Some important features of the nonmonotonic connectives are also discussed.展开更多
This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -l...This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.展开更多
Description logics （DLs） play an important role in representing and reasoning domain knowledge. Conjunctive queries stemmed from the domain of relational databases, and have attracted more attentions in semantic Web...Description logics （DLs） play an important role in representing and reasoning domain knowledge. Conjunctive queries stemmed from the domain of relational databases, and have attracted more attentions in semantic Web recently. To acquire a tractable DL for query answering, DL-Lite is proposed. Due to the large amount of imprecision and uncertainty in the real world, it is essential to extend DLs to deal with these vague and imprecise information. We thus propose a new fuzzy DL f-DLR-Lite.n, which allows for the presence of n-ary relations and the occurrence of concept conjunction on the left land of inclusion axioms. We also suggest an improved fuzzy query language, which supports the presence of thresholds and user defined weights. We also show that the query answering algorithm over the extended DL is still FOL reducible and shows polynomial data complexity. DL f-DLR-Lite,n can make up for the disadvantages of knowledge representation and reasoning of classic DLs, and the enhanced query language expresses user intentions more precisely and reasonably.展开更多
Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement....Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement;2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality.展开更多
The development of new wind energy project requires studying of many parameters to achieve maximum benefits at the cost of minimum environmental impacts. Using Geographic Information System (GIS), an analytical framew...The development of new wind energy project requires studying of many parameters to achieve maximum benefits at the cost of minimum environmental impacts. Using Geographic Information System (GIS), an analytical framework has been developed in this paper with fuzzy logic to evaluate the suitable site for turbines for optimum energy output. The criteria for suitable site for energy optimization are environmental, physical and human factors. The present study helps to assess the appropriate sites for the wind turbines in Gujarat. The result obtained from the study conveys the suitability of the development of wind turbines along the western parts of Gujarat. The suggested model could be used for the future site selection of the wind turbine which in turn could be of orientation for energy planners and decision makers.展开更多
A further reformulation of Naive Set Comprehension related to that proposed in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension＂ （2012） is possible in which contradiction i...A further reformulation of Naive Set Comprehension related to that proposed in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension＂ （2012） is possible in which contradiction is averted not by excluding sets such as the Russell Set but rather by treating sentences resulting from instantiation of such sets as the Russell Set in their own descriptions as invalid. So the set of all sets that are not members of thernselves in this further revision is a valid set but the claim that that set is or is not a member of itself is not validly expressible. Such an approach to set comprehension results in a set ontology co-extensive with that permitted by the Naive Set Comprehension Principle itself. This approach （that may be called Revised Set Comprehension Ⅱ） has as strong a claim to consistency as that formulated in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension.＂展开更多
1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved....1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).展开更多
a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncerta...a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncertain linguistic values-based information. Firstly the concepts of a-input resolution and a.unit resolution are presented, and the equivalence of them is shown. Then α-input （a-unit） resolution is equivalently transformed from Lv（ n × 2） F（X） into that of LnP（X）, and their soundness and completeness are also established. Finally an algorithm for a-unit resolution is contrived in LnP（ X）.展开更多
文摘By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results are intuitional and realizable for computer.
文摘Despite half a century of fuzzy sets and fuzzy logic progress, as fuzzy sets address complex and uncertain information through the lens of human knowledge and subjectivity, more progress is needed in the semantics of fuzzy sets and in exploring the multi-modal aspect of fuzzy logic due to the different cognitive, emotional and behavioral angles of assessing truth. We lay here the foundations of a postmodern fuzzy set and fuzzy logic theory addressing these issues by deconstructing fuzzy truth values and fuzzy set membership functions to re-capture the human knowledge and subjectivity structure in membership function evaluations. We formulate a fractal multi-modal logic of Kabbalah which integrates the cognitive, emotional and behavioral levels of humanistic systems into epistemic and modal, deontic and doxastic and dynamic multi-modal logic. This is done by creating a fractal multi-modal Kabbalah possible worlds semantic frame of Kripke model type. The Kabbalah possible worlds semantic frame integrates together both the multi-modal logic aspects and their Kripke possible worlds model. We will not focus here on modal operators and axiom sets. We constructively define a fractal multi-modal Kabbalistic L-fuzzy set as the central concept of the postmodern fuzzy set theory based on Kabbalah logic and semantics.
文摘Driven by market requirements, software services organizations have adopted various software engineering process models （such as capability maturity model （CMM）, capability maturity model integration （CMMI）, ISO 9001：2000, etc.） and practice of the project management concepts defined in the project management body of knowledge. While this has definitely helped organizations to bring some methods into the software development madness, there always exists a demand for comparing various groups within the organization in terms of the practice of these defined process models. Even though there exist many metrics for comparison, considering the variety of projects in terms of technology, life cycle, etc., finding a single metric that caters to this is a difficult task. This paper proposes a model for arriving at a rating on group maturity within the organization. Considering the linguistic or imprecise and uncertain nature of software measurements, fuzzy logic approach is used for the proposed model. Without the barriers like technology or life cycle difference, the proposed model helps the organization to compare different groups within it with reasonable precision.
基金This work was supported by the National Natural Science Foundation of China(No.59637200).
文摘Objective Due to the incompleteness and complexity of fault diagnosis for power transformers,a comprehensive rough-fuzzy scheme for solving fault diagnosis problems is presented.Fuzzy set theory is used both for representation of incipient faults' indications and producing a fuzzy granulation of the feature space.Rough set theory is used to obtain dependency rules that model indicative regions in the granulated feature space.The fuzzy membership functions corresponding to the indicative regions,modelled by rules,are stored as cases.Results Diagnostic conclusions are made using a similarity measure based on these membership functions.Each case involves only a reduced number of relevant features making this scheme suitable for fault diagnosis.Conclusion Superiority of this method in terms of classification accuracy and case generation is demonstrated.
