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Joan Torrens - One of the best experts on this subject based on the ideXlab platform.

  • Uninorm based residual implications satisfying the Modus Ponens property with respect to a uninorm
    Fuzzy Sets and Systems, 2019
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    Abstract In any fuzzy rules based system the inference management is usually carried out by the so-called fuzzy implication functions. In this framework, the Modus Ponens property becomes essential to make forward inferences and it is well known that this inference rule is guaranteed when the conjunction and the implication function used in the process satisfy the corresponding functional inequality. Such inequality has been extensively studied for many kinds of implication functions when the conjunction is modelled by a t-norm. However, the use of conjunctive uninorms to model conjunctions is an increasingly widespread option in fuzzy systems and for this reason the study of the Modus Ponens with respect to a conjunctive uninorm U instead of a t-norm T, which we call here U-Modus Ponens or U-conditionality, becomes very important. In this paper this new property is deeply analyzed and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the U-Modus Ponens for the case of residual implications derived from uninorms, or RU-implications, is investigated in detail when the uninorm U lies in any of the four most usual classes of uninorms.

  • generalized Modus Ponens for u n implications
    International Conference Information Processing, 2018
    Co-Authors: Margarita Mas, Daniel Ruizaguilera, Joan Torrens
    Abstract:

    The Modus Ponens becomes an essential property in approximate reasoning and fuzzy control when forward inferences are managed. Thus, the conjunctor and the fuzzy implication function used in the inference process are required to satisfy this property. Usually, the conjunctor is modeled by a t-norm, but recently also by conjunctive uninorms. In this paper we study when (U, N)-implications satisfy the Modus Ponens property with respect to a conjunctive uninorm U in general, in a similar way as it was previously done for RU-implications. The functional inequality derived from the Modus Ponens involves in this case two different uninorms and a fuzzy negation leading to many possibilities. So, this communication presents only a first step in this study and many cases depending on the classes of the involved uninorms are worth to study.

  • IPMU (1) - Generalized Modus Ponens for ( U , N )-implications
    Communications in Computer and Information Science, 2018
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    The Modus Ponens becomes an essential property in approximate reasoning and fuzzy control when forward inferences are managed. Thus, the conjunctor and the fuzzy implication function used in the inference process are required to satisfy this property. Usually, the conjunctor is modeled by a t-norm, but recently also by conjunctive uninorms. In this paper we study when (U, N)-implications satisfy the Modus Ponens property with respect to a conjunctive uninorm U in general, in a similar way as it was previously done for RU-implications. The functional inequality derived from the Modus Ponens involves in this case two different uninorms and a fuzzy negation leading to many possibilities. So, this communication presents only a first step in this study and many cases depending on the classes of the involved uninorms are worth to study.

  • on some classes of ru implications satisfying u Modus Ponens
    International Summer School on Aggregation Operators, 2017
    Co-Authors: Margarita Mas, Daniel Ruizaguilera, Joan Torrens
    Abstract:

    The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

  • AGOP - On Some Classes of RU-Implications Satisfying U -Modus Ponens
    Advances in Intelligent Systems and Computing, 2017
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

Margarita Mas - One of the best experts on this subject based on the ideXlab platform.

  • Uninorm based residual implications satisfying the Modus Ponens property with respect to a uninorm
    Fuzzy Sets and Systems, 2019
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    Abstract In any fuzzy rules based system the inference management is usually carried out by the so-called fuzzy implication functions. In this framework, the Modus Ponens property becomes essential to make forward inferences and it is well known that this inference rule is guaranteed when the conjunction and the implication function used in the process satisfy the corresponding functional inequality. Such inequality has been extensively studied for many kinds of implication functions when the conjunction is modelled by a t-norm. However, the use of conjunctive uninorms to model conjunctions is an increasingly widespread option in fuzzy systems and for this reason the study of the Modus Ponens with respect to a conjunctive uninorm U instead of a t-norm T, which we call here U-Modus Ponens or U-conditionality, becomes very important. In this paper this new property is deeply analyzed and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the U-Modus Ponens for the case of residual implications derived from uninorms, or RU-implications, is investigated in detail when the uninorm U lies in any of the four most usual classes of uninorms.

