Fuzzy Sets and Systems最新文献

{"title":"The Craig interpolation property in first-order Gödel logic","authors":"N.R. Tavana ,&nbsp;M. Pourmahdian ,&nbsp;S.M.A. Khatami","doi":"10.1016/j.fss.2024.108958","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108958","url":null,"abstract":"<div><p>In this article, a model-theoretic approach is proposed to prove that the first-order Gödel logic, <strong>G</strong>, as well as its extension <span><math><msup><mrow><mi>G</mi></mrow><mrow><mi>Δ</mi></mrow></msup></math></span> associated with first-order relational languages enjoy the Craig interpolation property. These results partially provide an affirmative answer to a question posed in <span>[1]</span>.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140536950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Approximate weak simulations and bisimulations for fuzzy automata over the product structure","authors":"Ivana Micić ,&nbsp;Miroslav Ćirić ,&nbsp;Jelena Matejić ,&nbsp;Stefan Stanimirović ,&nbsp;Linh Anh Nguyen","doi":"10.1016/j.fss.2024.108959","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108959","url":null,"abstract":"<div><p>In this article, we modify the product structure and turn it into the so-called <em>ε</em>-truncated product structure <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span>, for any <span><math><mi>ε</mi><mo>∈</mo><mo>(</mo><mn>0</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></span>. The new structure keeps the property of being a complete residuated lattice, and additionally, its semiring reduct is locally finite. We convert each fuzzy automaton <span><math><mi>A</mi></math></span> over the product structure into a fuzzy automaton <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> over <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span>, and accordingly, we turn the problems of testing the existence and computing weak simulations and bisimulations between fuzzy automata <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span> over the product structure into the corresponding problems for the automata <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span>. Those problems concerning the automata <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> are easier to solve, due to the local finiteness of the semiring reduct of <span><math><msub><mrow><mi>I</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span>, and can be solved even in cases where the corresponding problems for the automata <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span> cannot be solved. We show that weak simulations and bisimulations between the automata <span><math><msub><mrow><mi>A</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>B</mi></mrow><mrow><mi>ε</mi></mrow></msub></math></span> determine certain kinds of approximate weak simulations and bisimulations between the original automata <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span>, which we call <em>ε</em>-weak simulations and bisimulations. We also prove that the existence of an <em>ε</em>-weak simulation or bisimulation between automata <span><math><mi>A</mi></math></span> and <span><math><mi>B</mi></math></span> witnesses the existence of a certain kind of approximate inclusion or equivalence, where the deviation measure of the fuzzy languages of those automata from language inclusion or equality does not exceed <em>ε</em>.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140347955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two dimensional fuzzy context-free languages and tiling patterns","authors":"A. John Kaspar ,&nbsp;D.K. Sheena Christy ,&nbsp;V. Masilamani ,&nbsp;D.G. Thomas","doi":"10.1016/j.fss.2024.108961","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108961","url":null,"abstract":"<div><p>Fuzzy context-free languages are powerful compared to fuzzy regular languages as they are generated by fuzzy context-free grammars and fuzzy pushdown automata, which follow an enhanced computational mechanism. A two dimensional language (picture language) is a collection of two dimensional words, which are a rectangular array of symbols made up of finite alphabets. Two dimensional automata can recognize two dimensional languages that could not be recognized by one dimensional automata. In this paper, we introduce two dimensional fuzzy context-free languages generated by the two dimensional fuzzy context-free grammars and accepted by the two dimensional fuzzy pushdown automata in order to deal with the vagueness that arises in two dimensional context-free languages. We can construct a two dimensional fuzzy context free grammar from the given two dimensional fuzzy pushdown automata and vice versa. In addition, we prove that two dimensional fuzzy context-free languages are closed under union, column concatenation, column star, homomorphism, inverse homomorphism, reflection about right-most vertical, reflection about base, conjugation and half-turn and also show that two dimensional fuzzy context-free languages are not closed under matrix homomorphism, quarter-turn and transpose. Further, we have given the applications and the uses of closure properties in the formation of tiling patterns.