The ⊛-composition of fuzzy implications: Closures with respect to properties, powers and families

Recently, Vemuri and Jayaram proposed a novel method of generating fuzzy implications from a given pair of fuzzy implications. Viewing this as a binary operation ⊛ on the set II of fuzzy implications they obtained, for the first time, a monoid structure (I,⊛)(I,⊛) on the set II. Some algebraic aspects of (I,⊛)(I,⊛) had already been explored and hitherto unknown representation results for the Yager's families of fuzzy implications were obtained in [53] (N.R. Vemuri and B. Jayaram, Representations through a monoid on the set of fuzzy implications, fuzzy sets and systems, 247 (2014) 51–67). However, the properties of fuzzy implications generated or obtained using the ⊛-composition have not been explored. In this work, the preservation of the basic properties like neutrality, ordering and exchange principles , the functional equations that the obtained fuzzy implications satisfy, the powers w.r.t. ⊛ and their convergence, and the closures of some families of fuzzy implications w.r.t. the operation ⊛, specifically the families of (S,N)(S,N)-, R-, f- and g-implications, are studied. This study shows that the ⊛-composition carries over many of the desirable properties of the original fuzzy implications to the generated fuzzy implications and further, due to the associativity of the ⊛-composition one can obtain, often, infinitely many new fuzzy implications from a single fuzzy implication through self-composition w.r.t. the ⊛-composition

Lattice operations on fuzzy implications and the preservation of the exchange principle

In this work, we solve an open problem related to the preservation of the exchange principle (EP) of fuzzy implications under lattice operations ([3], Problem 3.1.). We show that generalizations of the commutativity of antecedents (CA) to a pair of fuzzy implications (I,J)(I,J), viz., the generalized exchange principle and the mutual exchangeability are sufficient conditions for the solution of the problem. Further, we determine conditions under which these become necessary too. Finally, we investigate the pairs of fuzzy implications from different families such that (EP) is preserved by the join and meet operations

PRESERVATION OF THE EXCHANGE PRINCIPLE UNDER LATTICE OPERATIONS ON FUZZY IMPLICATIONS

In this work, we solve an open problem related to the exchange principle of fuzzy implications [Problem 3.1, Fuzzy Sets and Systems 261(2015) 112-123]. We show that two important generalizations of the exchange principle, namely, the generalized exchange principle(GEP) and the mutual exchangeability(ME) are sufficient conditions for the solution of the problem. We also show that, under some conditions, these are necessary too. Finally, we investigate the pairs (I, J) from different families of fuzzy implications such that the exchange principle is preserved under the join and meet operations

The *-composition -A Novel Generating Method of Fuzzy Implications: An Algebraic Study

Fuzzy implications are one of the two most important fuzzy logic connectives, the other being t-norms. They are a generalisation of the classical implication from two-valued logic to the multivalued setting. A binary operation I on [0; 1] is called a fuzzy implication if (i) I is decreasing in the first variable, (ii) I is increasing in the second variable, (iii) I(0; 0) = I(1; 1) = 1 and I(1; 0) = 0. The set of all fuzzy implications defined on [0; 1] is denoted by I. Fuzzy implications have many applications in fields like fuzzy control, approximate reasoning, decision making, multivalued logic, fuzzy image processing, etc. Their applicational value necessitates new ways of generating fuzzy implications that are fit for a specific task. The generating methods of fuzzy implications can be broadly categorised as in the following: (M1): From binary functions on [0; 1], typically other fuzzy logic connectives, viz., (S;N)-, R-, QL- implications, (M2): From unary functions on [0,1], typically monotonic functions, for instance, Yager’s f-, g- implications, or from fuzzy negations, (M3): From existing fuzzy implications

ISIPTA'07: Proceedings of the Fifth International Symposium on Imprecise Probability: Theories and Applications

B

Deconstructing the ivory tower: identifying challenges of university-industry ecosystem partnerships

Collaboration between industry and academia necessitates the management of entrepreneurial dynamics within ecosystem contexts. However, such partnerships perpetuate numerous challenges that, without effective management, can impact upon the ecosystem as a whole. Limited research to date has addressed the challenges affecting these university-industry partnerships and ascertained their impact upon ecosystem management. This study identifies the challenges pervading university-industry partnerships across entrepreneurial ecosystems, with a view that through an exposition of such challenges, more specific strategies could be implemented to address them. Questionnaires were distributed to key ecosystem stakeholders, requesting their perceptions of the key challenges affecting their collaborative relationships. Empirical data was analysed utilising fuzzy-set qualitative comparative analysis to deduce the configurational nature of the conditions. Results reveal mutually exclusive solutions grounded upon distinct combinations of conditions, constituting distinct pathways to ineffective ecosystem management. Theoretical and practical implications are discussed, as well as acknowledged limitations of this study and suggestions for future research