基金the High Technology Research and Development Programme of China
文摘Commonsense representation and manipulation based on fuzzy logic is a new research field which handles the incompleteness, error-tolerability (allow exceptions) and uncertainty associated with commonsense knowledge. In this paper, we introduce a pair of nonmonotonic aggregation connectives on fuzzy sets-soft intersection and soft union, in the light of Zadeh’s fuzzy set theory. Some important features of the nonmonotonic connectives are also discussed.
基金supported by grants from the National Natural Science Foundation of China(Nos.61075120, 60673096 and 60773174)the Natural Science Foundation of Zhejiang Province in China(No.Y107262).
文摘This paper presents a general framework for the study of relation-based intuitionistic fuzzy rough sets determined by two intuitionistic fuzzy implicators.By employing two intuitionistic fuzzy implicators I and J,I -lower and J-upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined.Properties of(I,J) -intuitionistic fuzzy rough approximation operators are then examined.The connections between special types of intuitionistic fuzzy relations and properties of (I,J)-intuitionistic fuzzy approximation operators are also established.
基金the Program for New Century Excellent Talents in University (NCET-05-0288)the Specialized Research Fund for the Doctoral Program of Higher Education of China (20050145024)
文摘Description logics （DLs） play an important role in representing and reasoning domain knowledge. Conjunctive queries stemmed from the domain of relational databases, and have attracted more attentions in semantic Web recently. To acquire a tractable DL for query answering, DL-Lite is proposed. Due to the large amount of imprecision and uncertainty in the real world, it is essential to extend DLs to deal with these vague and imprecise information. We thus propose a new fuzzy DL f-DLR-Lite.n, which allows for the presence of n-ary relations and the occurrence of concept conjunction on the left land of inclusion axioms. We also suggest an improved fuzzy query language, which supports the presence of thresholds and user defined weights. We also show that the query answering algorithm over the extended DL is still FOL reducible and shows polynomial data complexity. DL f-DLR-Lite,n can make up for the disadvantages of knowledge representation and reasoning of classic DLs, and the enhanced query language expresses user intentions more precisely and reasonably.
文摘Based on bipolar dynamic logic (BDL) and bipolar quantum linear algebra (BQLA) this work introduces bipolar quantum logic gates and quantum cellular combinatorics with a logical interpretation to quantum entanglement. It is shown that: 1) BDL leads to logically definable causality and generic particle-antiparticle bipolar quantum entanglement;2) BQLA makes composite atom-atom bipolar quantum entanglement reachable. Certain logical equivalence is identified between the new interpretation and established ones. A logical reversibility theorem is presented for ubiquitous quantum computing. Physical reversibility is briefly discussed. It is shown that a bipolar matrix can be either a modular generalization of a quantum logic gate matrix or a cellular connectivity matrix. Based on this observation, a scalable graph theory of quantum cellular combinatorics is proposed. It is contended that this work constitutes an equilibrium-based logical extension to Bohr’s particle-wave complementarity principle, Bohm’s wave function and Bell’s theorem. In the meantime, it is suggested that the result may also serve as a resolution, rather than a falsification, to the EPR paradox and, therefore, a equilibrium-based logical unification of local realism and quantum non-locality.
文摘The development of new wind energy project requires studying of many parameters to achieve maximum benefits at the cost of minimum environmental impacts. Using Geographic Information System (GIS), an analytical framework has been developed in this paper with fuzzy logic to evaluate the suitable site for turbines for optimum energy output. The criteria for suitable site for energy optimization are environmental, physical and human factors. The present study helps to assess the appropriate sites for the wind turbines in Gujarat. The result obtained from the study conveys the suitability of the development of wind turbines along the western parts of Gujarat. The suggested model could be used for the future site selection of the wind turbine which in turn could be of orientation for energy planners and decision makers.
文摘A further reformulation of Naive Set Comprehension related to that proposed in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension＂ （2012） is possible in which contradiction is averted not by excluding sets such as the Russell Set but rather by treating sentences resulting from instantiation of such sets as the Russell Set in their own descriptions as invalid. So the set of all sets that are not members of thernselves in this further revision is a valid set but the claim that that set is or is not a member of itself is not validly expressible. Such an approach to set comprehension results in a set ontology co-extensive with that permitted by the Naive Set Comprehension Principle itself. This approach （that may be called Revised Set Comprehension Ⅱ） has as strong a claim to consistency as that formulated in ＂Resolving Insolubilia： Internal Inconsistency and the Reform of Naive Set Comprehension.＂
文摘1 Introduction A discrete dynamical system can be expressed as xn+1 ?f(xn), n = 0,1,2,... where X is a metric space and f : X →X is a continuous map. The study of it tells us how the points in the base space X moved. Nevertheless, this is not enough for the researches of biological species, demography, numerical simulation and attractors (see [1], [2]). It is necessary to know how the subsets of X moved. In this direction, we consider the set-valued discrete system associated to f, An+1 = (f|-)(An), n = 0,1,2,... where (f|-) is the natural extension of f to K(X) (the class of all compact subsets of X).
基金National Natural Science Foundations of China (No. 60875034,No. 61175055)
文摘a-Input resolution and a-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic （ Lv（ n × 2） F（X） ）, which can represent and handle uncertain linguistic values-based information. Firstly the concepts of a-input resolution and a.unit resolution are presented, and the equivalence of them is shown. Then α-input （a-unit） resolution is equivalently transformed from Lv（ n × 2） F（X） into that of LnP（X）, and their soundness and completeness are also established. Finally an algorithm for a-unit resolution is contrived in LnP（ X）.
