Implicational Partial Gaggle Logics and Matrix Semantics

Implicational tonoid logics and their extensions with abstract Galois properties have been introduced by Yang and Dunn. They introduced matrix semantics for the implicational tonoid logics but did not do for the extensions. Here we provide such semantics for implicational partial gaggle logics as one sort of such extensions. To this end, first we discuss implicational partial gaggle logics in Hilbert-style. We next introduce one kind of matrix semantics based on Lindenbaum– Tarski matrices for the logics and show that those logics are complete with respect to the matrix semantics. Finally, we further introduce a slightly different kind of matrix semantics based on reduced models for the logics and show that those logics are complete with respect to this matrix semantics

Relational Semantics for Fuzzy Extensions of R : Set-theoretic Approach

This paper addresses a set-theoretic completeness based on a relational semantics for fuzzy extensions of two versions Rt and R T of R (Relevance logic). To this end, two fuzzy logics FRt and FRT as extensions of Rt and R T, respectively, and the relational semantics, so called Routley-Meyer semantics, for them are first recalled. Next, on the semantics completeness results are provided for them using a set-theoretic way

Nilpotent Minimum Logic NM and Pretabularity

This paper deals with pretabularity of fuzzy logics. For this, we first introduce two systems NMnfp and NM½, which are expansions of the fuzzy system NM (Nilpotent minimum logic), and examine the relationships between NMnfp and the another known extended system NM—. Next, we show that NMnfp and NM½ are pretabular, whereas NM is not. We also discuss their algebraic completeness. &nbsp

Fuzzy R Systems and Algebraic Routley-Meyer Semantics

Here algebraic Routley-Meyer semantics is addressed for two fuzzy versions of the logic of relevant implication R. To this end, two versions R t and R T of R and their fuzzy extensions FRt and FRT , respectively, are first discussed together with their algebraic semantics. Next algebraic Routley-Meyer semantics for these two fuzzy extensions is introduced. Finally, it is verified that these logics are sound and complete over the semantics

Ordered homomorphisms and kernels of ordered BCI-algebras

Recently Yang-Roh-Jun introduced the notion of ordered BCI-algebras as a generalization of BCI-algebras. They also introduced the notions of homomorphisms and kernels of ordered BCI-algebras and investigated related properties. Here we extend their investigation to ordered homomorphisms, i.e., order-preserving homomorphisms. To this end, the notions of ordered homomorphism and kernel of ordered BCI-algebras are first defined. Next, properties associated with (ordered) subalgebras, (ordered) filters and direct products of ordered BCI-algebras are addressed

Ordered subalgebras of ordered BCI-algebras based on the MBJ-neutrosophic structure

The neutrosophic set consists of three fuzzy sets called true membership function, false membership function and indeterminate membership function. MBJ-neutrosophic structure is a structure constructed using interval-valued fuzzy set instead of indeterminate membership function in the neutrosophic set. In general, the indeterminate part appears in a wide range. So instead of treating the indeterminate part as a single value, it is treated as an interval value, allowing a much more comprehensive processing. In an attempt to apply the MBJ-neutrosophic structure to ordered BCI-algebras, the notion of MBJ-neutrosophic (ordered) subalgebras is introduced and their properties are studied. The relationship between MBJ-neutrosophic subalgebra and MBJ-neutrosophic ordered subalgebra is established, and MBJ-neutrosophic ordered subalgebra is formed using (intuitionistic) fuzzy ordered subalgebra