  • generalized Modus Ponens for u n implications
    International Conference Information Processing, 2018
    Co-Authors: Margarita Mas, Daniel Ruizaguilera, Joan Torrens
    Abstract:

    The Modus Ponens becomes an essential property in approximate reasoning and fuzzy control when forward inferences are managed. Thus, the conjunctor and the fuzzy implication function used in the inference process are required to satisfy this property. Usually, the conjunctor is modeled by a t-norm, but recently also by conjunctive uninorms. In this paper we study when (U, N)-implications satisfy the Modus Ponens property with respect to a conjunctive uninorm U in general, in a similar way as it was previously done for RU-implications. The functional inequality derived from the Modus Ponens involves in this case two different uninorms and a fuzzy negation leading to many possibilities. So, this communication presents only a first step in this study and many cases depending on the classes of the involved uninorms are worth to study.

  • IPMU (1) - Generalized Modus Ponens for ( U , N )-implications
    Communications in Computer and Information Science, 2018
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    The Modus Ponens becomes an essential property in approximate reasoning and fuzzy control when forward inferences are managed. Thus, the conjunctor and the fuzzy implication function used in the inference process are required to satisfy this property. Usually, the conjunctor is modeled by a t-norm, but recently also by conjunctive uninorms. In this paper we study when (U, N)-implications satisfy the Modus Ponens property with respect to a conjunctive uninorm U in general, in a similar way as it was previously done for RU-implications. The functional inequality derived from the Modus Ponens involves in this case two different uninorms and a fuzzy negation leading to many possibilities. So, this communication presents only a first step in this study and many cases depending on the classes of the involved uninorms are worth to study.

  • on some classes of ru implications satisfying u Modus Ponens
    International Summer School on Aggregation Operators, 2017
    Co-Authors: Margarita Mas, Daniel Ruizaguilera, Joan Torrens
    Abstract:

    The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

  • AGOP - On Some Classes of RU-Implications Satisfying U -Modus Ponens
    Advances in Intelligent Systems and Computing, 2017
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

Roman Slowinski - One of the best experts on this subject based on the ideXlab platform.

  • equivalence of fuzzy rough Modus Ponens and fuzzy rough Modus tollens
    Proceedings of the 2005 conference on Advances in Logic Based Intelligent Systems: Selected Papers of LAPTEC 2005, 2005
    Co-Authors: Masahiro Inuiguchi, Salvatore Greco, Roman Slowinski
    Abstract:

    We have proposed a fuzzy rough set approach to induce gradual decision rules from decision tables without using any fuzzy logical connective. In this paper, we discuss the equivalence between fuzzy-rough Modus Ponens and fuzzy-rough Modus tollens obtained from the induced gradual decision rules. We show the necessary and sufficient conditions for fuzzy-rough Modus Ponens and fuzzy-rough Modus tollens to be equivalent.

  • fuzzy rough Modus Ponens and Modus tollens as a basis for approximate reasoning
    Lecture Notes in Computer Science, 2004
    Co-Authors: Masahiro Inuiguchi, Salvatore Greco, Roman Slowinski
    Abstract:

    We have proposed a fuzzy rough set approach without using any fuzzy logical connectives to extract gradual decision rules from decision tables. In this paper, we discuss the use of these gradual decision rules within Modus Ponens and Modus tollens inference patterns. We discuss the difference and similarity between Modus Ponens and Modus tollens and, moreover, we generalize them to formalize approximate reasoning based on the extracted gradual decision rules. We demonstrate that approximate reasoning can be performed by manipulation of modifier functions associated with the gradual decision rules.

Daniel Ruiz-aguilera - One of the best experts on this subject based on the ideXlab platform.