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140344977","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On state monadic MV-algebras","authors":"Pengfei He ,&nbsp;Ya Wei ,&nbsp;Juntao Wang","doi":"10.1016/j.fss.2024.108960","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108960","url":null,"abstract":"<div><p>Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. In this paper, we extend monadic MV-algebras with a state operator that describes algebraic properties of states. The resulting variety of algebras will be called state monadic MV-algebras. First, we introduce state monadic MV-algebras and establish a natural equivalence between the category of state monadic MV-algebras and the category of state monadic <em>ℓ</em>-groups with strong units. Moreover, we prove that the class of all state monadic ideals in state monadic MV-algebras is a complete Heyting algebra. In particular, by studying extended state monadic ideals, we prove that the set of all stable state monadic ideals in state monadic MV-algebras is a complete Heyting algebra. Also, the class of all involutory state monadic ideals in state monadic MV-algebras is a complete Boolean algebra. Finally, we introduce and characterize some members in the variety of state monadic MV-algebras, which are subdirectly irreducible, simple, semisimple, local and semilocal, respectively.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140344976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A special fuzzy star-shaped number space with the sendograph metric","authors":"Wenjuan Liu ,&nbsp;Dongming Liu","doi":"10.1016/j.fss.2024.108950","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108950","url":null,"abstract":"<div><p>As a natural generalization of fuzzy numbers, fuzzy star-shaped numbers play a crucial role in fuzzy mathematics. Let <em>Y</em> be a non-degenerate compact convex subset of the <em>n</em>-dimensional Euclidean space, and let <span><math><msub><mrow><mi>FS</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub><mo>(</mo><mi>Y</mi><mo>)</mo></math></span> be the family consisting of all fuzzy star-shaped numbers with respect to <span><math><msub><mrow><mi>z</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> whose supports contained in <em>Y</em>. Using methods from infinite-dimensional topology, we mainly show that the space <span><math><msub><mrow><mi>FS</mi></mrow><mrow><msub><mrow><mi>z</mi></mrow><mrow><mn>0</mn></mrow></msub></mrow></msub><mo>(</mo><mi>Y</mi><mo>)</mo></math></span> with the topology induced by the sendograph metric is homeomorphic to the separable Hilbert space <span><math><msup><mrow><mi>ℓ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140342195","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distorted copulas","authors":"Roberto Ghiselli Ricci","doi":"10.1016/j.fss.2024.108947","DOIUrl":"10.1016/j.fss.2024.108947","url":null,"abstract":"<div><p>In this paper, we deal with the problem of preserving the copula property by means of a transformation called distortion where automorphisms of the real unit interval are involved. A new methodological approach is followed by resorting to a special branch of group theory. The crucial role of absolute continuity of one-dimensional sections of a distorted copula is illustrated. Some necessary and sufficient conditions concerning the automorphisms which preserve the copula property for a large class of bivariate copulas are proved. Several examples are presented.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424000939/pdfft?md5=6bc1529f77457f08dd6ac261452a5f79&pid=1-s2.0-S0165011424000939-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140277696","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Generating methods of some classes of fuzzy implications obtained by unary functions and algebraic structures","authors":"Isabel Aguiló ,&nbsp;Vikash Kumar Gupta ,&nbsp;Balasubramaniam Jayaram ,&nbsp;Sebastia Massanet ,&nbsp;Juan Vicente Riera ,&nbsp;Nageswara Rao Vemuri","doi":"10.1016/j.fss.2024.108948","DOIUrl":"10.1016/j.fss.2024.108948","url":null,"abstract":"<div><p>The existing generating methods of fuzzy implications are closed in the set of all fuzzy implications, but not when applied to some families of these operators. In this paper, some binary operations are defined on some well-established families of fuzzy implications. Namely, the families of <span><math><mo>(</mo><mi>S</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>-implications with continuous t-conorms, <em>R</em>-implications obtained from continuous t-norms, Yager's <em>f</em>- and <em>g</em>-generated implications, <em>h</em>- and generalized <span><math><mo>(</mo><mi>h</mi><mo>,</mo><mi>e</mi><mo>)</mo></math></span>-implications and <em>k</em>-implications are considered and it is proved that with these operations, they are lattices. Moreover, some other lattice substructures are defined in some of the families when some restrictions on the underlying generators of the implications are imposed. Furthermore, it is emphasized that these generating methods preserve important properties like the exchange principle and the law of importation.