Model-free generalized fiducial inference

Motivated by the need for the development of safe and reliable methods for uncertainty quantification in machine learning, I propose and develop ideas for a model-free statistical framework for imprecise probabilistic prediction inference. This framework facilitates uncertainty quantification in the form of prediction sets that offer finite sample control of type 1 errors, a property shared with conformal prediction sets, but this new approach also offers more versatile tools for imprecise probabilistic reasoning. Furthermore, I propose and consider the theoretical and empirical properties of a precise probabilistic approximation to the model-free imprecise framework. Approximating a belief/plausibility measure pair by an [optimal in some sense] probability measure in the credal set is a critical resolution needed for the broader adoption of imprecise probabilistic approaches to inference in statistical and machine learning communities. It is largely undetermined in the statistical and machine learning literatures, more generally, how to properly quantify uncertainty in that there is no generally accepted standard of accountability of stated uncertainties. The research I present in this manuscript is aimed at motivating a framework for statistical inference with reliability and accountability as the guiding principles

Assessing the contribution of ECa and NDVI in the delineation of management zones in a vineyard

Precision fertilization implies the need to identify the variability of soil fertility, which is costly and time-consuming. Remotely measured data can be a solution. Using this strategy, a study was conducted, in a vineyard, to delineate different management zones using two indicators: apparent soil electrical conductivity (ECa) and normalized difference vegetation index (NDVI). To understand the contribution of each indicator, three scenarios were used for zone definition: (1) using only NDVI, (2) only ECa, or (3) using a combination of the two. Then the differences in soil fertility between these zones were assessed using simple statistical methods. The results indicate that the most beneficial strategy is the combined use of the two indicators, as it allowed the definition of three distinct zones regarding important soil variables and crop nutrients, such as soil total nitrogen, Mg2+ cation, exchange acidity, and effective cation exchange capacity, and some relevant cation ratios. This strategy also allowed the identification of an ionic unbalance in the soil chemistry, due to an excess of Mg2+, that was harming crop health, as reported by NDVI. This also impacted ECa and NDVI relationship, which was negative in this study. Overall, the results demonstrate the advantages of using remotely sensed data, mainly more than one type of sensing data, and suggest a high potential for differential crop fertilization and soil management in the study areainfo:eu-repo/semantics/publishedVersio

Examining the existence of double jeopardy and negative double jeopardy within Twitter

Purpose: The theory of Double Jeopardy (DJ) is shown to hold across broad ranging geographies and physical product categories. However, there is very little research appertaining to the subject within an online environment. In particular, studies that investigate the presence of DJ and the contrasting view point to DJ, namely that of Negative Double Jeopardy (NDJ), are lacking. This study contributes to this identified research gap, and examines the presence of DJ and NDJ within a product category, utilising data from Twitter. Design/methodology/approach: 354,676 tweets are scraped from Twitter and their sentiment analysed and allocated into positive, negative and no-opinion clusters using fuzzy c-means clustering. The sentiment is then compared to the market share of brands within the beer product category to establish whether a DJ or NDJ effect is present. Findings: The data reveals an NDJ effect with regards to original tweets (i.e. tweets which have not been retweeted). That is, when analysing tweets relating to brands within a defined beer category, we find that larger brands suffer by having an increased negativity amongst the larger proportion of tweets associated with them. Research limitations/implications: The clustering approach to analyse sentiment in Twitter data brings a new direction to analysis of such sentiment. Future consideration of different numbers of clusters may further the insights this form of analysis can bring to the DJ/NDJ phenomenon. Managerial implications discuss the uncovered practitioner’s paradox of NDJ and strategies for dealing with DJ and NDJ effects. Originality/value: This study is the first to explore the presence of DJ and NDJ through the utilisation of sentiment analysis derived data and fuzzy clustering. DJ and NDJ are under-explored constructs in the online environment. Typically, past research examines DJ and NDJ in separate and detached fashions. Thus, the study is of theoretical value because it outlines boundaries to the DJ and NDJ conditions. Second, this research is the first study to analyse the sentiment of consumer-authored tweets to explore DJ and NDJ effects. This study also highlights the need to separate original tweets from retweets because our data shows that jeopardy dynamics differ in these different domains. Finally, the current study offers valuable insight into the DJ and NDJ effects for practicing marketing managers. Examining the existence of double jeopardy and negative double jeopardy within Twitter. Available from: https://www.researchgate.net/publication/313056508_Examining_the_existence_of_double_jeopardy_and_negative_double_jeopardy_within_Twitter [accessed May 2, 2017]