  • IPMU (2) - Modus Ponens Tollens for RU-Implications
    Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2020
    Co-Authors: Isabel Aguilo, Sebastia Massanet, Juan Vicente Riera, Daniel Ruiz-aguilera
    Abstract:

    In fuzzy rules based systems, fuzzy implication functions are usually considered to model fuzzy conditionals and to perform forward and backward inferences. These processes are guaranteed by the fulfilment of the Modus Ponens and Modus Tollens properties by the fuzzy implication function with respect to the considered conjunction and fuzzy negation. In this paper, we investigate which residual implications derived from uninorms satisfy both Modus Ponens and Modus Tollens properties with respect to the same t-norm and a fuzzy negation simultaneously. The most usual classes of uninorms are considered and many solutions are obtained which allow to model the fuzzy conditionals in a fuzzy rules based systems (and perform backward and forward inferences) with a unique residual implication derived from a uninorm.

  • Uninorm based residual implications satisfying the Modus Ponens property with respect to a uninorm
    Fuzzy Sets and Systems, 2019
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    Abstract In any fuzzy rules based system the inference management is usually carried out by the so-called fuzzy implication functions. In this framework, the Modus Ponens property becomes essential to make forward inferences and it is well known that this inference rule is guaranteed when the conjunction and the implication function used in the process satisfy the corresponding functional inequality. Such inequality has been extensively studied for many kinds of implication functions when the conjunction is modelled by a t-norm. However, the use of conjunctive uninorms to model conjunctions is an increasingly widespread option in fuzzy systems and for this reason the study of the Modus Ponens with respect to a conjunctive uninorm U instead of a t-norm T, which we call here U-Modus Ponens or U-conditionality, becomes very important. In this paper this new property is deeply analyzed and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the U-Modus Ponens for the case of residual implications derived from uninorms, or RU-implications, is investigated in detail when the uninorm U lies in any of the four most usual classes of uninorms.

  • IPMU (1) - Generalized Modus Ponens for ( U , N )-implications
    Communications in Computer and Information Science, 2018
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    The Modus Ponens becomes an essential property in approximate reasoning and fuzzy control when forward inferences are managed. Thus, the conjunctor and the fuzzy implication function used in the inference process are required to satisfy this property. Usually, the conjunctor is modeled by a t-norm, but recently also by conjunctive uninorms. In this paper we study when (U, N)-implications satisfy the Modus Ponens property with respect to a conjunctive uninorm U in general, in a similar way as it was previously done for RU-implications. The functional inequality derived from the Modus Ponens involves in this case two different uninorms and a fuzzy negation leading to many possibilities. So, this communication presents only a first step in this study and many cases depending on the classes of the involved uninorms are worth to study.

  • AGOP - On Some Classes of RU-Implications Satisfying U -Modus Ponens
    Advances in Intelligent Systems and Computing, 2017
    Co-Authors: Margarita Mas, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    The Modus Ponens property for fuzzy implication functions is essential in the inference process in approximate reasoning. It is usually considered with respect to a continuous t-norm T but it can be generalized to any conjunctor and, in particular, to a conjunctive uninorm U. In this paper, it is investigated when RU-implications derived from uninorms satisfy the Modus Ponens with respect to a conjunctive uninorm U. The new property, called here U-Modus Ponens, is studied in detail for RU-implications derived from uninorms lying in the classes of representable uninorms and uninorms continuous in the open unit square.

  • IPMU (1) - On a Generalization of the Modus Ponens: U-conditionality
    Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2016
    Co-Authors: Margalida Mas, Daniel Ruiz-aguilera, Miquel Monserrat, Joan Torrens
    Abstract:

    In fuzzy logic, the Modus Ponens property for fuzzy implication functions is usually considered with respect to a continuous t-norm T and for this reason this property is also known under the name of T-conditionality. In this paper, the t-norm T is substituted by a uninorm U leading to the property of U-conditionality. The new property is studied in detail and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the case of residual implications derived from uninorms or RU-implications is investigated in detail for some classes of uninorms.