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0165011424000940/pdfft?md5=26beaf6124502fc3cd468475cd09974b&pid=1-s2.0-S0165011424000940-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140274282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Construction of fuzzy classification systems by fitness sharing based genetic search and boosting based ensemble","authors":"Jidong Li,&nbsp;Xuejie Zhang","doi":"10.1016/j.fss.2024.108949","DOIUrl":"10.1016/j.fss.2024.108949","url":null,"abstract":"<div><p>This paper concentrates on the development of precise fuzzy rule-based classification systems for high-dimensional and multi-class problems. The approach begins with the extraction on potential fuzzy if-then rules using fitness sharing based genetic algorithms, this ensures effective searching for productive niches, thereby evolving and maintaining a diverse, cooperative population. Subsequently, for the purpose of combining the obtained fuzzy rules and eliminating their conflicts, an adaboost ensemble method is utilized, enhancing the accuracy of the fuzzy classification systems.</p><p>Experiments have been conducted on 10 UCI datasets and 3 well-known image classification problems. The features for these image tasks were derived from the activation values of the final convolutional layer in pre-trained convolutional neural networks. These datasets, which were chosen to evaluate the effectiveness of the proposed approach, exhibit significant variation in terms of dimensionality and the number of class labels. Comparative analyses are carried out with conventional fuzzy rule-based classification methods, and the results demonstrate that the classification systems can be developed for complex problems, while maintaining a high-level of prediction accuracy.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140272818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Separable programming problem with bipolar max-T fuzzy relation equation constraints","authors":"Ali Abbasi Molai","doi":"10.1016/j.fss.2024.108944","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108944","url":null,"abstract":"<div><p>One of the most important classes of nonlinear programming problems is separable programming problem due to its applications in theory and practice. This paper studies this class of the problems subject to a system of bipolar fuzzy relation equations using the max-T composition operator, where T is a continuous and Archimedean t-norm. Its feasible solution set structure is determined by two vectors called lower and upper bound vector of its feasible domain. It is shown that there exists an optimal solution for the problem with max-continuous and Archimedean t-norm such that its components are the corresponding components of either the lower or upper bound vector. Based on the interesting property, some sufficient conditions are proposed to detect some of its optimal components or one of its optimal solutions. These conditions can reduce the dimensions of the original problem when some its optimal components are determined. The objective function of the reduced problem is equivalently rewritten in a specific form. This form guides us to design a value matrix based on the characteristic matrix and ascending or descending of univariate functions constituting the objective function. An approach is extended on the matrix to find the optimal solution of the (reduced) problem. It is important to note that a number of problems can completely be solved using the sufficient conditions.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140187081","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Existence of solutions to a class of interval-valued differential equation with impulses relative to length constraints","authors":"Hongzhou Wang ,&nbsp;Rosana Rodríguez-López ,&nbsp;Alireza Khastan","doi":"10.1016/j.fss.2024.108943","DOIUrl":"https://doi.org/10.1016/j.fss.2024.108943","url":null,"abstract":"<div><p>This paper provides a new model framework to study interval-valued dynamical systems with length constraints. We use impulses instead of switching points to control the length of solutions to interval-valued differential equation under <em>gH</em>-differentiability. Firstly, we consider a class of interval-valued differential equation with impulses. Then, we study interval-valued differential equation with impulses relative to length constraints. Applying fixed point theory in metric space, we prove some existence results. Several examples are given to illustrate the theoretical results.</p></div>","PeriodicalId":55130,"journal":{"name":"Fuzzy Sets and Systems","volume":null,"pages":null},"PeriodicalIF":3.9,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140191110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}