A design methodology for evolutionary air transportation networks

The air transportation demand at large hubs in the U.S. is anticipated to double in the near future. Current runway construction plans at selected airports can relieve some capacity and delay problems, but many are doubtful that this solution is sufficient to accommodate the anticipated demand growth in the National Airspace System (NAS). With the worsening congestion problem, it is imperative to seek alternative solutions other than costly runway constructions. In this respect, many researchers and organizations have been building models and performing analyses of the NAS. However, the complexity and size of the problem results in an overwhelming task for transportation system modelers. This research seeks to compose an active design algorithm for an evolutionary airline network model so as to include network specific control properties. An airline network designer, referred to as a network architect, can use this tool to assess the possibilities of gaining more capacity by changing the network configuration. Since the Airline Deregulation Act of 1978, the airline service network has evolved from a point-to-point into a distinct hub-and-spoke network. Enplanement demand on the H&S network is the sum of Origin-Destination (O-D) demand and transfer demand. Even though the flight or enplanement demand is a function of O-D demand and passenger routings on the airline network, the distinction between enplanement and O-D demand is not often made. Instead, many demand forecast practices in current days are based on scale-ups from the enplanements, which include the demand to and from transferring network hubs. Based on this research, it was found that the current demand prediction practice can be improved by dissecting enplanements further into smaller pieces of information. As a result, enplanement demand is decomposed into intrinsic and variable parts. The proposed intrinsic demand model is based on the concept of 'true' origin-destination demand which includes the direction of each round trip travel. The result from using true O-D concept reveals the socioeconomic functional roles of airports on the network. Linear trends are observed for both the produced and attracted demand from the data. Therefore, this approach is expected to provide more accurate prediction capability. With the intrinsic demand model in place, the variable part of the demand is modeled on an air transportation network model, which is built with accelerated evolution scheme. The accelerated evolution scheme was introduced to view the air transportation network as an evolutionary one instead of a parametric one. The network model takes in intrinsic demand data before undergoing an evolution path to generate a target network. The results from the network model suggests that air transportation networks can be modeled using evolutionary structure and it was possible to generate the emulated NAS. A dehubbing scenario study of Lambert-St. Louis International Airport demonstrated the prediction capability of the proposed network model. The overall process from intrinsic demand modeling and evolutionary network modeling is a unique and it is highly beneficial for simulating active control of the transportation networks.Ph.D.Committee Chair: Mavris, Dimitri N.; Committee Member: Baik, Hojong; Committee Member: DeLaurentis, Daniel; Committee Member: Lewe, Jung-Ho; Committee Member: Schrage, Danie

Fixpointed Idempotent Uninorm (Based) Logics

Idempotent uninorms are simply defined by fixpointed negations. These uninorms, called here fixpointed idempotent uninorms, have been extensively studied because of their simplicity, whereas logics characterizing such uninorms have not. Recently, fixpointed uninorm mingle logic (fUML) was introduced, and its standard completeness, i.e., completeness on real unit interval [ 0 , 1 ] , was proved by Baldi and Ciabattoni. However, their proof is not algebraic and does not shed any light on the algebraic feature by which an idempotent uninorm is characterized, using operations defined by a fixpointed negation. To shed a light on this feature, this paper algebraically investigates logics based on fixpointed idempotent uninorms. First, several such logics are introduced as axiomatic extensions of uninorm mingle logic (UML). The algebraic structures corresponding to the systems are then defined, and the results of the associated algebraic completeness are provided. Next, standard completeness is established for the systems using an Esteva⁻Godo-style approach for proving standard completeness

Some Implicational Semilinear Gaggle Logics: (Dual) Residuated-Connected Logics

Implicational partial Galois logics and some of their semilinear extensions, such as semilinear extensions satisfying abstract Galois and dual Galois connection properties, have been introduced together with their relational semantics. However, similar extensions satisfying residuated, dual residuated connection properties have not. This paper fills the gaps by introducing those semilinear extensions and their relational semantics. To this end, the class of implicational (dual) residuated-connected prelinear gaggle logics is defined and it is verified that these logics are semilinear. In particular, associated with the contribution of this work, we note the following two: One is that implications can be introduced by residuated connection in semilinear logics. This shows that the residuated, dual residuated connection properties are important and so need to be investigated in semilinear logics. The other is that set-theoretic relational semantics can be provided for semilinear logics. Semilinear logics have been dealt with extensively in algebraic context, whereas they have not yet been performed in the set-theoretic one

Basic Core Fuzzy Logics and Algebraic Routley–Meyer-Style Semantics

Recently, algebraic Routley–Meyer-style semantics was introduced for basic substructural logics. This paper extends it to fuzzy logics. First, we recall the basic substructural core fuzzy logic MIAL (Mianorm logic) and its axiomatic extensions, together with their algebraic semantics. Next, we introduce two kinds of ternary relational semantics, called here linear Urquhart-style and Fine-style Routley–Meyer semantics, for them as algebraic Routley–Meyer-style semantics