Miquel Monserrat - One of the best experts on this subject based on the ideXlab platform.

  • on a generalization of the Modus Ponens u conditionality
    International Conference Information Processing, 2016
    Co-Authors: Margalida Mas, Daniel Ruizaguilera, Miquel Monserrat, Joan Torrens
    Abstract:

    In fuzzy logic, the Modus Ponens property for fuzzy implication functions is usually considered with respect to a continuous t-norm T and for this reason this property is also known under the name of T-conditionality. In this paper, the t-norm T is substituted by a uninorm U leading to the property of U-conditionality. The new property is studied in detail and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the case of residual implications derived from uninorms or RU-implications is investigated in detail for some classes of uninorms.

  • IPMU (1) - On a Generalization of the Modus Ponens: U-conditionality
    Information Processing and Management of Uncertainty in Knowledge-Based Systems, 2016
    Co-Authors: Margalida Mas, Daniel Ruiz-aguilera, Miquel Monserrat, Joan Torrens
    Abstract:

    In fuzzy logic, the Modus Ponens property for fuzzy implication functions is usually considered with respect to a continuous t-norm T and for this reason this property is also known under the name of T-conditionality. In this paper, the t-norm T is substituted by a uninorm U leading to the property of U-conditionality. The new property is studied in detail and it is shown that usual implications derived from t-norms and t-conorms do not satisfy it, but many solutions appear among those implications derived from uninorms. In particular, the case of residual implications derived from uninorms or RU-implications is investigated in detail for some classes of uninorms.

  • RU and (U,N)-implications satisfying Modus Ponens
    International Journal of Approximate Reasoning, 2016
    Co-Authors: Margarita Mas, Miquel Monserrat, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    In this paper it is investigated when some kinds of fuzzy implication functions derived from uninorms satisfy the Modus Ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. The study is done for RU-implications and ( U , N ) -implications with N a continuous fuzzy negation leading to a lot of solutions in both cases. For RU-implications T-conditionality only depends on the underlying t-norm of the uninorm used to derive the residual implication. On the contrary, for ( U , N ) -implications the underlying t-norm is never relevant and only the region out of the t-norm is so. Even the t-conorm can be not relevant also in some cases. Characterization of all residual implications for uninorms satisfying Modus Ponens.Study of Modus Ponens for ( U , N ) -implications.Modus Ponens (T-conditionality) for implications generated from uninorms.

  • residual implications derived from uninorms satisfying Modus Ponens
    Conference of International Fuzzy Systems Association and European Society for Fuzzy Logic and Technology, 2015
    Co-Authors: Margarita Mas, Daniel Ruizaguilera, Miquel Monserrat, Joan Torrens
    Abstract:

    Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RUimplications, satisfy the Modus Ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. For RU-implications it is proved that T-conditionality only depends on the underlying t-norm TU of the uninorm U used to derive the residual implication and this fact leads to a lot of new solutions of the Modus Ponens property. Along the paper the particular cases when the uninorm lies in any of the most usual classes of uninorms are considered.

  • IFSA-EUSFLAT - Residual implications derived from uninorms satisfying Modus Ponens
    Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and Technology, 2015
    Co-Authors: Margarita Mas, Miquel Monserrat, Daniel Ruiz-aguilera, Joan Torrens
    Abstract:

    Modus Ponens is a key property for fuzzy implication functions that are going to be used in fuzzy inference processes. In this paper it is investigated when fuzzy implication functions derived from uninorms via residuation, usually called RUimplications, satisfy the Modus Ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. For RU-implications it is proved that T-conditionality only depends on the underlying t-norm TU of the uninorm U used to derive the residual implication and this fact leads to a lot of new solutions of the Modus Ponens property. Along the paper the particular cases when the uninorm lies in any of the most usual classes of uninorms are considered.